We consider the spread of an infectious disease in a heterogeneous environment, modelled as a network of patches. We focus on the invasibility of the disease, as quantified by the corresponding value of an approximation to the network basic reproduction number, $mathcal{R}_0$, and study how changes in the network structure affect the value of $mathcal{R}_0$. We provide a detailed analysis for two model networks, a star and a path, and discuss the changes to the corresponding network structure that yield the largest decrease in $mathcal{R}_0$. We develop both combinatorial and matrix analytic techniques, and illustrate our theoretical results by simulations with the exact $mathcal{R}_0$.

Erythropoiesis is a tightly regulated process beginning from hematopoietic stem cells (HSCs) and ending with mature red blood cells (RBCs). Hemoglobin within RBCs is responsible for transporting oxygen to body tissues. During erythropoiesis, about 20 to 25 mg of iron are used each day for hemoglobin synthesis, and most of this comes from recycling senescent RBCs. Many mathematical models of erythropoiesis in the literature neglect iron metabolism during erythropoiesis. However, such models are not useful in scenarios where there is iron overload or iron deficiency. At the same time, to understand the underlying control mechanisms, we seek to minimize the number of variables in the model, to circumvent issues with parameter identifiability that arise in ODE many-compartment models. In this talk, I will discuss a mathematical model we propose to capture the main physiological features of erythropoiesis. The model consists of five coupled delay differential equations, three of which track the iron during erythropoiesis including the hemoglobin iron within RBCs, and the other two equations model the dynamics of the major regulating hormones. I will present the derivation of the model, the positivity property of the model's solutions and the stability of its homeostatic steady state, and its numerical implementation.

We develop a mean-field model to study clogging in microfluidic devices and microvascular networks. Clogging in microfluidic cell sorters, which sort cells based on deformability, leads to disruptions in their performance, lower predictability and reliability, and a shorter lifetime in some cases. Our mean-field approach predicts the time of failure of single-column devices with a constant pressure gradient, constant flow rate, or independent channels. In addition, it provides insight into the clogging time and behavior of multiple-column devices and more complex porous structures, such as microvascular networks. To confirm our results, we use a time-driven stochastic simulation, numerically solve systems of differential equations, and use tools from probability theory and reliability engineering. In the case of capillary beds, we consider how the graph Laplacian spectrum provides some insight into the progress of clogging in the network.

Many organs develop left-right (LR) asymmetrical shapes and positions internally. Failure to properly establish LR asymmetry causes common, severe birth defects. The leftward curvature of the stomach is one of the most recognized LR asymmetries in the body. During its development the left side of the stomach undergo a specialized type of cell rearrangement (radial intercalation) that expands the left layers of the tube, thus forcing it to curve. Experiments with frog embryos (X. Laevis), however, show that inhibiting these cell rearrangements alone is not sufficient to prevent curvature, indicating the presence of additional left- and/or right-specific mechanisms. To explore what these mechanisms may be, I am integrating 2D and 3D agent-based computational modeling and animal experimentation. Starting with stomach shapes derived from nano-CT tomography, I am exploring which combinations of LR mechanisms, such as radial intercalation, cell shape changes, and differential adhesion, can reproduce patterns of stomach curvature under different conditions. The knowledge gained will help prioritize and contextualize the study of candidate genes from our ongoing genomic sequencing of human LR birth defects patients. On a broader level, we will gain novel insights into the physical forces that shapes 3D tissues, revealing general “rules” of tubular morphogenesis.

Horizontal gene transfer (HGT) allows the transmission of genetic information between microorganisms. Integrative Conjugative Elements (ICE) are segments of DNA that contain genes for insertion and excision from the genome, and transfer between microorganisms. ICE frequently contain antimicrobial resistance (AMR) genes and are significant contributors to the global increase in AMR incidence. Despite being widely distributed and contributing to the spread of AMR genes, their role, transfer rate, and impact on the fitness of the host are largely unexplored. In this study, we have developed a Partial Differential Equation model that considers the distribution of ICE across a population of bacteria. We assume that after a time step, this distribution may change due to four processes, each of which has a corresponding parameter in the model: excision, HGT, mutational degradation, and conference of a selective advantage. We fit this PDE to the data obtained from more than a thousand genomes from the genus Enterococcus, an opportunistic pathogen that is a frequent cause of hospital-derived infections. This will result in the estimation of transfer rate, conjugation rate, degradation rate, and selective advantage, which can be further utilized to study the genetic repertoire of ICEs.

The intrinsic genetic programme of a cell is not always sufficient to explain the cell's activities. External mechanical stimuli are increasingly being recognized as determinants of cell behavior. In the epithelial folding event that constitutes the beginning of gastrulation in Drosophila, the genetic programme of the future mesoderm leads to the establishment of a contractile actomyosin network that triggers apical constriction of cells, and thereby, furrow formation. However, some cells do not constrict but instead stretch, even though they share the same genetic programme as their constricting neighbors. We show here that tissue-wide interactions override the intrinsic programme of a subset of cells, forcing them to expand even when an otherwise sufficient amount and concentration of apical, active actomyosin has been accumulated. Models based on contractile forces and linear stress-strain responses are not sufficient to reproduce experimental observations, but simulations in which cells behave as materials with non-linear mechanical properties do. Our models also show that this behavior is an emergent property of supracellular actomyosin networks, in accordance with our experimental observations of actin reorganization within stretching cells, with this event being stochastic and rare in cells with high myosin levels, but reproducible in cells with lower concentrations.

We analyze a class of cell-bulk coupled ODE-PDE models that characterize communication between localized spatially segregated dynamically active signaling compartments/cells. In this model, the cells are disks of a common radius coupled through a passive extracellular bulk diffusion field in a bounded 2-D domain. Each cell secretes a signaling chemical into the bulk region at a constant rate and receives bulk chemical feedback from the entire collection of cells. This global feedback, which activates signaling pathways within the cells, modifies their intracellular dynamics according to the external environment. In the limit of finite diffusion, the method of matched asymptotic expansions is used to construct steady-state solutions of the ODE-PDE model and to derive a globally coupled nonlinear matrix eigenvalue problem (GCEP) that characterizes the linear stability properties of the steady-states. We also used matched asymptotic analysis to derive a nonlinear ODE system from the coupled ODE-PDE model in the limit of asymptotically large bulk diffusivity. For Sel'kov reaction kinetics, we investigated oscillatory instabilities in the dynamics of the cells triggered by global coupling. We also studied quorum sensing and how coupling defective cells to a group of identical cells change the intracellular dynamics of the cells.

We study the influence of spatial heterogeneity on the antiviral activity of mouse embryonic fibroblasts (MEF) infected with influenza A. MEF of type Ube1L^-/- are composed of two distinct sub-populations, the strong type that sustains a strong viral infection and the weak type, sustaining a weak viral load. These show different antiviral activity. When arranged in a checker board pattern, the total viral load significantly depends on the spatial arrangement of the cells. We explain this observation by using a reaction diffusion model and we show that mathematical homogenization can explain the observed inhomogeneities.

Population dynamics are generally modelled without taking behaviour into account. This in spite of the largest daily feeding times for predators, namely at dawn and dusk, being driven by behaviour. This is usually explained by prey avoiding visual predators, and visual predators seeking to find prey. We develop a game-theoretical model of predator-prey interactions in continuous time and space, finding the Nash equilibrium at every instant. By using the general resolution of polymatrix games, and an efficient discretization, we solve the spatial game nearly instantaneously. Our approach allows a unified model for the slow time-scale of population dynamics, and the fast time-scale of behaviour. We use the diel vertical migration as a case, examining emergent phenomena from the introduction of the fast dynamics. On the behavioural time-scale, we see the emergence of a deep scattering layer from the game dynamics. On the longer time-scale of population dynamics, the introduction of optimal behaviour has a strong stabilizing effect. In a seasonal environment, we observe a change in daily migration patterns throughout the seasons, driven by changes in population and light levels. The framework we propose can easily be adapted to population games in inhomogeneous terrestrial environments, and more complex food-webs.

Cooperation significantly impacts a species' population dynamics as individuals choose with whom to associate based upon fitness opportunities. Models of these dynamics typically assume that individuals can freely disperse between groups which works well for facultative co-operators like flocking birds, schooling fish, and swarming locusts. However, obligate co-operators like canids, cetaceans, and primates may be more discerning and selective over their associations, rejecting new members and even removing current members, thereby limiting dispersal. Incorporating such aspects into population models may better reflect the population dynamics of obligately cooperative species. We created and analyzed a model of the population dynamics of obligate co-operators where a behavioral game determines within-group population dynamics that then spill over into between-group dynamics. We identify a fundamental mismatch between the stability of the behavioral dynamics and the stability of the population dynamics; when one is stable, the other is not. Our results suggest that group turnover may be inherent to the population dynamics of obligate co-operators. If our model is true. the instability arises from a non-chaotic deterministic process, and such dynamics should be predictable and testable. Furthermore, we identify four key features that impact the conservation of obligate cooperative species and make recommendations on such.

Spatial memory, the storage and recovery of the locations of important landmarks on the landscape, plays a role in the way animals perceive their environments, resulting in memory-informed movement patterns that are observable to ecologists. Developing mathematical techniques to understand how animals use memory in their environments allows for an increased understanding of animal cognition. We developed a model that accounts for the memory of seasonal or ephemeral qualities of an animal's environment. The model builds on existing research to test hypotheses about the mechanisms driving animal movement behavior. Our model allows for comparison of four different hypotheses that detail the important of resource selection and spatial memory in animal movement. We used simulation analyses to verify that our model appropriately identifies memory and resource selection in simulated movement data, and these analyses have been informative about the data required to use the model properly. This model has potential to identify cognitive mechanisms for memory in a variety of ecological systems where periodic or seasonal revisitation patterns within a home range may take place.

When we examine the life history of humans against our close primate relatives, the great apes, we see that human adult lifespans include a post-menopausal life stage. This led to the question, “how did human females evolve to have old-age infertility?”Morton et al. suggested that ancestral male mating choices, particularly forgoing mating with older females, was the driving force behind the evolution of menopause. As their agent-based model is difficult to analyse, we propose an analogous system of ordinary differential equations (ODE) to examine their conclusions. Our conclusions contradict that of Morton et al., as we find that even the slightest deviation from an exclusive mating preference for younger females would counteract the evolution of menopause.

Mutators (individuals with uncommonly high mutation rate) are subject to second-order selection on the mutations they acquire. Mutators can be selected for since they can attain adaptive genotypes faster than their non-mutator counterparts. However, when the population is well-adapted to its environment, most mutations will be deleterious and hence mutators will be selected against. A mutator phenotype can be due to mutations in mismatch repair genes and DNA polymerases, and hence be strongly inherited from parent to offspring. But, it can also be caused by stochastic factors, such as protein concentrations, and hence be only inherited for few generations. Recently, an epigenetic mechanism for generating variability in mutation rate within the population and between parent and offspring was observed (Uphoff et al. Science 2016). We wondered which level of mutation rate inheritance – high, due to genetic factors, intermediate, due to epigenetic factors, or random, due to stochastic factors - leads to fastest adaptation. Using a combination of stochastic simulations and mathematical modelling, we show that intermediate levels of mutation rate inheritance, corresponding to epigenetic inheritance, result in fastest adaptation over rugged landscapes. This is due to an association between mutator phenotypes and pre-existing mutations, which aids crossing fitness valleys.

Transient dynamics can often differ drastically from the asymptotic dynamics of systems. In this talk we provide a unifying framework for analysing transient dynamics in marinemetapopulations, from the choice of norms to the addition of stage structure. We use the $ell_1$ norm, because of its biological interpretation, to extend the transient metrics of reactivityand attenuation to marine metapopulations, and use examples to compare these metrics under the more commonly used $ell_2$ norm. We then connect the reactivity and attenuation of marine metapopulations to the source-sink distribution of habitat patches and demonstrate how to meaningfully measure reactivity when metapopulations are stage-structured.

In order to prevent the spread of HIV, antiretroviral therapy (ART) for HIV drugs can be administered to high-risk individuals in advance of exposure, as pre-exposure prophylaxis (PrEP). PrEP with the ART combination drug Truvada taken daily has been demonstrated to effectively reduce the risk of HIV infection. However daily dosing can be onerous, and studies suggest that short-term use of ARTs around the time of exposure may be just as effective at reducing HIV risk. Here we investigate such “on-demand” PrEP. We build a mathematical framework in which we integrate a pharmacokinetic/pharmacodynamic (PK/PD) model developed by measuring mucosal tissue concentrations of tenofovir and emtricitabine (Truvada) (Cottrell et al. 2016) into an in-host stochastic model of early HIV infection with PrEP treatment based on virus dynamics. Armed with this model, we predict risk of infection under different on-demand PrEP regimens with regards to time of dosing and dosage relative to time of exposure. Thus we predict practical on-demand PrEP regimens in terms of dosage and timing required to obtain most effective protection for lower female genital tract (FGT).

Pathogens have important implications in many aspects of health, epidemiology, and evolution. Topological Data Analysis (TDA) is used here to help in identifying the behaviour of a biological system from a global perspective. Using data sets of the immune response during influenza-pneumococcal co-infection in mice, we employ here topological data analysis to simplify and visualise high dimensional data sets. Persistent shapes of the simplicial complexes of the data in the three infection scenarios were found: single viral infection, single bacterial infection, and co-infection. The immune response was found to be distinct for each of the infection scenarios and it was uncovered that the immune response during the co-infection has three phases and two transition points.

Current antiretroviral therapy (ART) effectively controls HIV in most patients but does not cure it. To develop drugs towards a HIV cure, novel approaches – such as reactivation of latent provirus (“shock”) and immunotherapies – are being explored. Mechanistic mathematical models that describe both within-host viral load dynamics and immunologic control of HIV infection are essential to integrate clinical data, assess therapeutic response, and generate hypotheses in support of HIV cure drug development. We built the Immune Viral Dynamics Modeling (IVDM) platform, based on recently developed mathematical models which integrate potential mechanisms that may lead to a cure. To inform the IVDM parameters, we created a dataset of “artificial” subjects by concatenating post-ATI (analytical treatment interruption) viral load profiles from eight ACTG clinical studies with on-ART viral load from a clinical study of raltegravir. This way, we created a dataset that describes the course of infection from initiation of treatment to ATI. Key parameters that govern latent reservoir seeding and immunological control were estimated using a nonlinear mixed effects approach (Monolix). From the estimated parameter distributions, we sampled a virtual population and ran clinical trial simulations (CTS) to assess potential curative interventions.

A mathematical model with the compartments of susceptible, exposed, mildly infected individuals, patients staying in intensive care units (ICUs) and ventilation units is developed and fitted with the daily reported symptomatic cases, deaths, patients staying in ICUs and ventilation units in Turkey for the period 11 March-31 May 2020. Then, this model has been modified after May 31, 2020 due to updated public restrictions and a time-dependent contact rate is derived via the effective reproduction number Rt, which is calculated using the daily reported cases, to capture the dynamics of the outbreak until vaccination. With the start of vaccination on January 13, 2021, the model is extended and COVID-19 outbreak in Turkey is successfully simulated and it is observed that vaccination rate is a more critical parameter than the vaccine efficacy to eliminate the disease successfully.

Each state in the United States exhibited a unique response to the COVID-19 outbreak, along with variable levels of testing, leading to different actual case burdens in the country. In this study, via per-capita testing dependent ascertainment rates, along with case and death data, we fit a minimal epidemic model for each state. We estimate infection-level responsive lockdown entry and exit rates (representing government and behavioral reaction), along with the true number of cases as of May 31, 2020. Ultimately we provide error corrected estimates for commonly used metrics such as infection fatality ratio and overall case ascertainment for all 55 states and territories considered, along with the United States in aggregate, in order to correlate outbreak severity with first wave intervention attributes and suggest potential management strategies for future outbreaks. We observe a theoretically predicted inverse proportionality relation between outbreak size and lockdown rate, with scale dependent on the underlying reproduction number and simulations suggesting a critical population quarantine ``half-life'' of 30 days independent of other model parameters.

The Eastern Equine Encephalitis Virus (EEEV) is an erratic and deadly neurological disease that spans across the northeastern coast of the United States. To determine the rate at which the virus is spread between the Black-Tailed Mosquito (Culiseta melanura) and select avian species we began by analyzing the migration patterns of both the mosquito and the avian species. It was found that certain species of avians shared similar, or even identical, flight patterns with the Black-Tailed Mosquito. Through this research, we develop and analyze a system of Ordinary Differential Equations (ODEs) to gain insight into how and when transmission of the virus to avians is at its highest. We incorporate a host stage-structured model where the avian host group is split into two categories, adults and young-of-the-year birds (YOY). Using this we explored the extent to which fluctuations occurred in transmission rates according to host/vector abundances, mosquito biting rate, and type of host. We evaluate the hypothesis that YOY avians are more readily exposed to the mosquito vector as they lack a defense mechanism, unlike their adult counterpart using the compartmental model.

Mathematical models, particularly in biology and biochemistry, can increase in complexity very quickly. The steady-state approximation (SSA) is an extremely powerful and valuable tool for simplifying the behaviour of a dynamical system. This model reduction process results in fewer variables, which allows equations to integrate faster, and fewer parameters to find values for, thus making the modelling process much more efficient. Rigorously establishing conditions that validate the SSA is laborious, and requires detailed time scale estimates specific to each system of interest. We have developed a versatile algorithm that provides a stepwise prescription for scaling from which conditions for the validity of the SSA based on Tikhonov's theorem can be elucidated. The algorithm requires only elementary algebraic manipulations to determine sufficient conditions at which the SSA is valid, making this algorithm more accessible to non-specialists. The algorithm recovers the Segel and Slemrod scaling for the Michaelis-Menten mechanism. The algorithm is robust, and can also be applied relatively easily to much more complex mechanisms.

This talk presents new methods for modeling and simulation of the aortic and mitral heart valves and use of these methods to study congenital heart disease. To construct model heart valves, we specify that the heart valve supports a pressure and derive an associated system of partial differential equations for its loaded state. Using the solution to this system, we then derive reference geometry and material properties. By tuning the parameters in this process, we design the model valves. This process produces material properties that are consistent with known values, yet also includes material heterogeneity. Results will be shown for both the aortic and mitral valves. When used in fluid-structure interaction simulations, these models are highly effective, producing realistic flow rates and robust closure under physiological driving pressures. Using these models, we study flows through the bicuspid aortic valve. Simulations show that a bicuspid valve, without alterations to the aorta anatomy, alters blood flow patterns dramatically. These flows suggest that hemodynamics play a strong role in aortic dilation and aneurysm formation.

The transport of various chemical species through cellular tissues is a widespread and important phenomenon in biology. At a microscopic level, such processes are often extremely complicated, possibly involving binding, diffusive transport, chemical changes, among other steps - all of this occurring in domains with non-trivial geometry. Nonetheless, at a tissue-scale, these processes are often modeled, as advection-diffusion-reaction equations occurring in homogeneous media. Thus, an important question is how the parameters that appear in such macro-scale models relate to what occurs at the cellular level (and vice-versa). In this talk, I will discuss how multi-state continuous-time random walks and generalized master equations can be used to model transport processes involving spatial jumps, immobilization at particular sites, and stochastic internal state changes. The underlying spatial models, which are framed as graphs, may have different types of nodes and edges, and walkers may have internal states that are governed by a Markov process. I will then discuss the key question of how macro-scale coefficients may be obtained from such models. This work is motivated by problems arising in the transport of proteins in biological tissues, specifically the Drosophila wing-imaginal disc, but the results are applicable to a broad array of problems.

Nonstandard finite difference (NSFD) methods have been widely used to numerically solve various problems in Biology. NSFD methods also have several advantages over standard techniques, such as preserving many of the essential properties of the solutions of the differential equations with no restriction on the time-step size. However, most of the NSFD methods developed to date are only of first-order accuracy. In this talk, we discuss the construction and analysis of a new class of second-order modified NSFD methods for general classes of autonomous differential equations. The proposed new methods are easy to implement and represent higher-order generalizations of the positive and elementary stable nonstandard (PESN) methods. Numerical simulations are also presented to support the theoretical results.

Kidney stones, also known as renal calculi, are hard deposits of salts and minerals that form in the kidney. When the stones get stuck in the urinary tract and obstruct the path of urine, they may cause excruciating pain in the lower abdomen. The most common type of kidney stones is made of calcium and oxalate, and they form during the bodily process of creating urine, especially when the urine becomes supersaturated and does not allow minerals to dissolve. In fact, recent studies have shown that drinking plenty of water dilutes the substances in urine and thereby reduces the likelihood of contracting kidney stones. Overall, this project devises two mathematical models that accurately and systematically determine the behavior of chemicals in the system. Then, we present a quantitative mechanism, namely the method of matched asymptotic expansions, and different modeling techniques to explain how an increase in fluid consumption decreases the amount of calcium-oxalate complex in the body and consequently the risk of contracting kidney stones.

Fibrin is the main determinant of the mechanical stability of blood clots and thrombi. Here, we explored the rupture of blood clots, emulating thrombus breakage by stretching fibrin gels with single-edge cracks. The stress-strain profiles display the weakly non-linear regime I of the gel due to alignment of fibrin fibers; linear elastic regime II owing to reversible stretching of fibers; and the rupture regime III for large deformations, during which irreversible breakage of fibers occurs. These dynamic mechanical regimes correlate with structural changes in the fibrin network. To model the stress-strain curves, we developed the Fluctuating Spring model, which maps the fibrin alignment, elastic network stretching, and cooperative rupture of coupled fibrin fibers into a mathematical framework to obtain a formula for stress as a function of strain. Cracks render network rupture stochastic. The free energy change for fiber deformation and rupture decreases with the crack size, thereby making the network rupture more spontaneously, but mechanical cooperativity due to the inter-fiber coupling strengthens the fibrin network. These results provide a basis for understanding of blood clot breakage that underlies thrombotic embolization. The mathematical Fluctuating Spring model can be used to characterize the dynamics of mechanical deformation of other protein networks.

We develop a novel paradigm of cancer therapy based on the 'anti-fragility' of cancer cell lines. Anti-fragility is a situation where the dose response function is convex. Treatment schedules with high variance of dose delivered result in maximum cell kill. For example, if the curvature is convex near a dose of 'x', continuous administration of x may have a less efficacious response compared to a regimen that switches equally between 120% and 80% of x, even though both regimens use the same total drug. We advocate for the need to disentangle first- and second-order treatment effects.Recent advances in personalized treatment scheduling known as 'adaptive' therapies typically result in a high level of variance in dose delivered in patients, similar to the theory behind anti-fragility. In this work we develop mathematical models of tumor pharmacodynamics (PKPD) and treatment resistance (Lotka-Volterra) to improve personalized dose protocols using principles from anti-fragile theory. PKPD dynamics are parameterized using in vitro dose response of H3122 non-small cell lung cancer cell lines confronted to ALK inhibitors. Competition between subpopulations (sensitive and resistant subclones) is the key determinant of optimal dose variance for individual patients. This work has implications for cancer therapy, antibiotics, and beyond.

Radiotherapy efficacy is the result of radiation-mediated cytotoxicity coupled with stimulation of anti-tumor immune responses. We developed an in silico three-dimensional agent-based model of diverse tumor-immune ecosystems (TIES) represented as anti- or pro-tumor immune phenotypes. We validate the model in 10,469 patients by demonstrating clinically-detected tumors have pro-tumor TIES. We then quantify the likelihood radiation induces anti-tumor TIES shifts by developing the individual Radiation Immune Sensitivity (iRIS), a novel biomarker. We show iRIS distribution across 31 tumor types is consistent with the clinical effectiveness of radiotherapy and predicts for local control and survival in a separate cohort of 59 lung cancer patients. This is the first clinically and biologically-validated model to represent the perturbation of the TIES by radiotherapy.

CAR-T cell immunotherapy has been obtaining expressive results in therapies against hematological cancers. Different antineoplastic targets are under investigation as well as therapy combinations with immune checkpoint blockade drugs, minimum effective CAR-T cell dose, memory pool formation, patient specificity, among others. Many of these studies require a preclinical proof-of-concept experiment using immunodeficient mouse models. Aiming at minimizing and optimizing in vivo experiments, we developed an open-source software in a Shiny R-based platform, named CARTmath. It allows simulating a three population mathematical model that represents the dynamics of tumor cells and effector and memory CAR-T cells in immunodeficient mouse models. Designed to be a friendly platform, even researchers unfamiliar with mathematical modeling can investigate the effects of different CAR-T cell immunotherapy protocols, types of tumors, immunosuppressive mechanisms, to mention a few, hopefully reducing in vivo experiments. CARTmath is available at github.com/tmglncc/CARTmath or directly on the webpage cartmath.lncc.br.

Prostate cancer (PCa) is the second most frequent cancer in men. The limited individualization of the clinical management beyond risk-group definition leads to significant overtreatment/undertreatment rate. PCa is a paradigmatic condition in which an individualized predictive technology could make a difference in treatment.Mathematical modeling and simulation highlight the mechanisms behind disease progression. The prostate is a small organ with a structure composed by a network of glands within smooth muscle connectivity tissue. To explore the prostate structure in PCa growth we developed 2 mathematical models. The first, a 2D cellular Potts model (CPM), simulates the interactions between the different types of cells and the deformation of the glands in time. The second is a 3D phase-field model with tumor growth, prostate gland dynamics and nutrient consumption.The CPM gives important clues: how the cells and the glands rearrange locally in tumor growth. We import these insights to the 3D phase-field model to study how the adaptation of the grand morphology influences the lesion morphology.We conclude that the ramified structure of the prostate has a determinant impact in the tumor growth. The model parameter range that creates a ramified tumor phenotype is dramatically extended when prostate glands are considered.