Microtubules are dynamic intracellular filaments which provide structure to cells and facilitate cargo transport. While cargo transport on stable microtubules has been previously studied in various settings, the impact of microtubule dynamics on transport as well as the influence of cargo signaling to direct microtubule growth remain open questions. This is of particular interest in neurons where microtubule dynamics and cargo localization are key to the cellular response to axon injury. Motivated by experiments in sea slugs, this project investigates the progression of microtubule geometries following axon injury to understand the impact on cargo localization. Preliminary results validate the biologically hypothesized geometries by demonstrating the expected cargo localization. We are currently coupling microtubule dynamics with cargo transport using multi-scale modeling to better understand these cellular processes which support neuronal regrowth.
Creating models in which a protein has multiple states due to the binding of effectors or covalent modification is challenging. These challenges are multiplied when the protein dimerizes due to the combinatorial increase in the number of states of the assembly. In bacteria, NsrR controls the expression of genes associated with nitrogen oxide metabolism. The NsrR holoprotein holds an iron-sulfur cluster that reacts with nitric oxide (NO) in multiple steps, and typically acts as a repressor. The various nitrosylation states of NsrR are functionally important because binding to different gene promoters is differentially sensitive to the nitrosylation state of NsrR's iron-sulfur cluster. Moreover, the active form of NsrR is a dimer, leading to the combinatorial complexity mentioned above. Based on a model for the control of Hmp, an NO dioxygenase, by NsrR in emph{Streptomyces coelicolor}, conditions under which it may be possible to ignore the dimeric nature of a transcription factor or, conversely, conditions under which it would be prudent to consider transcription factor dimers explicitly, are studied.
Cell migration is a fundamental process in various biological phenomena, including development, tissue repair, immune responses, and cancer metastasis. Understanding the regulation of cell migration is crucial for developing therapies for various diseases and designing biomaterials for tissue engineering applications. Although there has been an extensive characterization of individual cell movements, the collective migration of cell clusters through diverse and complex extracellular environments has received limited attention. Chemical attractants can stimulate cells to move, and to further explore this phenomenon, we focused on the migration of border cells during Drosophila egg development, specifically examining the concentration of chemoattractant. To obtain the distribution of chemoattractant throughout the egg chamber, we developed a 1D model that incorporated the geometrical features of the chamber. We also determined biophysical parameters of the chemoattractant that were reasonable. To analyze and simulate the motion of the cluster center, we constructed a force-based model that related the concentration to receptor activation and force generation. By controlling the locations and depths of nurse cell junctures, we were able to produce model predictions of cluster trajectories comparable to experimental results.
Insulin is secreted in pulses by beta-cells located within pancreatic islets. This pulsatility is reflected in blood insulin measurements, indicating that the activity of hundreds of thousands of islets is synchronized. One possible mechanism for this synchronization is a negative feedback loop between the pancreas and liver hepatocytes, in which the action of hepatocytes to lower glucose levels in response to insulin serves as a global coordinating signal to pancreatic islets. With a time delay in the glucose response, small populations of in vitro and computer simulated model islets display bistability, capable of producing both fast and slow coordinated oscillations. We investigate the dynamic mechanism for this bistability through simulations with large islet populations, long time delays, and a reduced model that captures the dynamics of the full closed-loop system with only two variables.
While cell mapping and gene mapping are on the radar to have in-depth knowledge about the human body, it is equally important to understand the interactions happening at the cellular and tissue level. In this project, we are utilizing the HubMap data to understand the functionality of each cell in a functional tissue unit. Once the HubMap (The Human BioMolecular Atlas Program) data is attained, we use PhysiCell, a physics-based simulator, to create a similar 3D environment that integrates the agent-based modeling (ABM). Our first step in the project is to fetch the single-cell RNA(scRNA seq) sequence data of healthy or diseased tissue. Once the data is analyzed and reduced to machine-readable format, we filter out the mapped cells that act as secretors and cells that act as receivers. These sets of chemical secretors and receivers respond to chemicals in varied ways. Combining chemical communication graphs for the actions obtained in the biological world and multiscale agent-based modeling will help us visually interpret the chemical interactions between the cells and functional units of human tissue. The goal is to develop mathematical models that visually interpret the chemical interactions between cells and the functional unit of each human tissue.
The role of Ca2+ release-activated Ca2+ (CRAC) channels mediated by ORAI isoforms in calcium signalling has been extensively investigated. It has been shown that the presence or absence of different isoforms has a significant effect on Store Operated Calcium Entry (SOCE). Yoast et al. [Nature Communications, 11(1), 2444 (2020)] have shown that, in addition to the reported narrow-spike oscillations (whereby cytosolic calcium decreases quickly after a sharp increase), ORAI1 knockout HEK293 cells were able to oscillate with broad-spike oscillations (whereby cytosolic calcium decreases in a prolonged manner after a sharp increase) when stimulated with a muscarinic agonist. This suggests that Ca2+ influx through ORAI1-mediated CRAC channels negatively regulates the duration of Ca2+ oscillations. We hypothesize that, through the activation of protein kinase C (PKC), ORAI1 negatively regulates phospholipase C (PLC) activity to decrease IP3 production and limit the duration of agonist-evoked Ca2+ oscillations. Based on this hypothesis, we construct a new mathematical model, which shows that the formation of broad-spike oscillations is highly dependent on the absence of ORAI1. Predictions of this model are consistent with the experimental results.
Invasive species are spreading worldwide, causing damage to ecosystems, biodiversity, agriculture, and human health. Efforts to prevent the establishment of invasive species in new areas sometimes fail, which necessitates the containment of established invaders to prevent or slow their spread to the rest of the country or continent. A major question is, therefore, how to cost-effectively allocate treatment efforts over space and time to contain the species’ population. However, identifying the optimal strategy for containing a species that propagates over large areas is a complex and challenging task that requires novel methodology and computational techniques. I will present a model with an integral-differential equation characterizing the spatial dynamics of the invasive species, incorporating the response of the species to some treatment. I will then present a novel algorithm, which finds (a) the optimal allocation of treatment efforts over space and (b) the optimal target speed at which the species should be allowed to propagate. The results show that, when using the optimal treatment, the annual cost of treatment could be tens or hundreds of percentages lower than that of some other treatments that result in the same propagation speed. It also reveals when it is cost-effective to abandon the species, when to slow or stop its spread, and when to reverse the species’ propagation and slowly eradicate it. In particular, I will show that the optimal strategy often comprises eradication in the yet-uninvaded area, and under certain conditions, it also comprises maintaining a “suppression zone” - an area between the invaded and the uninvaded areas, where treatment reduces the invading population but without eliminating it.
Tipping points occur in many ecosystems through environmental drivers, such as fishing, deforestation, and desertification. Understanding the causes of tipping points is vital to prevent dramatic population shifts and extinction events. Phenotypic plasticity, the ability of one genotype to express multiple phenotypes depending on environmental conditions, has a substantial but unknown implication on these tipping points. Potential consequences of phenotypic plasticity include loss, delay, and an inability to predict tipping points. Using a system of delay-differential equations that accurately replicate experimental data, we show how phenotypic plasticity can cause, change, and mask tipping points. Using simulations and analytical techniques, we determine how and why tipping points occur in this system, demonstrating that phenotypic plasticity is indispensable in many ecosystems to predict population dynamics.
Predation and harvesting play critical roles in maintaining biodiversity in ecological communities. Too much harvesting may drive a species to extinction, while too little harvesting may allow a population to drive out competing species. The spatial features of a habitat can also significantly affect population dynamics within these communities. Here, we formulate and analyze three ordinary differential equation models for the population density of a single species. Each model differs in its assumptions about how the species is harvested. We then extend each of these models to analogous partial differential equation models that more explicitly describe the spatial habitat and the movement of individuals using reaction-diffusion equations. We study the existence and stability of non-zero equilibria of these models in terms of each model’s parameters. Biological interpretations for these results are discussed.
The origin of phenotypic novelty is a perennial question in evolutionary genetics, as it is a fundamental aspect of both adaptive evolution and intergenerational phenotypic change. However, there are few studies of biological pattern formation that specifically address multigenerational aspects of inheritance and phenotypic novelty. For quantitative traits influenced by many segregating alleles, offspring phenotype is often intermediate to parental values. In other cases, offspring phenotype can be transgressive to parental values. For example, in the model organism Mimulus (monkeyflower), offspring of parents with solid-colored petals exhibit novel spotted petal phenotypes. Previous research in monkeyflowers has shown that a gene regulatory network subserves a Turing-type pattern formation mechanism (Ding et al., 2020). It is known that this gene regulatory network is controlled by a small number of loci. In this work we develop and analyze a hierarchical model of pattern formation, its underlying regulatory network, and the genetics of inheritance. The model gives insight into how non-patterned parent phenotype can yield phenotypically transgressive, patterned offspring. Using recombinant inbred lines, we hope to identify the mechanism that is responsible for the transgressive petal phenotypes that we observe in Mimulus.
Quantifying the relationship between predator and prey populations under the influence of disease provides important insight into their roles and behaviors in the ecosystem. This paper uses two models as the base for the analysis: the Lotka-Volterra predation model and the SIR disease model. In the modelling process, the disease only affects the prey, introducing a new variable for the infected prey, and the force of infection decays with time. The proposed system is a nonlinear, non-autonomous system of three ordinary differential equations. This paper aims to quantify the impact of the infection on the behavior of the three populations by numerically determining the critical time when the system switches from having one eigenvector in the basis of the center eigenspace to three eigenvectors. The results show that as time increases, the infected population tends to zero, and the remaining healthy prey and predator populations return to a periodic orbit, equivalent to a level set of the original Lotka-Volterra model. Additionally, the relationship between the force of infection and the critical time behaves as an exponential function, and a future goal is to successfully derive this formula.
We propose a discrete-time host-parasitoid model with stage structure in both species. For this model, we establish conditions for the existence and global stability of the extinction and parasitoid-free equilibria as well as conditions for the existence and uniqueness of an interior equilibrium. We study the model numerically to examine how pesticide spraying may interact with natural enemies (parasitoids) to control the pest (host) species. We then extend the model to an impulsive difference system that incorporates both periodic pesticide spraying and augmentation of the natural enemies to suppress the pest population. For this system we determine when the pest-eradication periodic solution is globally attracting. We also examine how varying the control measures (pesticide concentration, natural enemy augmentation, and the frequency of applications) may lead to different pest outbreak or persistence outcomes when eradication does not occur.
The global spread of antibiotic microbial resistance (AMR) is an increasing health concern, and has been mainly attributed to antibiotics abuse and misuse. Dissemination of AMR is largely associated to plasmids, extrachromosomal genetic elements. As opposed to chromosomal resistance, plasmid-carried resistance is able to transfer to new host cells through conjugation, which plays a crucial role in the ecological success of plasmids in bacterial communities. The regulation of gene expression allowing conjugation is hypothesized to be a negative auto-regulation mechanism depending on environmental conditions. This explains how even sub-inhibitory concentrations of metals or contaminants can promote conjugation, and hence the dissemination of AMR. However, in the absence of selective pressure, this ecological success contrasts with the high costs of plasmid maintenance and very low rates of conjugation, generating the so called plasmid paradox. Biofilms are sessile bacterial communities and have been identified as a hotspot for conjugation, due to the high bacterial density allowing physical proximity of plasmid carrying bacteria and potential donors. This study presents a mathematical model simulating the social behaviour of bacteria regulating plasmid transfer under selective pressure from metals and more specifically in the case of co-resistance and cross-resistance to antibiotics and metals within a growing biofilm. The model is formulated as a nonlocal system of hybrid PDEs with a convolution integral modelling the regulation of transfer genes expression. Gene expression is modelled as a rate depending on the presence of potential receptors around a donor, called recipient-sensing. A promotion function is also introduced to account for the increase in conjugation in the presence of trace metals or inhibition when metals interfere with gene expression, based on experimental results from literature. This mathematical ecology study aims to give an insight into how bacterial social behaviour might answer the plasmid paradox, and how metal contamination participates in the spread of AMR. Numerical simulations showed that the model is able to qualitatively reproduce the influence of conjugation on plasmid dynamics in a growing biofilm. The relative influence of conjugation and vertical gene transfer was compared, including under selective pressure exerted by trace metals.
Incorporation of spatial heterogeneity remains a major hurdle to modeling population dynamics in complex environments. Random-walk models are the foundation of many spatially explicit analyses of population growth and dispersal. The linearized eigenvalue problem of the reaction-diffusion equation yields results on short-term or asymptotic population dynamics, but has only been analyzed in patchy domains with at most two types of patches. Our research develops a novel approach to finding solutions to the eigenvalue problem that allows for analysis of landscapes with any finite number of patches where each patch may have a unique type and at each interface between patches an interface condition reflecting organism behavior may be chosen independently. We determine an implicit relation which allows for analysis of the dependence of eigenvalue (population growth rate) and eigenfunction (population spatial distribution) solutions on patch parameters and interface conditions. The implicit relation is continuous on a bounded interval that contains the principal eigenvalue. A java program using Newton’s method was used to generate solutions to the eigenvalue problem. A set of simulations are shown for a simple landscape that illustrate how our model can be used to analyze population persistence, spatial distributions, and migration dynamics in spatially heterogeneous environments. We show that previously used interface conditions with different interpretations of organism behavior can simultaneously produce similar eigenvalues and significantly different population distributions. In the reaction diffusion model at extrema in the eigenfunction there is zero flux in population density, and our simulations show that the relative properties of source patches, the boundary conditions chosen, and the inclusion of matrix landscape can all affect whether source patches are separated by a minimum in population density. As a result, our simulations demonstrate that our model may be used to advance understanding of how patches act in concert to produce source-sink dynamics across a landscape or to produce alternate methods for classifying source and sink populations. Future work will examine how organism movement rates within patches affect population dynamics and how movement and foraging strategies affect population persistence and spread. The results of the eigenvalue problem may also be used in empirical studies as a reference model to interpret mark and recapture data. While the boundary conditions addressed in our work cover all symmetric periodic cases, our results also lay the foundation needed to address periodic landscapes that are asymmetric which are common in nature and relevant to processes of invasion. Our results will enable future analysis of population dynamics in landscapes that include spatially heterogeneous features such as ecotones, matrix landscape, corridors, and fragmented reserves with diverse interspersed human land-use areas.
In recent years, many microbiome habitats, such as human guts, soils and oceans, have been simplified as a result of human activity. By choosing less complex and varied diets, for example, we decrease the number of different chemicals available to our gut microbes, decreasing gut microbiome diversity and causing a poor digestive health. Likewise, practicing monoculture farming instead of polyculture diminishes soil nutrients availability to microbes resulting in loss of soil fertility. Many studies show that simplified habitat complexity leads to less diversity in microbial communities. What is less clear is if this simplicity also affects functional redundancy, which is the number of species that perform a given function, of these communities. High levels of functional redundancy are important, because they contribute to ecosystem stability. To answer this question, we use metacommunity models to explore the connection between functional redundancy and habitat complexity. Specifically, we consider various paradigms for local community assembly within a larger metacommunity, including environmental filtering and niche partitioning. Our model for environmental filtering indicates that functional redundancy is constant with respect to the local habitat complexity. As for niche partitioning, we observe that functional redundancy rises with the local habitat complexity. These models suggest that different modes of community assembly yield different relationships between habitat complexity and functional redundancy. We explore these findings as they pertain consequences for maintaining stable microbial ecosystem services in anthropogenically simplified landscapes.
The evolution of biological species can emerge from the various phenomenon, such as various type of diffusion and the interaction between individuals. Nonuniform diffusion is one of phenomenon that can be identified as part of evolution of a species. This work focuses on the effect of nonuniform diffusion on a predator--prey population dynamic with spatial heterogeneity. We consider a predator--prey model with nonuniform dispersal, representing the one species motility depending on the size of the others density in a spatially heterogeneous region. We present results about local stability of two different semitrivial steady state solutions to the model where only one species survives, and the other species is absent between two species is investigated. Additionally, we investigate the existence and non-existence of coexistence states.
Biofilms are colonies of microorganisms embedded in a matrix of extracellular polymeric substances (EPS). They play major roles in many fields such as biotechnology and health, cite{flemming2016biofilms}. Mathematical modelling is an essential tool in understanding biofilms and their interactions with the media in which they evolve and in particular with inorganic materials because it reduces experimental testing and scale up,cite{delavar2022advanced}. In this work, we present a mathematical model that describes the growth of a granular biofilm and accounts for the two major interactions between trace metals and biofilms, namely precipitation and complexation. Indeed, experimental results show that in most cases precipitation is not an isolated phenomenon; and complexation is the other major process occurring simultaneously with it. To our knowledge, our model is the first to consider simultaneously these two phenomena inside a granule. More precisely, the general formulation of the model following the mass conservation includes: begin{itemize} item A system of first order quasi-linear hyperbolic equations that describes the growth of the biofilm. In this system, we have $n$ equations for the growth of biomasses within the biofilm, $m$ equations for the accumulation of precipitates throughout the life of the biofilm, and one equation that takes into account the evolution of porosity over time and space. The source terms of the porosity and precipitation equations are formulated so that the space occupied by the precipitates and porosity remains constant over time. item A system of diffusion-reaction equations of soluble components in the biofilm. The first system comprises $p$ equations for biomass nutrients, $q$ equations for cations in the biofilm, $r$ equations for anions which combine with cations to form precipitates, and $k$ equations for complexes. item A nonlinear ordinary differential equation which is the free boundary of the problem and takes into account the temporal evolution of the biofilm thickness. end{itemize} The entire model is therefore a free boundary problem that can be adapted to any type of biofilms (including all the evolution phases of the biofilm), ligands, and trace-metals. An existence and uniqueness theorem was proved and numerical application of the model is proposed.
begin{thebibliography}{} bibitem{delavar2022advanced} Delavar, Mojtaba Aghajani, and Junye Wang. Advanced Methods and Mathematical Modeling of Biofilms: Applications in Health Care, Medicine, Food, Aquaculture, Environment, and Industry. Academic Press, 2022. bibitem{flemming2016biofilms} Flemming, Hans-Curt, et al. 'Biofilms: an emergent form of bacterial life.' Nature Reviews Microbiology 14.9 (2016): 563-575. end{thebibliography}
Atherosclerosis is a disease characterized by the buildup of cholesterol plaque in blood vessels, leading to increased risk of cardiac events as blood flow is restricted. Lipopolysaccharides (LPS), while found naturally in the gut, can stimulate an inflammatory response when moved into general circulation which can exacerbate the risk factors of atherosclerosis. Under normal conditions, intestinal alkaline phosphatase (IAP) detoxifies LPS, preventing it from entering circulation. A high-fat diet such as the Western Diet can introduce high levels of LPS which overwhelm this interaction.
We use ordinary differential equation (ODE) modeling to study the effect of the Western Diet on the systemic factors that contribute to atherosclerosis. This model includes dynamics in the Gut involving IAP and LPS with and without the effects of Western Diet. It also accounts for changes in gut permeability, which affect levels of circulating LPS when on a Western Diet. The model is fit to available experimental data for pre-and post-diet Wild Type (WT) mice and IAP Transgenic (IAPTg) mice, which express normal levels of IAP and elevated levels of IAP respectively. We then use the model to evaluate the effect of modulating IAP on circulating LPS.
The significant increase in fluconazole-resistant Candida albicans calls for a need to search for other possible drug targets. In this study, we constructed a mathematical model, based from the data collected from the literature, of the ergosterol biosynthesis pathway in C. albicans. Interestingly, we found an increase in the susceptibility of C. albicans to fluconazole with increasing concentrations of the sterol-methyltransferase enzyme, making it a potential drug target as an adjunct to fluconazole.
Tuberculosis (TB) is a disease of major public health concern with an estimated one fourth of the world currently infected with M. tuberculosis (Mtb). The hallmark structure of TB is the granuloma, a highly organized immune cell structure that both sequesters bacteria, helping prevent further infection progression but also allows a niche for persistence. While primarily studied within lungs, granulomas are also found within the lymph nodes (LNs). Both lung and LN granulomas vary in ability to control infection, ranging from completely clearing to persisting for decades. Many questions remain surrounding the impact of LN infection such as: development of LN granulomas effects on pulmonary infection, causes for heterogeneity of LN granulomas, and differences between within-host clearance strategies and control between LN and lung granulomas. To address these questions, we developed a non-linear ODE model of LNs allowing for development of granulomas to occur within lymph nodes. We connect this model within the context of an infected whole-host model of Mtb infection, we call HostSim. We calibrate our model, which represents both LN and multiple lung granulomas, and blood using data derived from necropsy from cynomolgus macaques, a nonhuman primate which closely mimics human TB pathology. Our calibrated model reproduces general kinetics of macrophages and bacteria observed within LN granulomas over time. With this model, we will determine cellular mechanisms driving heterogeneity in LN granulomas and the impacts of LN granulomas on pulmonary infection, reactivation and dissemination using sensitivity analysis and in silico experimentation.
More than one-third of all virus genera consist of positive-sense RNA (+ssRNA) viruses. Some well-known examples of highly pathogenic +ssRNA viruses in humans include Hepatitis C virus and SARS-CoV-2, which pose significant public health threats. In an effort to combat these threats, many have created or expanded upon mechanistic models of the replication of these viruses. Here we present a comprehensive review of mechanistic models describing positive-sense RNA virus replication in mammalian cells. We discuss the wide range of applications from these models and potential future research directions in this field. One common strategy to enhance the understanding of +ssRNA virus replication was to expand upon previous models. Viral RNA allocation, negative-sense RNA, and patient level dynamics are some example expansions. Another approach to advancing existing models is to improve their reproducibility, creating a more streamlined experience when using those models. Some models investigate the interplay between virus and innate immune response, exploring the effects on virus production and comparing signaling pathways. Finally, numerous models incorporate antiviral treatments, ranging from gene therapy strategies to nonstructural protein inhibitors like daclatasvir. An analysis of the reviewed models revealed some potential future directions. For instance, nearly half of the reviewed models were of Hepatitis C virus, leaving opportunities for modeling other +ssRNA viruses. Furthermore, every model features RNA replication, but the steps that become before or after RNA replication are not as prominently represented. In conclusion, positive-sense RNA viral replication models have been applied to a diverse set of pathogens, immune system components, and potential therapies, and hold considerable promise for helping develop future therapies for viral diseases.
Progress towards controlling dengue has proven to be difficult, with clear examples of successful control being few and far between and typically not sustained over time. At the same time, evidence from trials indicates that a range of interventions should be capable of reducing transmission. This contradiction raises the possibility that there is scope to improve how interventions are used. We addressed this possibility using a mathematical model of seasonally varying dengue virus transmission in nearly 2,000 cities. The model was informed principally by Aedes aegypti occurrence maps, temperature and its effects on mosquito and virus traits, and spatial estimates of dengue virus force of infection. We applied optimal control theory to models for each city, resulting in estimates of the frequency with which each of several interventions should be deployed if cost-effectiveness is to be maximized. While our results indicate that some combinations of interventions may be more cost-effective than others, especially in some settings, there are challenges that all interventions face. Namely, limits to intervention coverage impair effectiveness, and increased intervention effort is required over time to counterbalance the effect of rising susceptibility, particularly for more effective interventions. We also found that cities with more seasonally marginal levels of transmission and higher costs incurred by dengue morbidity and mortality have greater scope to engage in cost-effective control programs. Our results offer a novel piece of information that decision makers could use to inform rational choices about efforts to control dengue within their communities.
The ongoing COVID-19 pandemic has highlighted the importance of early detection and accurate forecasting of infectious disease outbreaks. Recent research has shown that incorporating wastewater data and virus variant modeling into mathematical models of epidemics can significantly improve our ability to achieve these goals. In this paper, we present a novel approach to epidemic modeling that utilizes both wastewater data and virus variant analysis. Specifically, we propose a mathematical model that combines a compartmental model of disease transmission with a model of two viral strains, allowing us to track the spread of different strains over time. We then apply this model to real-world data from a community in the United States and demonstrate its ability to accurately forecast the trajectory of the epidemic and identify potential hotspots for targeted intervention. Our results suggest that the incorporation of wastewater data and virus variant modeling can provide valuable insights into the transmission dynamics of infectious diseases and inform more effective public health interventions. Overall, these studies highlight the potential of this approach to revolutionize the field of epidemic modeling and improve our ability to control the spread of infectious diseases.
Most integrated models of the Covid pandemic have been developed under the assumption that the policy-sensitive reproduction number is certain. The decision to exit from the lockdown has been made in most countries without knowing the reproduction number that would prevail after the deconfinement. In this paper, I explore the role of uncertainty and learning on the optimal dynamic lockdown policy. I limit the analysis to suppression strategies. In the absence of uncertainty, the optimal confinement policy is to impose a constant rate of lockdown until the suppression of the virus in the population. I show that introducing uncertainty about the reproduction number of deconfined people reduces the optimal initial rate of confinement.
Onchocerciasis is a parasitic disease endemic in Sub-Saharan Africa and South America that spreads from black flies to humans. The disease causes skin nodules, itching, and in severe cases, permanent blindness; Contributing to its nickname, River Blindness. The World Health Organization’s current approach to Onchocerciasis is mass drug administration of Ivermectin. The first issue concerns the prolonged use of Ivermectin may cause drug resistance which we’ve shown is likely present within the population at present. The second issue is that even without resistance eradication is still not possible and the only method of eliminating the parasite is in a joint treatment of Ivermectin and Doxycycline. It also should be said that this method isn’t perfect either since resistance is even more likely with the antibiotic Doxycycline. The goal of our project is to model the spread of Onchocerciasis with resistance, analyze the impact of possible Ivermectin resistance and figure out a treatment plan with doxycycline that can eliminate the disease without causing widespread resistance. After obtaining this goal we hope to expand the model to include Loiasis, another eye worm disease that may cause death when taking ivermectin
The COVID-19 outbreak of 2020 has required many governments to develop and adopt mathematical-statistical models of the pandemic for policy and planning purposes. To this end, this work provides a tutorial on building a compartmental model using Susceptible, Exposed, Infected, Recovered, Deaths and Vaccinated (SEIRDV) status through time. The proposed model uses interventions to quantify the impact of various government attempts made to slow the spread of the virus. Furthermore, a vaccination parameter is also incorporated in the model, which is inactive until the time the vaccine is deployed. A Bayesian framework is utilized to perform both parameter estimation and prediction. Predictions are made to determine when the peak Active Infections occur. We provide inferential frameworks for assessing the effects of government interventions on the dynamic progression of the pandemic, including the impact of vaccination. The proposed model also allows for quantification of number of excess deaths averted over the study period due to vaccination.
The timing of disease emergence is influenced by many factors including social behavior and seasonal weather patterns that affect temperature and humidity. We examine how seasonal variation in transmission, recovery, or dispersal rates impact disease emergence in several well-known continuous-time Markov chain (CTMC) SIR, SEIR epidemic models with one or two patches. An ODE framework which incorporates periodic parameters for transmission, recovery, or dispersal serves as a basis for each stochastic model. The basic reproduction numbers and seasonal reproduction numbers from the ODE and branching process approximations of the CTMC are useful in predicting some of the stochastic behavior of the CTMC epidemic models. In particular, we apply these techniques to estimate a time-periodic probability of disease extinction, or equivalently, the probability of no disease emergence at the initiation of an epidemic. We also compute the mean and standard deviation for time to disease extinction and test the branching process approximations against simulations of the full CTMC epidemic models. Our numerical investigations illustrate how the magnitude and seasonal synchrony or asynchrony in transmission, recovery, or dispersal impact the probability of disease extinction. The numerical outcomes show that seasonal variation in transmission, recovery, or dispersal generally increases the probability of disease extinction (reducing disease emergence) and the shape of the seasonal reproduction number provides information about the shape of the periodic probability of disease extinction. However, the time of peak disease emergence precedes that predicted by the peak of the seasonal reproduction number.
We present a novel branching process model of disease spread in an open population (one which allows cases to arrive from outside the local community) with disease testing as well as forward and backward contact tracing. The local outbreak will never go extinct by chance alone due to the exogenous transmission. In the presented model contact tracing is resource constrained; not all cases identified can be contact traced and the probability of a case (found via testing) being traced decreases monotonically with the number of traced cases. Several well-known diseases are used to parameterize the offspring distribution, and for each disease, we explore the relative efficacy of contact tracing as a non-pharmaceutical intervention (NPI). Relative efficacy is estimated by comparing to outbreaks with no intervention. Importantly, we show that testing and tracing does not guarantee a better outcome due to the stochastic nature of early disease spread. Additionally, we discuss the relative efficacy of a test and trace approach to NPI in terms of the disease parameters and the resource constraints.
Polygenic risk scores are commonly used to estimate the multi-gene effects on a single phenotype such as disease status in a case-control study. These scores are the weighted sums of individual single nucleotide polymorphism (SNP) effects used to predict the phenotype of interest. There has been little work on the estimation of polygenetic risk scores when the phenotype is a longitudinal trajectory. We develop a linear mixed modeling framework for estimating polygenic risk scores for characterizing the genetic effects on the baseline and trajectory of a longitudinal continuous trait. The sets of random effects are crossed since the genetic effects vary over genome-location and the longitudinal effects vary over individual. We propose an EM algorithmic approach for parameter estimation, discuss computational challenges, and consider robustness of the model to key assumptions. We illustrate the methodology by examining the genetic effects on the prostate-specific antigen (PSA) level trajectory of male controls from the Prostate, Lung, Colorectal and Ovarian (PLCO) Cancer Screening Trial.
On September 20th, 2022, Uganda declared an outbreak of Ebolavirus disease (EVD) a day after confirming the index case in Mubende district in the central part of the country. After investigation, it was found that the index case was hospitalized on September 11th and there were 6 deaths before confirmation of the index case. In this talk, we introduce a stochastic modeling study of EVD outbreak and discuss the risk of delay. Motivated by the 2022 Uganda EVD outbreak, our model contains unreported cases and healthcare workers. We simulated the model using the modified Gillespie algorithm to reflect delayed events. From our scenario-based study, we found that depending on the delay in noticing the EVD outbreak, the maximum number of administered patients can range from 8 to 70 when noticing delay ranges from 0 to 50 days. Additionally, the outbreak duration can range from 64 to 133 days. We expect that our simulation study can provide guidance to healthcare authorities in areas where natural EVD reservoirs are suspected to exist.
Stable estimation of system parameters for infectious disease outbreaks is important for the design of an adequate forecasting algorithm. Stable estimation of disease parameters is also paramount in studying epidemics after the fact. In particular, for compartmental epidemic models, the transmission rate is important in evaluating one’s response to an outbreak.
The Coronavirus disease 2019 (COVID-19) pandemic triggered a global response as countries and organizations mobilized to combat the epidemic. The World Health Organization provided guidance and recommendations including lockdowns, quarantine, travel restrictions, and social distancing. Local governments, enacted responses based on their specific socio-economic contexts as the pandemic exposed many systemic vulnerabilities in many countries’ health systems, disaster preparedness, and adequate response capabilities.
In this study, we offer a retrospective look at the Pandemic in Côte D’Ivoire through the stable estimation of the time-dependent transmission rate of the disease throughout the epidemic from 2019 to 2022.
As a first approach, we use a Suceptible-Exposed-Infectious-Recovered compartmental model and pre-estimated disease parameters to fit the number of reported cases with respect to the time-dependent transmission rate comparing different functions to find the best-suited model. We estimate the transmission rate as a function of time using both parametric and non-parametric functions to capture the evolution of the transmission of the disease along with the control measures put in place by the local government and draw conclusions and lessons for the future.
Aedes aegypti and Aedes albopictus mosquitoes are the causative agents of dengue (DENV), chikungunya (CHIKV), and Zika (ZIKV) virus infections in humans. The co-circulation of at least two viruses/serotypes, which is common in countries worldwide, such as Columbia and Brazil in Latin America, can cause potential interactions among the viruses/serotypes and misdiagnosis in the lack of adequate laboratory tests due to similar clinical symptoms among their disease courses. We generalized a deterministic compartmental model to analyze how each disease dynamics changes under the potential antagonistic or synergistic interaction among the viruses/serotypes. Our simulation studies showed that under no DENV vaccine, vector control, and interaction among the viruses/serotypes, the peak of the incidence rates for people with no prior infections happens earlier than those cases with one or two prior infections, mostly because the proportion of fully susceptible people is larger than people with at least one prior infection. We observed higher incidence rates for single/multi infections and an earlier peak of the epidemics for single infections when a prior infection by a virus such as ZIKA causes synergistic cross-immunity against CHIKV and DENV serotypes, compared to the situation when it causes antagonistic cross-immunity. Identification of the cross-immunity is not possible when susceptibility statuses of the population are unknown because the high/low incidence rates could be either the results of high/low baseline transmission rates or antagonistic/synergistic interaction effects among the viruses.
A field scale model for heavy metals biosorption in homogeneous soils is constructed while considering the influence of biofilm and heavy metals interactions at the pore scale. The biofilm processes at the mesoscale are described by the Wanner-Gujer model for biofilm growth and then upscaled using the volume averaging approach to distinguish its effective parameters at the field scale [Gaebler et. al., 2022]. A laminar and convection-dominated regime is assumed for the flow within the soil. Within the soil pores, two separately growing bacteria species are assumed in the biofilm phase. Dissolved substrates and suspended bacteria are injected in the soil at a constant rate. A generic heavy metal is assumed to be transported in the soil and diffuse within the biofilm, affecting its overall growth rate. In turn, the biofilm retains this toxic metal through biosorption, and prevents it from reaching the underground water. The resulting macroscale model is described by a stiff system of hyperbolic equations to be solved numerically by the uniformly accurate central scheme of order 2 (UCS2) and using MATLAB platform. Different simulation scenarios have been investigated by varying the biofilm growth and biosorption parameters. The upscaled model accurately capture the mesoscale biosorption processes after a rigorous mathematical derivation.
In this presentation, we discuss a recent analysis of the variability of human leg stiffness across strides during running. We analyze the effects of speed, mass, and age on the dependence of the stiffness across strides. The major finding of our analysis is that the time series of several measurements of human leg stiffness show autocorrelation at large lags. Our results hint at the fact that feedforward strategies might be preferred at higher velocities. Furthermore, our analysis questions the common practice in biomechanics that researchers consider each stride as independent. We recommend caution in doing so, without first confirming the independence of any biomechanical measurements across strides with rigorous statistical tests such as those developed in our work. This is a joint work with Prof. Kathleen Lois Foster, Department of Biology, Ball State University.
We presented a mathematical model of swallowing in a catheterized oesophageal tube by duly considering the peripheral and core layers. We adequately account for the fluid mass conservation in both these layers. According to Kahrilas et al. (1995) and Pandey et al. (2017), peristaltic waves that govern the flow are thought to have gradually dilating amplitudes so that the distal oesophagus experiences higher pressure to ensure smooth delivery of gradually globular getting bolus into the abdomen through the cardiac sphincter. The technique of long wavelength and low Reynolds number is used to get the solutions in terms of stream function. Mass conservation in the two layers is taken care of by resolving the interface as a streamline from a fourth-order algebraic equation. The previous researchers' attempt to uniform wave amplitude had ignored mass conservation identically in the two layers by a wrong assumption of a fixed ratio between the layers. Due to unrealistic assumptions, those results cannot be accepted. Pressure, flow rate, and forces expressions are obtained for the tube with the catheter. The findings are accepted, and the interface between the two layers is explored. One wavelength's worth of pressure variation with flow rate is investigated. It is found that pressure and flow rate have a linear relationship even when the tube is catheterized. With pressure, the flow rate rises. It has been discovered that pressure rises as the peripheral layer viscosity does. Moreover, it has been found that when peripheral viscosity increases, the flow rate rises. Additionally, it has been found that as the flow rate in a catheterized oesophagus increases for a given difference in pressure, the peripheral layer thins down.
Data disparity remains a persistent challenge for the broader translational science community. At present, models working with observational data frequently encounter difficulties stemming from inconsistent measurement frequencies and insufficiently diverse patient populations. Approaching this as a compounded problem we seek to develop a novel framework that utilizes the concept of Time series Generative Adversarial Networks (TGAN) originally proposed by Yoon et.al [1]. While generative frameworks have been introduced, none can fully provide a sound solution for the temporal dynamics involved with time series observations. TGAN specifically aims to address temporal dynamics by utilizing a jointly optimized embedding space. Here we propose utilizing TGAN to generate both synthetic patients and semi-synthetic time series. Previously TGAN has been shown to outperform similar approaches, both qualitatively (tSNE) and quantitatively (discriminative and predictive scoring) on a variety of real-world datasets. For this research we aim to provide a conceptual methodology for aiding in the discovery of underlying mechanistic models via the integration of SINDy [2].By utilizing synthetic data that capture underlying dynamics we hypothesize that we can train models while holding out all real observation data for testing. Similarly with semi-synthetic time series we anticipate a better overall capture of disease dynamics.
References [1] J. Yoon, D. Jarrett, and M. van der Schaar, “Time-series Generative Adversarial Networks,” in Advances in Neural Information Processing Systems, Curran Associates, Inc., 2019. Accessed: Feb. 14, 2023. [Online]. Available: https://proceedings.neurips.cc/paper/2019/hash/c9efe5f26cd17ba6216bbe2a7d26d490-Abstract.html [2] S. L. Brunton, J. L. Proctor, and J. N. Kutz, “Discovering governing equations from data by sparse identification of nonlinear dynamical systems,” Proc. Natl. Acad. Sci. U.S.A., vol. 113, no. 15, pp. 3932–3937, Apr. 2016, doi: 10.1073/pnas.1517384113.
Stochastic modelling is key to understanding the dynamics of intracellular events in most biochemical systems, including gene-expression models. The stochasticity in the levels of gene products, e.g., messenger RNA (mRNA) and protein, is referred to as noise, which leads to cell-to-cell variability. The contributions to noise can emerge from different sources, such as structural elements. Recent studies have demonstrated that mRNA structure can be more complex than the most straightforward assumptions. Here, we study a structuration/generalisation of a stochastic gene-expression model in which mRNA molecules can be found in one of its finite number of different states and can transition among these states. In addition to characterising and deriving non-trivial analytical expressions for the steady-state protein distribution, we provide two different examples, which can be readily obtained from the structured/generalised model. The main example pertains to the formation of stem-loops; here, we reinterpret previous data and provide additional insights. Our analysis reveals that stem loops that restrict translation can reduce noise.
Mood episode prediction is an essential task for the treatment of bipolar disorder patients. Recent studies revealed that sleep patterns and circadian rhythm misalignment are valuable information to predict mood episodes. However, the specific contributions of different sleep and circadian rhythm information to mood prediction are less understood. Here, we employed the XGBoost model and compare the importance of sleep and circadian rhythm features in predicting mood episodes. Additionally, we used SHAP value analysis to show the circadian rhythm and mood relationship difference between depressive episodes and hypomanic episodes.
Idiopathic pulmonary fibrosis (IPF) is a disease characterized by remodeling and stiffening of fibrous collagen leading to septal thickening, alveolar destruction, and a stiffer lung. Little is known about how healthy parenchyma transitions to the characteristic IPF pattern seen on computed tomography (CT) scans. We investigate the morphogenesis of IPF with an agent-based model (ABM) that simulates cells interaction with extracellular matrix to imitate the progression of tissue accumulation. We incorporate alveolar architecture so that the model can simulate the conversion of real lung structure into a fibrotic environment. Lungs from mice with bleomycin-induced fibrosis and control mice were fixed at constant pressure and scanned with micro-CT at 4.9-micron slices. The lung architecture from the control serves as the scaffolding our agents traverse. Agents representing pro-fibrotic phenotypes increased tissue density by a fixed amount and were allowed to build off this tissue into airspaces while anti-fibrotic agents removed a fraction of tissue density. The ABM was run until the control lung architecture resembled the fibrotic lung architecture. The addition of agents acting on anatomically realistic alveolar architectures results in tissue remodeling reminiscent of that seen in pulmonary fibrosis, and thus can provide insight into emergent structures arising in fibrosis.
PhenoCellPy is an open-source Python package that defines methods for modeling sequences of cell behaviors and states (e.g., the cell cycle, or the Phases of cellular necrosis). PhenoCellPy defines Python classes for the Cell Volume (which it subdivides between the cytoplasm and nucleus) and its evolution, the state of the cell and the behaviors the cell displays in each state (called the Phase), and the sequence of behaviors (called the Phenotype). PhenoCellPy's can extend existing modeling frameworks as an embedded model. It supports integration with modeling frameworks in a number of ways, e.g. by messaging the main simulation when a change in behavior occurs. PhenoCellPy can function with any python-based modeling framework that supports Python 3, NumPy and SciPy.
Muscle regeneration is a complex process due to dynamic and multiscale biochemical and cellular interactions, making it difficult to determine optimal treatments for muscle injury using experimental approaches alone. To understand the degree to which individual cellular behaviors impact endogenous mechanisms of muscle recovery, we developed an agent-based model (ABM) using the Cellular Potts framework to simulate the dynamic microenvironment of a cross-section of murine skeletal muscle tissue. We referenced more than 200 published studies to define over 100 parameters and rules that dictate the behavior of muscle fibers, satellite stem cells (SSC), fibroblasts, neutrophils, macrophages, microvessels, and lymphatic vessels, as well as their interactions with each other and the microenvironment. We utilized parameter density estimation to calibrate the model to temporal biological datasets describing cross-sectional area (CSA) recovery, SSC, and fibroblast cell counts at multiple time points following injury. The calibrated model was validated by comparison of other model outputs (macrophage, neutrophil, and capillaries counts) to experimental observations. Predictions for eight model perturbations that varied cell or cytokine input conditions were compared to published experimental studies to validate model predictive capabilities. Latin hypercube sampling and partial rank correlation coefficient were used to identify optimal therapeutic strategies which guided in-silico perturbations of cytokine diffusion coefficients and decay rates. This analysis suggests a new hypothesis that a combined alteration of specific cytokine decay and diffusion parameters results in greater fibroblast and SSC proliferation and increased fiber recovery at 28 days (97% vs 82%, p<0.001) as compared to the baseline condition. Future work will explore this new hypothesis through novel coupled in-vivo and in-silico experiments to understand treatment responses with various injury types and microenvironmental conditions.
Defining a multicellular model can be challenging. There may be hundreds of parameters that specify the attributes and behaviors of multiple cell types and diffusible substrates in a model. If the model can be defined using a format specification, e.g., a markup language, then it can be readily shared in a minimal first step towards reproducibility. However, specifying the parameters of cell behaviors and substrates by hand is time consuming, error-prone, and ultimately a limiting factor in rapidly developing and refining sophisticated multicellular models. PhysiCell is an open source physics-based multicellular simulation system with an active and growing user community. It uses XML (extensible markup language) to define a model. To date, users needed to manually edit the XML to modify a model. PhysiCell Studio is a graphical tool to simplify this task. It provides a multi-tabbed GUI (graphical user interface) that allows graphical editing of the model and its associated XML, including the creation/deletion of fundamental objects, e.g., cell types and substrates/signals in the microenvironment. It also lets users run their model and interactively visualize results, allowing for more rapid model refinement. Using PhysiCell Studio in the classroom and training workshops has significantly reduced the training time for new learners, allowing them to develop sophisticated modeling. Conversely, frequent classroom and workshop use of the Studio has driven substantial improvements to the GUI. Like PhysiCell, the Studio is open source software, and contributions from the community are encouraged.
Plant cell morphology and growth are essential for plant development and adaptation. Some key cell types, such as pollen tubes, root hairs, and moss protonemata, develop specifically by tip growth. Cell wall material deposition and internal structure rearrangement (wall loosening) are the major contributing factors to the growth and morphogenesis of tip cells. As the cell wall is physically extended due to turgor pressure, we must understand the wall mechanical response against turgor pressure in order to elucidate this complex process. Studies into this process include theoretical modeling of tip growing cells, which are mostly based on the classical Lockhart theory, where the wall extends irreversibly in response to turgor pressure. These models predict that the shape of growing cells is critically dependent on a dramatic gradient of elastic moduli or effective viscosities from the tip domain to the shank region. While the elastic moduli have been measured experimentally in yeast and other tip-growing cells in simplified settings, the dramatic gradient transcending a difference in the order of several magnitudes has never been found. We argue the previous prediction is biased because these models do not distinguish wall deformation due to active processes, such as wall material deposition and wall loosening, from its elastic properties. Our research attempts to address these concerns by first measuring elastic moduli using our model organism, the moss Physcomitrium patens. We use a novel technique of measuring the elastic property by quantifying wall deformation from fluorescent bead tracking and surface region triangulation; and quantifying the wall tension from wall surface shape analysis. We find that there does exist a gradient of moduli between the tip and shank, but with a difference within an order of magnitude. Additional samples and improvement of error analysis will allow us to confirm this and investigate further into differences between cell types in P. patens. We will then apply this technique on other experiments to study how these elastic moduli differ during growth, or when cell wall composition is modified. This novel method will help bring advancements to the field of cell wall mechanics and the understanding of tip cell growth.
BACKGROUND: Radiation therapy is the single most utilized therapeutic agent in oncology, yet in the biology-driven medicine era, advances in radiation oncology have primarily focused on improving physical dose properties. As a result, the field of radiation oncology currently does not individualize radiation dose prescription based on the intrinsic biology of a patient’s tumor. METHODS: We develop a high resolution, 3D multiscale agent-based model that simulates the interactions of cancer cells with antitumor immune effector T-cells and immune-inhibitory suppressor cells. The immune cells and cancer cells are treated to be on a staggered lattice, where the immune cells are located at the cell vertices and the cancer cells are located at the centroid of the 3D unit lattice. Each cell is considered as an individual agent, and their behavior at any time is determined by a stochastic decision-making process based on biological-driven mechanistic rules. The absolute numbers of effector and suppressor immune cells in conjunction with the cancer cell burden were used to define the tumor-immune ecosystem (TIES). RESULTS: Simulations of tumor growth in various TIES reveal that in our model, the tumor-immune ecosystem yields 2 functional phenotypes: where tumors evade immune predation and where tumors are eradicated by the immune system. The immune cells are seen to dynamically move via chemokinesis with components of Brownian motion (exploration) and of directed motion toward the highest gradient of dead cancer cells (exploitation). Mechanistic rules are defined at a local and individual level to impose spatial restrictions on the immune cells and prevent immediate infiltration to the center of the tumor. The resulting movement and spatial rules lead to an emergent local immune swarming and formation of tertiary lymphoid structures. CONCLUSION: This is the first clinically and biologically validated computational model to simulate and predict pan-cancer response and outcomes via the perturbation of the TIES by radiotherapy. This work was supported by the NIH/NCI 1U01CA244100
Genetic oscillators arise from delayed transcriptional negative feedback loops, wherein repressor proteins inhibit their own synthesis after a temporal production delay. This delay, generated by sequential processes involved in gene expressions such as transcription, translation, folding, and translocation, is distributed due to the inherent noise of the processes. Because the delay determines repression timing and therefore the oscillation period, it has been commonly believed that delay noise weakens oscillatory dynamics. However, in this talk, we demonstrate that noisy delay can actually denoise genetic oscillators by improving the temporal peak reliability.
Single-cell genomic technologies offer vast new resources with which to study cells, but their potential to inform parameter inference of cell dynamics has yet to be fully realized. Here we develop methods for Bayesian parameter inference with data that jointly measure gene expression and Ca2+ dynamics in single cells. We propose to share information between cells via transfer learning: for a sequence of cells, the posterior distribution of one cell is used to inform the prior distribution of the next. In application to intracellular Ca2+ signaling dynamics, we fit the parameters of a dynamical model for thousands of cells with variable single-cell responses. We show that transfer learning accelerates inference with sequences of cells regardless of how the cells are ordered. However, only by ordering cells based on their transcriptional similarity can we distinguish Ca2+ dynamic profiles and associated marker genes from the posterior distributions. Inference results reveal complex and competing sources of cell heterogeneity: parameter covariation can diverge between the intracellular and intercellular contexts. Overall, we discuss the extent to which single-cell parameter inference informed by transcriptional similarity can quantify relationships between gene expression states and signaling dynamics in single cells.
In 2016, Hao and Friedman developed a deterministic model of Alzheimer’s disease progression using a system of partial differential equations. This model describes the general behavior of the disease, however it does not incorporate the molecular and cellular stochasticity intrinsic to the underlying disease processes. Here we extend the Hao and Friedman model by modeling each event in disease progression as a stochastic Markov process. This model identifies stochasticity in disease progression, as well as changes to the mean dynamics of key agents. We find that the pace of neuron death decreases whereas the production of the two key measures of progression, Tau and Amyloid beta proteins, accelerates when stochasticity is incorporated into the model. These results suggest that the non-constant reactions and time-steps have a significant effect on the overall progression of disease.
BACKGROUND: Cancer is a disease with an incredible ability to adapt when exposed to clinical treatment. This evolution of resistance presents a real challenge to the long-term success of treatments like targeted therapies. Taking into account tumor evolutionary dynamics like inter-clonal competition could provide insight to how to design therapies to best utilize the drugs that are already available to clinicians.
METHODS: To allow for a model that could be validated through laboratory work, we worked with an ordinary differential equation (ODE) system of an in vitro cell population approximating a heterogeneous tumor. The ODE system is composed of four individual cell populations that respond to two drugs, with one cell population being fully susceptible, one being fully resistant, and the other two populations being resistant to one or the other drug. Competition and growth are modeled through the logistic growth term, while cell death is based on each drug’s concentration. Three different regimen categories were simulated using MATLAB – alternation, combination, and sequential. In order to explore fully explore different regimen designs, drug concentration was varied in all of the regimens, while the ratio between the two drugs was varied in the combination regimen settings and the frequency of alternation was varied in the alternation settings. The population parameters of total initial cell burden and the ratios between susceptible and various resistant populations were also varied to explore patient impact on regimen effectiveness. A regimen’s ability to control a population was defined as how long it could maintain the population below a chosen threshold less than the carrying capacity of the system. The regimens were then analyzed for their ability to control both the fully resistant population and the total population and compared to the control achieved by minimal and maximal competition scenarios established by previous work.
RESULTS: The most important parameter varied in regimen design was concentration, as alternation and combination regimens with the same total concentration achieved grossly similar population control. In terms of the impact of alternation frequency, daily and weekly alternation had similar control of the fully resistant population and total population. Longer frequency alternations, like monthly, achieved better fully resistant control but had worse total population control.
DISCUSSION: Earlier work suggests that incorporating competition into regimen design could extend control of a tumor population, though the similarities between the performance of different regimens suggests that maintaining a certain level of competition is more important than the method used to manage the population. However, this resemblance may be attributable to the simplicity of the model and the lack of consideration of consequences like toxicity for each regimen or of tumor abilities like mutation. Future work would include analysis to see if inclusion of more complex pharmacokinetics or more complex cell behaviors significantly change these results.
Purpose: Quantifying and characterizing DNA damage is critical for optimizing radiation therapy treatments, particularly in advanced modalities like proton and alpha-targeted therapy. This study presents the Microdosimetric Gamma Model (MGM), a novel approach that predicts DNA damage properties by utilizing microdosimetry theory.
Methods: MGM provides the number of DNA damage sites and their complexities, which follow a Gamma distribution. Unlike current methods, MGM can characterize DNA damage for beams with multi-energy components, various time configurations, and spatial distributions. The output can be incorporated into repair models to predict cell killing, protein recruitment, chromosome aberrations, and other biological effects. We validated the MGM using TOPAS-nBio simulations for various radiation types.
Results: MGM demonstrated excellent agreement with the simulated data, accurately predicting damage complexities for protons and alpha particles. We also predicted survival fraction curves for different cell lines, providing insights into the relative biological effectiveness (RBE) of different radiation types.
Conclusions: The Microdosimetric Gamma Model offers a flexible framework for studying ionizing radiation's energy, time, and spatial aspects. It is a valuable tool for understanding and optimizing the biological effects of radiation therapy modalities like proton therapy, targeted alpha therapy, and helium therapy.
Tumor cell line organoid cultures are widely used in wet lab cancer research. Different from monolayer cell cultures, organoids preserve many phenotypic features demonstrated by cancer cells in vivo. In contrast to tissue microarrays, organoids offer a simplified, controllable environment. Recently, two-compartment matrigel/collagen1 organoids were developed [Lee2022], enabling scientists to mimic DCIS (ductal carcinoma in situ), IDS (invasive ductal carcinoma), and PDAC (pancreatic ductal adenocarcinoma) in extracellular matrix environments, as well as healthy mammary epithelial and fallopian tube epithelial extracellular matrix systems.
Utilizing the C++ based PhysiCell software framework [Ghaffarizade2018], we implemented an agent-based model of these two-compartment organoids. Our model was calibrated on the available data from a study from Crawford et al., who used these two-compartment organoids to explore the effect of collagen1 density conditions on cancer cell proliferation and invasion ability. Based on the results, the authors suggested that the cancer cell’s proliferation and invasiveness are being linked to cell-extracellular matrix friction [Crawford2022]. In our research work, we determine whether we can recapitulate these wet lab experiment findings.
Having a mathematical model which can capture the emergent phenomena, will extend our understanding of the two-compartment organoid wet lab model. Furthermore, the mathematical model makes it possible to quickly process a variety of experimental parameter settings in silico. The results will help to determine and plan the most interesting experimental parameters to explore in the wet lab.
[Lee2022] https://doi.org/10.1016/j.mattod.2022.07.006 [Crawford2022] https://doi.org/10.1101/2022.11.15.516548 [Ghaffarizade2018] https://doi.org/10.1371/journal.pcbi.1005991
Intratumor cellular heterogeneity and non-genetic cell plasticity in tumors pose a recently recognized challenge to cancer treatment. Because of the dispersion of initial cell states within a clonal tumor cell population, a perturbation imparted by a cytocidal drug only kills a fraction of cells. Due to dynamic instability of cellular states the cells not killed are pushed by the treatment into a variety of functional states, including a “stem-like state” that confers resistance to treatment and regenerative capacity. This immanent stress-induced stemness competes against cell death in response to the same perturbation and may explain the near-inevitable recurrence after any treatment. This double-edged-sword mechanism of treatment complements the selection of preexisting resistant cells in explaining post-treatment progression. Unlike selection, the induction of a resistant state has not been systematically analyzed as an immanent cause of relapse. Here, we present a generic elementary model and analytical examination of this intrinsic limitation to therapy. We show how the relative proclivity towards cell death versus transition into a stem-like state, as a function of drug dose, establishes either a window of opportunity for containing tumors or the inevitability of progression following therapy. The model considers measurable cell behaviors independent of specific molecular pathways and provides a new theoretical framework for optimizing therapy dosing and scheduling as cancer treatment paradigms move from “maximal tolerated dose,” which may promote therapy induced-stemness, to repeated “minimally effective doses” (as in adaptive therapies), which contain the tumor and avoid therapy-induced progression.
Glioblastoma multiforme (GBM) is one of the fastest-growing brain tumors and it has very low survival rates. Mathematical modeling can be used to predict the growth and treatment of brain cancer. However, one of the difficulties lies in the ability to estimate patient-specific parameters in the mathematical model from magnetic resonance imaging (MRI) data. We constructed a numerical solver to simulate tumor growth over a realistic 3D brain geometry derived from segmented-MRI. Then, using information about the size of the different glioma sub-regions, we are developing a method that estimates the patient-specific model parameters to inform the forward simulation. Ultimately, we hope to predict the overall survival of a patient from a single pre- operative scan.
While tumoral heterogeneity play a major role in the development of malignancy, the tumor microenvironment and the initial immune response are equally as important. The immune system is responsible for cancer surveillance and the initial suppression of malignancy. However, with the correct evolutionary mutations, cancer immunoediting can result in immune evasion. Yet, few models incorporate immune components to study the progression and impact of such mutations. In this work, we developed an agent-based model to explore this fitness strategy represented as an evolutionary game. Then, in a phased experimental approach, we plan to validate our model with various immune components, such as CD8+ T cells, NK cells, and other lymphocytes. Ultimately, this work will begin to elucidate the impact of the immune system on cancer evolution and allow us to begin to steer evolution towards more favorable outcomes.
Boolean networks, or logical models, are proven methods for simulating a cell’s response to its environment [1], [2]. In these models, nodes represent components of the system, such as genes or proteins, and an edge from a “parent” node to a “child” node indicates that the parent has a causal influence on the child, such as a transcription factor activating a gene. Each node is assigned a time-varying binary variable that can be ON (representing presence or activity of the system component) or OFF (representing its absence or inactivity). Often, a node state (or set of node states) is taken to represent a cellular behavior of interest. In the context of Boolean networks, the process of identifying interventions that lead to a particular cellular behavior (encoded as node states that represent known phenotypic markers) is called the target control problem [3], [4]. We address this problem in selected cancer-related Boolean networks by developing and applying a new method for edgetic perturbations, which involves intervening in specific interactions (e.g., analogous to blocking specific binding sites) rather than suppressing entire biomolecules. We separately determine node interventions solving the target control problem using two previously published methods: one based on a mean field approximation and a second, percolation-based method [5], [6]. We then implement the identified node and edge interventions in a multiscale context using the combined agent-based and Boolean network simulator PhysiBoSS [7], [8]. Using this approach, we test the effectiveness of the interventions devised in an isolated, single-cell context in a more realistic in silico environment that can account for spatial features (such as chemical gradients), heterogeneity of signal response in cell populations, and cell-cell interactions.
[1] A. A. Hemedan, A. Niarakis, R. Schneider, and M. Ostaszewski, “Boolean modelling as a logic-based dynamic approach in systems medicine,” Computational and Structural Biotechnology Journal, vol. 20, pp. 3161–3172, Jan. 2022, doi: 10.1016/j.csbj.2022.06.035. [2] J. D. Schwab, S. D. Kühlwein, N. Ikonomi, M. Kühl, and H. A. Kestler, “Concepts in Boolean network modeling: What do they all mean?,” Computational and Structural Biotechnology Journal, vol. 18, pp. 571–582, 2020, doi: 10.1016/j.csbj.2020.03.001. [3] J. C. Rozum, D. Deritei, K. H. Park, J. Gómez Tejeda Zañudo, and R. Albert, “pystablemotifs: Python library for attractor identification and control in Boolean networks,” Bioinformatics, vol. 38, no. 5, pp. 1465–1466, Mar. 2022, doi: 10.1093/bioinformatics/btab825. [4] C. Su and J. Pang, “A Dynamics-based Approach for the Target Control of Boolean Networks,” in Proceedings of the 11th ACM International Conference on Bioinformatics, Computational Biology and Health Informatics, in BCB ’20. New York, NY, USA: Association for Computing Machinery, Nov. 2020, pp. 1–8. doi: 10.1145/3388440.3412464. [5] T. Parmer, L. M. Rocha, and F. Radicchi, “Influence maximization in Boolean networks,” Nature Communications, vol. 13, no. 1, p. 3457, Jun. 2022, doi: 10.1038/s41467-022-31066-0. [6] J. G. T. Zañudo and R. Albert, “Cell Fate Reprogramming by Control of Intracellular Network Dynamics,” PLOS Computational Biology, vol. 11, no. 4, p. e1004193, Apr. 2015, doi: 10.1371/journal.pcbi.1004193. [7] G. Letort et al., “PhysiBoSS: a multi-scale agent-based modelling framework integrating physical dimension and cell signalling,” Bioinformatics, vol. 35, no. 7, pp. 1188–1196, Apr. 2019, doi: 10.1093/bioinformatics/bty766. [8] M. Ponce-de-Leon et al., “PhysiBoSS 2.0: a sustainable integration of stochastic Boolean and agent-based modelling frameworks.” bioRxiv, p. 2022.01.06.468363, Mar. 27, 2023. doi: 10.1101/2022.01.06.468363.
High-grade glioma continues to have dismal survival with current standard-of-care treatment, owing in part to its intra- and inter-patient heterogeneity. Typical diagnostic clinical biopsies are taken from the dense tumor core to determine the presence of abnormal cells and the status of a few key genes. However, the tumor core is removed during surgery, leaving behind possibly genetically, transcriptomically and/or phenotypically distinct invasive margins that repopulate the disease. As these remaining populations are the ones ultimately being treated, it is important to know their compositional differences from the tumor core. We aim to identify the phenotypic niches defined by the relative composition of key cellular populations and understand their variation amongst patients. We have established an image-localized research biopsy study, that samples from both the invasive margin and tumor core. From this protocol, we currently have 202 samples from 58 patients with available bulk RNA-Seq, collected between Mayo Clinic and Barrow Neurological Institute. Using a single-cell reference dataset from our collaborators at Columbia University, we used CIBERSORTx, a support vector machine deconvolution method, to predict relative abundances of normal, glioma, and immune cell states for each sample. We also applied Monocle, an algorithm that uses reversed graph embedding, to this dataset. Monocle orders samples on a low dimensional space by pseudotime, and provides a graph of transitions between end states. We find that these cell state abundances connect to patient survival and show regional differences. We analyze the robustness of these methods, and highlight the importance of characterizing residual glioma to better understand the recurrent disease.
Despite rapid initial responses and low toxicity, targeted therapies commonly fail to provide long-term benefits to cancer patients due to the development of therapy resistance. In multiple solid tumors, this resistance emerges due to gradual, multifactorial adaptation, i.e., a selective process combining genetic and non-genetic methods of cell diversification. This suggests a significant link between the evolution of cancer treatment resistance and evolvability – a selective trait of generating heritable phenotypic variation. However, the interplay between selection, evolvability, and resistance has not yet been fully investigated. We addressed this problem by studying the selection for mutator phenotype.
The mutator phenotype is common in many cancers and results from errors in DNA repair mechanisms. This phenotype generates mutations at a higher frequency than other phenotypes. Since mutations can both benefit or reduce cell viability, we hypothesized that the selection for a mutator phenotype changes during the evolution of resistance to cancer targeted therapies.
We tested this hypothesis by developing a 2D on-lattice Agent-Based Model (ABM). In the model, a cell can die, divide and mutate, yet mutations have a stochastic impact that can be beneficial, neutral, or deleterious for the individual cell fitness. Consequently, the resistance emerges as a stochastic event depending on the mutation frequency. Our results demonstrate that 1) the mutator phenotype initially accelerates adaptation to treatment, but 2) only intermediate mutation frequencies can sustain high fitness long-term.
This work provides a versatile experimental platform that can be adjusted to study the evolution of resistance in other cancers and treatments. Moreover, our results challenge the commonly held assumption that resistance develops only due to pre-existing driver mutations and provide an opportunity to integrate evolutionary theory and oncology to improve treatment in cancer patients.
Over the past two decades it has become clear that cancers are complex and evolving diseases. Genetic and non-genetic processes generate diverse subpopulations of tumor cells which can thrive under a variety of conditions and stressors. This provides a rich pool of variation that by means of natural selection and continued evolution enables adaptation to even the most modern treatments, especially in advanced cancers. Based on this novel understanding, so-called “evolutionary therapy” or “evolution-informed treatment strategies” have emerged which try to leverage, and potentially even steer, tumour evolution by strategically and dynamically sequencing and combining existing therapies and adjusting dose levels. In particular, adaptive therapy, which dynamically changes treatment levels to maintain drug-sensitive cells in order to competitively suppress emerging drug resistance, has produced a number of promising theoretical, preclinical and also clinical results. However, unlike for new drugs for which there are clear established frameworks for translation from bench to bedside, the design of preclinical protocols to ensure efficacy and safety of evolutionary therapies is an open question.
In this study, we use mathematical modeling to develop and interpret in vitro experimental protocols and apply them towards the development of an adaptive therapy for Osimertinib for the treatment of Non-Small Cell Lung Cancer. In the first step, we consider the question of how to measure ecological interactions between tumor subpopulations. To do so, we build on the “Game Assay” previously developed by our group, in which cells are co-cultured at different frequencies to measure how a population’s fitness depends on its frequency in the environment. Using an agent-based model of our in vitro experiments, we study how different aspects of the design (number of replicates, number of proportions) and analysis (regression technique, regression window) impact the accuracy and precision of the assay. Subsequently, we use our optimized protocol to quantify the frequency-dependent interactions between Osimertinib sensitive and resistant PC9 cells under different drug levels. In the next step, we use our model to explore whether and how so-obtained fitness differences translate to the ability to steer the composition of the tumor in long-term in vitro experiments, in which cells are co-cultured and passaged at regular intervals. In particular, we explore the role of the population size, passaging frequency, and passage fraction (proportion of cells carried forward to next passage). To conclude, we will present preliminary data in which we use this assay to trial a potential adaptive Osimertinib therapy protocol in vitro. Overall, we demonstrate how mathematical models can help to understand and improve experimental assays, and we contribute towards the important discussion as to how to translate evolutionary therapies from the blackboard to the bedside.
Resistance to prostate cancer treatment is a serious concern in modern oncology due to the risk it poses for poor patient outcomes. A key facet of treatment resistance is that traditional therapies can select for resistant cells. Understanding the heterogeneity of sensitivity to treatment in heterogeneous tumors is key to predicting and delaying the time to treatment resistance. We construct a novel random differential equation (RDE) model that incorporates sensitivity to treatment, then use inverse problem methods to recover the distribution of sensitive and resistant cells from noisy simulated data. We use the Akaike Information Criteria (AIC) to pinpoint the optimal mesh for the recovered distribution, which can help optimize individual treatment plans.
One of the major challenges in successfully treating glioblastoma (GBM) is the significant heterogeneity in cellular composition observed within and between patients. Recent single cell transcriptomics suggests there can be as many as eighteen distinct cell types in a single tumour [1]. Furthermore, advances in cellular deconvolution techniques, such as CIBERSORTx, allow us to accurately determine the cellular composition of imaged localised biopsies from bulk RNA-Seq [2]. Understanding this heterogeneity and how the complex interactions between cellular populations impacts the progression of GBM may lead to novel treatments which exploit the unique cellular composition within individual tumours. We group these eighteen cell types into sub-populations, e.g., glioma, immune, astrocyte, then attempt to learn the dynamics of these sub-populations by considering various interacting ODE/PDE models. Typically, a GBM patient will have biopsies taken at most twice, as well as only a handful of MRI scans. Therefore, the number of temporal data points to fit any model to are very limited. Thus, we apply trajectory inference methods, such as Monocle, to biopsy data, which allows us to order samples via pseudotime, an arbitrary unit of progress akin to real time [3]. We illustrate our modelling approach with a simplified two species Lotka-Volterra style competition model.
[1] O. Al-Dalahmah, et al., Re-convolving the compositional landscape of primary and recurrent glioblastoma using single nucleus RNA sequencing. bioRxiv (2021) https://doi.org/10.1101/2021.07.06.451295
[2] C. B. Steen, C. L. Liu, A. A. Alizadeh, A. M. Newman, Profiling Cell Type Abundance and Expression in Bulk Tissues with CIBERSORTx. Methods Mol. Biol. 2117, 135–157 (2020).
[3] C. Trapnell, et al., The dynamics and regulators of cell fate decisions are revealed by pseudotemporal ordering of single cells. Nat. Biotechnol. 32, 381–386 (2014).
Metastasis is a complex process that involves the spread of cancer cells from the primary tumor location to distant organs. During metastasis, cancer cells acquire migratory phenotypes, which allow them to detach from the primary tumor and invade the surrounding tissue. Cancer cells migrate through various mechanisms in the tumor microenvironment (TME), including single and collective migration phenotypes. These migration phenotypes are regulated by a complex interplay between the TME, particularly the extracellular matrix (ECM), and the signaling pathways. Here, we developed a computational model using open-source software CompuCell3D (a cellular Potts lattice-based model) that mimics in vitro migration studies of single and collective migration. We consider cancer cells as discrete agents, and their interactions with the TME are simulated in Compucell3D. Using the model, we analyzed the effect of cell-cell adhesion force, non-invasive and invasive phenotypes and structures, and cell-TME interactions in single and collective cell migration. Our aim is to identify key parameters and regulators of cancer metastasis and migration phenotypes. Our model will provide a better understanding of the underlying mechanisms essential for developing more targeted and personalized therapies for cancer metastasis.
In response to prolonged tumor-induced stimulation, T cells will dysfunctionally develop into a state of exhaustion. The hypo-functionality of exhausted CD8+ T cells ineffectively combats solid tumors, creating a localized stalemate rather than promoting tumor eradication. In recent years, cellular exhaustion has been a promising target of modern immunotherapy efforts. Exhaustion based therapies attempt to “reverse” this exhaustion, thereby restoring normal effector cell function to better fight the tumor. In this talk we will describe a new mathematical model for modeling the dynamics of exhausted T cells as they interact with cancer. This model follows the development of an exhausted CD8+ T cell population and the subsequent tumor-immune stalemate. Analysis and modeling simulations provide potential future targets for immunotherapy.
Hepatocellular carcinoma (HCC) is a molecularly heterogeneous solid malignancy, and its fitness may be shaped by how its tumor cells evolve. However, ability to monitor tumor cell evolution is hampered by the presence of numerous passenger mutations that do not provide any biological consequences. Here, we developed a strategy to determine the tumor clonality of three independent HCC cohorts from 524 patients with diverse etiologies and race/ethnicity by utilizing somatic mutations in cancer driver genes. We identified two main types of tumor evolution, i.e., linear, and non-linear models where non-linear type could be further divide into shallow branching and deep branching. We found that linear evolving HCC is less aggressive than other types. GTF2IRD2B mutations were enriched in HCC with linear evolution while TP53 mutations were the most frequent genetic alterations in HCC with shallow branching and deep branching models. In addition, myeloid cells were more frequently associated with HCC`s non-linear evolution while lymphoid cells were more frequently associated with HCC`s linear evolution. These results suggest that tumor cells and their microenvironment shape the tumor evolution process.
While tumoral heterogeneity play a major role in the development of malignancy, the tumor microenvironment and the initial immune response are equally as important. The immune system is responsible for cancer surveillance and the initial suppression of malignancy. However, with the correct evolutionary mutations, cancer immunoediting can result in immune evasion. Yet, few models incorporate immune components to study the progression and impact of such mutations. In this work, we developed an agent-based model to explore this fitness strategy represented as an evolutionary game. Then, in a phased experimental approach, we plan to validate our model with various immune components, such as CD8+ T cells, NK cells, and other lymphocytes. Ultimately, this work will begin to elucidate the impact of the immune system on cancer evolution and allow us to begin to steer evolution towards more favorable outcomes.
Glioblastoma multiforme (GBM) is one of the fastest-growing brain tumors and it has very low survival rates. Mathematical modeling can be used to predict the growth and treatment of brain cancer. However, one of the difficulties lies in the ability to estimate patient-specific parameters in the mathematical model from magnetic resonance imaging (MRI) data. We constructed a numerical solver to simulate tumor growth over a realistic 3D brain geometry derived from segmented-MRI. Then, using information about the size of the different glioma sub-regions, we are developing a method that estimates the patient-specific model parameters to inform the forward simulation. Ultimately, we hope to predict the overall survival of a patient from a single pre- operative scan.
Classical compartment models of pharmacokinetics are represented by deterministic kinetic equations and embedded in a probability theoretical context in terms of residence time random variables. Several parameter estimation and test methods are available to estimate related model parameters. The aim of this study is to examine the performance of these methods in the context of individual and population pharmacokinetics.
A simulation study for four standard compartment models for individual and population pharmacokinetics is conducted assessing the performance of the parameter estimation methods (a) minimum least squares, (b) maximum likelihood, and (c) minimum chi-squared estimation, as well as for the Chi-squared goodness of fit test. Performance measures include bias and standard error for the parameter estimators, and error probabilities for the Chi-squared test.
In the simpler compartment models and given an appropriate choice of measurement time points, all three estimators show satisfying results with regard to bias and standard error. Parameter estimates are asymptotically normal distributed. Further, distribution of the Chi-squared test statistic approaches the Chi-squared distribution asymptotically. In case of non-optimal choice of measurement time points, performance is poor for all estimation methods. Maximum likelihood method appears to be most robust for parameter estimation, but subsequent Chi-squared test statistic fails to asymptotically approach the Chi-squared distribution. In the more complex compartment models, minimum Chi-squared estimation appears to be most robust with regard to test errors of subsequent Chi-squared goodness of fit test. For minimum least squares and maximum likelihood parameter estimation, subsequent Chi-squared test statistic shows severely distorted error probabilities, suggesting that the asymptotic distribution of the Chi-squared test statistic is not the Chi-squared distribution.
Performance depends on the underlying model and the measurement time points in relation to the speed of elimination and dosage of the pharmakon. A simulation study can help to decide upon which method is most suitable in the application case.
Outside of laboratories, microbial communities (biofilms and other types) often exist in relatively stable environments where, on average, resource quality and quantity are predictable. Under such conditions, these communities are able to organize into tuned chemical factories, efficiently turning resources into biomass and waste byproducts. To do so, community scale physical, chemical, and biological constraints must be accommodated. At the cell scale, extensive omics data has enabled detailed, genome scale (GEM) modeling of metabolic response to chemical conditions. These two scale are coupled of course. Techniques to connect GEMs to community scale transport processes will be presented.
Women and other gender minorities are still under-represented in academic mathematics, with only 20% non-cis-male PhD students and 6% non-cis-male professors in the UK (London Mathematical Society’s Good Practice Report). Here we will present the results from a study at Newcastle University UK which explored the lived experiences of female-identifying mathematics PhD students through a series of one-to-one interviews. We seek to understand the extent to which the participants feel their gender has impacted their experiences as mathematics PhD students, including their relationships with supervisors, their view of role models, their identity as a mathematician, and their post-PhD choices.
Thoracoabdominal asynchrony (TAA), the asynchronous volume changes between the rib cage and abdomen during breathing, is associated with respiratory distress, progressive lung volume loss, and chronic lung disease in the newborn infant. Preterm infants are prone to TAA risk factors such as weak intercostal muscles, surfactant deficiency, and a flaccid chest wall. The causes of TAA in this fragile population are not fully understood and, to date, the assessment of TAA has not included a mechanistic modeling framework to explore the role these risk factors play in breathing dynamics and how TAA can be resolved. We present a dynamic compartmental model of pulmonary mechanics that simulates TAA in the preterm infant under various adverse clinical conditions, including high chest wall compliance, applied inspiratory resistive loads, bronchopulmonary dysplasia, anesthesia-induced intercostal muscle deactivation, weakened costal diaphragm, impaired lung compliance, and upper airway obstruction. Sensitivity analyses performed to screen and rank model parameter influence on model TAA and respiratory volume outputs show that risk factors are additive so that maximal TAA occurs in a virtual preterm infant with multiple adverse conditions, and addressing risk factors individually causes incremental changes in TAA. An abruptly obstructed upper airway caused immediate nearly paradoxical breathing and tidal volume reduction despite greater effort. In most simulations, increased TAA occurred together with decreased tidal volume. Simulated indices of TAA are consistent with published experimental studies and clinically-observed pathophysiology, motivating further investigation into the use of computational modeling for assessing and managing TAA.
Homeostasis is a regulatory mechanism by which a distinguished output variable remains approximately constant as an external input parameter varies over an interval. When perceived from a mathematical perspective, a natural interpretation of this phenomenon is that the derivative of the output variable with respect to the external input parameter vanishes. In the recent literature, this interpretation of homeostasis has been called 'infinitesimal homeostasis' and has the advantage that it allows one to apply results from singularity theory. While there are a variety of interesting questions one can try to answer using this theory, the question taken up in this project is: 'What can one say about which variables in a given network exhibit infinitesimal homeostasis along with the output variable?' Such questions relate to patterns of homeostasis in input-output networks, and our goal is to provide an answer based on rigorous mathematics.
SMB2023 Follow
Monday, July 17 at 6:00pm during the "PS01" time block. Room assignment: Performance Hall.