Dysregulated FGFR3 signaling alters the immune landscape in bladder cancer and presents therapeutic possibilities in an agent-based model.

Bladder cancer is an increasingly prevalent global disease that continues to cause morbidity and mortality despite recent advances in treatment. Immune checkpoint inhibitors (ICI) and fibroblast growth factor receptor (FGFR)-targeted therapeutics have had modest success in bladder cancer when used as monotherapy. Emerging data suggests that the combination of these two therapies could lead to improved clinical outcomes, but the optimal strategy for combining these agents remains uncertain. Mathematical models, specifically agent-based models (ABMs), have shown recent successes in uncovering the multiscale dynamics that shape the trajectory of cancer. They have enabled the optimization of treatment methods and the identification of novel therapeutic strategies. To assess the combined effects of anti-PD-1 and anti-FGFR3 small molecule inhibitors (SMI) on tumor growth and the immune response, we built an ABM that captures key facets of tumor heterogeneity and CD8+ T cell phenotypes, their spatial interactions, and their response to therapeutic pressures. Our model quantifies how tumor antigenicity and FGFR3 activating mutations impact disease trajectory and response to anti-PD-1 antibodies and anti-FGFR3 SMI. We find that even a small population of weakly antigenic tumor cells bearing an FGFR3 mutation can render the tumor resistant to combination therapy. However, highly antigenic tumors can overcome therapeutic resistance mediated by FGFR3 mutation. The optimal therapy depends on the strength of the FGFR3 signaling pathway. Under certain conditions, ICI alone is optimal; in others, ICI followed by anti-FGFR3 therapy is best. These results indicate the need to quantify FGFR3 signaling and the fitness advantage conferred on bladder cancer cells harboring this mutation. This ABM approach may enable rationally designed treatment plans to improve clinical outcomes.

Mathematical model predicts tumor control patterns induced by fast and slow cytotoxic T lymphocyte killing mechanisms.

Immunotherapy has dramatically transformed the cancer treatment landscape largely due to the efficacy of immune checkpoint inhibitors (ICIs). Although ICIs have shown promising results for many patients, the low response rates in many cancers highlight the ongoing challenges in cancer treatment. Cytotoxic T lymphocytes (CTLs) execute their cell-killing function via two distinct mechanisms: a fast-acting, perforin-mediated process and a slower, Fas ligand (FasL)-driven pathway. Evidence also suggests that the preferred killing mechanism of CTLs depends on the antigenicity of tumor cells. To determine the critical factors affecting responses to ICIs, we construct an ordinary differential equation model describing in vivo tumor-immune dynamics in the presence of active or blocked PD-1/PD-L1 immune checkpoint. Specifically, we identify important aspects of the tumor-immune landscape that affect tumor size and composition in the short and long term. We also generate a virtual cohort of mice with diverse tumor and immune attributes to simulate the outcomes of immune checkpoint blockade in a heterogeneous population. By identifying key tumor and immune characteristics associated with tumor elimination, dormancy, and escape, we predict which fraction of a population potentially responds well to ICIs and ways to enhance therapeutic outcomes with combination therapy.

Connecting Agent-Based Models with High-Dimensional Parameter Spaces to Multidimensional Data Using SMoRe ParS: A Surrogate Modeling Approach.

Across a broad range of disciplines, agent-based models (ABMs) are increasingly utilized for replicating, predicting, and understanding complex systems and their emergent behavior. In the biological and biomedical sciences, researchers employ ABMs to elucidate complex cellular and molecular interactions across multiple scales under varying conditions. Data generated at these multiple scales, however, presents a computational challenge for robust analysis with ABMs. Indeed, calibrating ABMs remains an open topic of research due to their own high-dimensional parameter spaces. In response to these challenges, we extend and validate our novel methodology, Surrogate Modeling for Reconstructing Parameter Surfaces (SMoRe ParS), arriving at a computationally efficient framework for connecting high dimensional ABM parameter spaces with multidimensional data. Specifically, we modify SMoRe ParS to initially confine high dimensional ABM parameter spaces using unidimensional data, namely, single time-course information of in vitro cancer cell growth assays. Subsequently, we broaden the scope of our approach to encompass more complex ABMs and constrain parameter spaces using multidimensional data. We explore this extension with in vitro cancer cell inhibition assays involving the chemotherapeutic agent oxaliplatin. For each scenario, we validate and evaluate the effectiveness of our approach by comparing how well ABM simulations match the experimental data when using SMoRe ParS-inferred parameters versus parameters inferred by a commonly used direct method. In so doing, we show that our approach of using an explicitly formulated surrogate model as an interlocutor between the ABM and the experimental data effectively calibrates the ABM parameter space to multidimensional data. Our method thus provides a robust and scalable strategy for leveraging multidimensional data to inform multiscale ABMs and explore the uncertainty in their parameters.

Phenotype switching in a global method for agent-based models of biological tissue.

Agent-based models (ABMs) are an increasingly important tool for understanding the complexities presented by phenotypic and spatial heterogeneity in biological tissue. The resolution a modeler can achieve in these regards is unrivaled by other approaches. However, this comes at a steep computational cost limiting either the scale of such models or the ability to explore, parameterize, analyze, and apply them. When the models involve molecular-level dynamics, especially cell-specific dynamics, the limitations are compounded. We have developed a global method for solving these computationally expensive dynamics significantly decreases the computational time without altering the behavior of the system. Here, we extend this method to the case where cells can switch phenotypes in response to signals in the microenvironment. We find that the global method in this context preserves the temporal population dynamics and the spatial arrangements of the cells while requiring markedly less simulation time. We thus add a tool for efficiently simulating ABMs that captures key facets of the molecular and cellular dynamics in heterogeneous tissue.

Analysis of HIV latent infection model with multiple infection stages and different drug classes.

Latently infected CD4+ T cells represent one of the major obstacles to HIV eradication even after receiving prolonged highly active anti-retroviral therapy (HAART). Long-term use of HAART causes the emergence of drug-resistant virus which is then involved in HIV transmission. In this paper, we develop mathematical HIV models with staged disease progression by incorporating entry inhibitor and latently infected cells. We find that entry inhibitor has the same effect as protease inhibitor on the model dynamics and therefore would benefit HIV patients who developed resistance to many of current anti-HIV medications. Numerical simulations illustrate the theoretical results and show that the virus and latently infected cells reach an infected steady state in the absence of treatment and are eliminated under treatment whereas the model including homeostatic proliferation of latently infected cells maintains the virus at low level during suppressive treatment. Therefore, complete cure of HIV needs complete eradication of latent reservoirs.

Implementing a global approach for efficiently simulating molecular dynamics in agent-based models of biological tissue.

This protocol explains how to take an agent-based model (ABM) with molecular dynamics and set it up to solve the molecular dynamics with a global approach. It can be used to speed up simulations significantly while retaining high levels of accuracy with the original ABM. Two options are presented for implementing this global approach, depending on the desired spatial variability in molecular concentrations. Both options coarse-grain the molecular dynamics in space by dividing the microenvironment into regions with uniform concentrations. For complete details on the use and execution of this protocol, please refer to Bergman et al. (2022).

Understanding the mechanisms of HPV-related carcinogenesis: Implications for cell cycle dynamics.

The role of human papillomavirus (HPV) as a causative agent for epithelial cancers is well-known, but many open questions remain regarding the downstream gene regulatory effects of viral proteins E6 and E7 on the cell cycle. Here, we extend a cell cycle model originally presented by Gérard and Goldbeter (2009) in order to capture the effects of E6 and E7 on key actors in the cell cycle. Results suggest that E6 is sufficient to reverse p53-induced quiescence, while E7 is sufficient to reverse p16INK4a-induced quiescence; both E6 and E7 are necessary when p53 and p16INK4a are both active. Moreover, E7 appears to play a role as a "growth factor substitute", inducing cell division in the absence of growth factor. Low levels of E7 may permit regular cell division, but the results suggest that higher levels of E7 dysregulate the cell cycle in ways that may destabilize the cellular genome. The mechanisms explored here provide opportunities for developing new treatment targets that take advantage of the cell cycle regulatory system to prevent HPV-related cancer effects.

Tumor growth towards lower extracellular matrix conductivity regions under Darcy's Law and steady morphology.

We study a classic Darcy's law model for tumor cell motion with inhomogeneous and isotropic conductivity. The tumor cells are assumed to be a constant density fluid flowing through porous extracellular matrix (ECM). The ECM is assumed to be rigid and motionless with constant porosity. One and two dimensional simulations show that the tumor mass grows from high to low conductivity regions when the tumor morphology is steady. In the one-dimensional case, we proved that when the tumor size is steady, the tumor grows towards lower conductivity regions. We conclude that this phenomenon is produced by the coupling of a special inward flow pattern in the steady tumor and Darcy's law which gives faster flow speed in higher conductivity regions.

A global method for fast simulations of molecular dynamics in multiscale agent-based models of biological tissues.

Agent-based models (ABMs) are a natural platform for capturing the multiple time and spatial scales in biological processes. However, these models are computationally expensive, especially when including molecular-level effects. The traditional approach to simulating this type of multiscale ABM is to solve a system of ordinary differential equations for the molecular events per cell. This significantly adds to the computational cost of simulations as the number of agents grows, which contributes to many ABMs being limited to around 10 5 cells. We propose an approach that requires the same computational time independent of the number of agents. This speeds up the entire simulation by orders of magnitude, allowing for more thorough explorations of ABMs with even larger numbers of agents. We use two systems to show that the new method strongly agrees with the traditionally used approach. This computational strategy can be applied to a wide range of biological investigations.

SMoRe ParS: A novel methodology for bridging modeling modalities and experimental data applied to 3D vascular tumor growth.

Multiscale systems biology is having an increasingly powerful impact on our understanding of the interconnected molecular, cellular, and microenvironmental drivers of tumor growth and the effects of novel drugs and drug combinations for cancer therapy. Agent-based models (ABMs) that treat cells as autonomous decision-makers, each with their own intrinsic characteristics, are a natural platform for capturing intratumoral heterogeneity. Agent-based models are also useful for integrating the multiple time and spatial scales associated with vascular tumor growth and response to treatment. Despite all their benefits, the computational costs of solving agent-based models escalate and become prohibitive when simulating millions of cells, making parameter exploration and model parameterization from experimental data very challenging. Moreover, such data are typically limited, coarse-grained and may lack any spatial resolution, compounding these challenges. We address these issues by developing a first-of-its-kind method that leverages explicitly formulated surrogate models (SMs) to bridge the current computational divide between agent-based models and experimental data. In our approach, Surrogate Modeling for Reconstructing Parameter Surfaces (SMoRe ParS), we quantify the uncertainty in the relationship between agent-based model inputs and surrogate model parameters, and between surrogate model parameters and experimental data. In this way, surrogate model parameters serve as intermediaries between agent-based model input and data, making it possible to use them for calibration and uncertainty quantification of agent-based model parameters that map directly onto an experimental data set. We illustrate the functionality and novelty of Surrogate Modeling for Reconstructing Parameter Surfaces by applying it to an agent-based model of 3D vascular tumor growth, and experimental data in the form of tumor volume time-courses. Our method is broadly applicable to situations where preserving underlying mechanistic information is of interest, and where computational complexity and sparse, noisy calibration data hinder model parameterization.

An Agent-Based Model of Combination Oncolytic Viral Therapy and Anti-PD-1 Immunotherapy Reveals the Importance of Spatial Location When Treating Glioblastoma.

Oncolytic viral therapies and immunotherapies are of growing clinical interest due to their selectivity for tumor cells over healthy cells and their immunostimulatory properties. These treatment modalities provide promising alternatives to the standard of care, particularly for cancers with poor prognoses, such as the lethal brain tumor glioblastoma (GBM). However, uncertainty remains regarding optimal dosing strategies, including how the spatial location of viral doses impacts therapeutic efficacy and tumor landscape characteristics that are most conducive to producing an effective immune response. We develop a three-dimensional agent-based model (ABM) of GBM undergoing treatment with a combination of an oncolytic Herpes Simplex Virus and an anti-PD-1 immunotherapy. We use a mechanistic approach to model the interactions between distinct populations of immune cells, incorporating both innate and adaptive immune responses to oncolytic viral therapy and including a mechanism of adaptive immune suppression via the PD-1/PD-L1 checkpoint pathway. We utilize the spatially explicit nature of the ABM to determine optimal viral dosing in both the temporal and spatial contexts. After proposing an adaptive viral dosing strategy that chooses to dose sites at the location of highest tumor cell density, we find that, in most cases, this adaptive strategy produces a more effective treatment outcome than repeatedly dosing in the center of the tumor.

Standing Variations Modeling Captures Inter-Individual Heterogeneity in a Deterministic Model of Prostate Cancer Response to Combination Therapy.

Sipuleucel-T (Provenge) is the first live cell vaccine approved for advanced, hormonally refractive prostate cancer. However, survival benefit is modest and the optimal combination or schedule of sipuleucel-T with androgen depletion remains unknown. We employ a nonlinear dynamical systems approach to modeling the response of hormonally refractive prostate cancer to sipuleucel-T. Our mechanistic model incorporates the immune response to the cancer elicited by vaccination, and the effect of androgen depletion therapy. Because only a fraction of patients benefit from sipuleucel-T treatment, inter-individual heterogeneity is clearly crucial. Therefore, we introduce our novel approach, Standing Variations Modeling, which exploits inestimability of model parameters to capture heterogeneity in a deterministic model. We use data from mouse xenograft experiments to infer distributions on parameters critical to tumor growth and to the resultant immune response. Sampling model parameters from these distributions allows us to represent heterogeneity, both at the level of the tumor cells and the individual (mouse) being treated. Our model simulations explain the limited success of sipuleucel-T observed in practice, and predict an optimal combination regime that maximizes predicted efficacy. This approach will generalize to a range of emerging cancer immunotherapies.

A validated mathematical model of FGFR3-mediated tumor growth reveals pathways to harness the benefits of combination targeted therapy and immunotherapy in bladder cancer.

Bladder cancer is a common malignancy with over 80,000 estimated new cases and nearly 18,000 deaths per year in the United States alone. Therapeutic options for metastatic bladder cancer had not evolved much for nearly four decades, until recently, when five immune checkpoint inhibitors were approved by the U.S. Food and Drug Administration (FDA). Despite the activity of these drugs in some patients, the objective response rate for each is less than 25%. At the same time, fibroblast growth factor receptors (FGFRs) have been attractive drug targets for a variety of cancers, and in 2019 the FDA approved the first therapy targeted against FGFR3 for bladder cancer. Given the excitement around these new receptor tyrosine kinase and immune checkpoint targeted strategies, and the challenges they each may face on their own, emerging data suggest that combining these treatment options could lead to improved therapeutic outcomes. In this paper, we develop a mathematical model for FGFR3-mediated tumor growth and use it to investigate the impact of the combined administration of a small molecule inhibitor of FGFR3 and a monoclonal antibody against the PD-1/PD-L1 immune checkpoint. The model is carefully calibrated and validated with experimental data before survival benefits, and dosing schedules are explored. Predictions of the model suggest that FGFR3 mutation reduces the effectiveness of anti-PD-L1 therapy, that there are regions of parameter space where each monotherapy can outperform the other, and that pretreatment with anti-PD-L1 therapy always results in greater tumor reduction even when anti-FGFR3 therapy is the more effective monotherapy.

Modeling Oncolytic Viral Therapy, Immune Checkpoint Inhibition, and the Complex Dynamics of Innate and Adaptive Immunity in Glioblastoma Treatment.

Oncolytic viruses are of growing interest to cancer researchers and clinicians, due to their selectivity for tumor cells over healthy cells and their immunostimulatory properties. The immune response to an oncolytic virus plays a critical role in treatment efficacy. However, uncertainty remains regarding the circumstances under which the immune system either assists in eliminating tumor cells or inhibits treatment via rapid viral clearance, leading to the cessation of the immune response. In this work, we develop an ordinary differential equation model of treatment for a lethal brain tumor, glioblastoma, using an oncolytic Herpes Simplex Virus. We use a mechanistic approach to model the interactions between distinct populations of immune cells, incorporating both innate and adaptive immune responses to oncolytic viral therapy (OVT), and including a mechanism of adaptive immune suppression via the PD-1/PD-L1 checkpoint pathway. We focus on the tradeoff between viral clearance by innate immune cells and the innate immune cell-mediated recruitment of antiviral and antitumor adaptive immune cells. Our model suggests that when a tumor is treated with OVT alone, the innate immune cells' ability to clear the virus quickly after administration has a much larger impact on the treatment outcome than the adaptive immune cells' antitumor activity. Even in a highly antigenic tumor with a strong innate immune response, the faster recruitment of antitumor adaptive immune cells is not sufficient to offset the rapid viral clearance. This motivates our subsequent incorporation of an immunotherapy that inhibits the PD-1/PD-L1 checkpoint pathway by blocking PD-1, which we combine with OVT within the model. The combination therapy is most effective for a highly antigenic tumor or for intermediate levels of innate immune localization. Extreme levels of innate immune cell activity either clear the virus too quickly or fail to activate a sufficiently strong adaptive response, yielding ineffective combination therapy of GBM. Hence, we show that the innate and adaptive immune interactions significantly influence treatment response and that combining OVT with an immune checkpoint inhibitor expands the range of immune conditions that allow for tumor size reduction or clearance.

In Silico Models Accurately Predict In Vivo Response for IL6 Blockade in Head and Neck Cancer.

Malignant features of head and neck squamous cell carcinoma (HNSCC) may be derived from the presence of stem-like cells that are characterized by uniquely high tumorigenic potential. These cancer stem cells (CSC) function as putative drivers of tumor initiation, therapeutic evasion, metastasis, and recurrence. Although they are an appealing conceptual target, CSC-directed cancer therapies remain scarce. One promising CSC target is the IL6 pathway, which is strongly correlated with poor patient survival. In this study we created and validated a multiscale mathematical model to investigate the impact of cross-talk between tumor cell- and endothelial cell (EC)-secreted IL6 on HNSCC growth and the CSC fraction. We then predicted and analyzed the responses of HNSCC to tocilizumab (TCZ) and cisplatin combination therapy. The model was validated with in vivo experiments involving human ECs coimplanted with HNSCC cell line xenografts. Without artificial tuning to the laboratory data, the model showed excellent predictive agreement with the decrease in tumor volumes observed in TCZ-treated mice, as well as a decrease in the CSC fraction. This computational platform provides a framework for preclinical cisplatin and TCZ dose and frequency evaluation to be tested in future clinical studies. SIGNIFICANCE: A mathematical model is used to rapidly evaluate dosing strategies for IL6 pathway modulation. These results may lead to nonintuitive dosing or timing treatment schedules to optimize synergism between drugs.

Mechanistic Deconvolution of Oral Absorption Model with Dynamic Gastrointestinal Fluid to Predict Regional Rate and Extent of GI Drug Dissolution.

Multiple approaches such as mathematical deconvolution and mechanistic oral absorption models have been used to predict in vivo drug dissolution in the gastrointestinal (GI) tract. However, these approaches are often validated by plasma pharmacokinetic profiles, but not by in vivo drug dissolution due to the limited data available regarding the local GI environment. It is also challenging to predict and validate in vivo dissolution in different regions of the GI tract (stomach, duodenum, jejunum, and ileum). In this study, the dynamic fluid compartment absorption and transport (DFCAT) model was used to predict the in vivo dissolution profiles of ibuprofen, which was administered as an 800-mg immediate-release tablet to healthy subjects, in different regions of the GI tract. The prediction was validated with concentration time-courses of ibuprofen (BCS class 2a) in different regions of the GI tract that we have obtained over the past few years. The computational model predicted that the dissolution of ibuprofen was minimal in the stomach (2%), slightly more in the duodenum (6.3%), and primarily dissolved in the jejunum (63%) and the ileum (25%). The detailed model prediction of drug dissolution in different regions of GI can provide a quantitative reference of in vivo dissolution that may provide valuable insight in developing in vitro tests for drug product optimization and quality.

A mathematical model for IL-6-mediated, stem cell driven tumor growth and targeted treatment.

Targeting key regulators of the cancer stem cell phenotype to overcome their critical influence on tumor growth is a promising new strategy for cancer treatment. Here we present a modeling framework that operates at both the cellular and molecular levels, for investigating IL-6 mediated, cancer stem cell driven tumor growth and targeted treatment with anti-IL6 antibodies. Our immediate goal is to quantify the influence of IL-6 on cancer stem cell self-renewal and survival, and to characterize the subsequent impact on tumor growth dynamics. By including the molecular details of IL-6 binding, we are able to quantify the temporal changes in fractional occupancies of bound receptors and their influence on tumor volume. There is a strong correlation between the model output and experimental data for primary tumor xenografts. We also used the model to predict tumor response to administration of the humanized IL-6R monoclonal antibody, tocilizumab (TCZ), and we found that as little as 1mg/kg of TCZ administered weekly for 7 weeks is sufficient to result in tumor reduction and a sustained deceleration of tumor growth.

Mathematical Modeling of Cellular Cross-Talk Between Endothelial and Tumor Cells Highlights Counterintuitive Effects of VEGF-Targeted Therapies.

Tumor growth and progression are critically dependent on the establishment of a vascular support system. This is often accomplished via the expression of pro-angiogenic growth factors, including members of the vascular endothelial growth factor (VEGF) family of ligands. VEGF ligands are overexpressed in a wide variety of solid tumors and therefore have inspired optimism that inhibition of the different axes of the VEGF pathway-alone or in combination-would represent powerful anti-angiogenic therapies for most cancer types. When considering treatments that target VEGF and its receptors, it is difficult to tease out the differential anti-angiogenic and anti-tumor effects of all combinations experimentally because tumor cells and vascular endothelial cells are engaged in a dynamic cross-talk that impacts key aspects of tumorigenesis, independent of angiogenesis. Here we develop a mathematical model that connects intracellular signaling responsible for both endothelial and tumor cell proliferation and death to population-level cancer growth and angiogenesis. We use this model to investigate the effect of bidirectional communication between endothelial cells and tumor cells on treatments targeting VEGF and its receptors both in vitro and in vivo. Our results underscore the fact that in vitro therapeutic outcomes do not always translate to the in vivo situation. For example, our model predicts that certain therapeutic combinations result in antagonism in vivo that is not observed in vitro. Mathematical modeling in this direction can shed light on the mechanisms behind experimental observations that manipulating VEGF and its receptors is successful in some cases but disappointing in others.

Mechanistic Fluid Transport Model to Estimate Gastrointestinal Fluid Volume and Its Dynamic Change Over Time.

Gastrointestinal (GI) fluid volume and its dynamic change are integral to study drug disintegration, dissolution, transit, and absorption. However, key questions regarding the local volume and its absorption, secretion, and transit remain unanswered. The dynamic fluid compartment absorption and transit (DFCAT) model is proposed to estimate in vivo GI volume and GI fluid transport based on magnetic resonance imaging (MRI) quantified fluid volume. The model was validated using GI local concentration of phenol red in human GI tract, which was directly measured by human GI intubation study after oral dosing of non-absorbable phenol red. The measured local GI concentration of phenol red ranged from 0.05 to 168 µg/mL (stomach), to 563 µg/mL (duodenum), to 202 µg/mL (proximal jejunum), and to 478 µg/mL (distal jejunum). The DFCAT model characterized observed MRI fluid volume and its dynamic changes from 275 to 46.5 mL in stomach (from 0 to 30 min) with mucus layer volume of 40 mL. The volumes of the 30 small intestine compartments were characterized by a max of 14.98 mL to a min of 0.26 mL (0-120 min) and a mucus layer volume of 5 mL per compartment. Regional fluid volumes over 0 to 120 min ranged from 5.6 to 20.38 mL in the proximal small intestine, 36.4 to 44.08 mL in distal small intestine, and from 42 to 64.46 mL in total small intestine. The DFCAT model can be applied to predict drug dissolution and absorption in the human GI tract with future improvements.

Sampling from single-cell observations to predict tumor cell growth in-vitro and in-vivo.

Cancer stem-like cells (CSCs) are a topic of increasing importance in cancer research, but are difficult to study due to their rarity and ability to rapidly divide to produce non-self-cells. We developed a simple model to describe transitions between aldehyde dehydrogenase (ALDH) positive CSCs and ALDH(-) bulk ovarian cancer cells. Microfluidics device-isolated single cell experiments demonstrated that ALDH+ cells were more proliferative than ALDH(-) cells. Based on our model we used ALDH+ and ALDH(-) cell division and proliferation properties to develop an empiric sampling algorithm and predict growth rate and CSC proportion for both ovarian cancer cell line and primary ovarian cancer cells, in-vitro and in-vivo. In both cell line and primary ovarian cancer cells, the algorithm predictions demonstrated a high correlation with observed ovarian cancer cell proliferation and CSC proportion. High correlation was maintained even in the presence of the EGF-like domain multiple 6 (EGFL6), a growth factor which changes ALDH+ cell asymmetric division rates and thereby tumor growth rates. Thus, based on sampling from the heterogeneity of in-vitro cell growth and division characteristics of a few hundred single cells, the simple algorithm described here provides rapid and inexpensive means to generate predictions that correlate with in-vivo tumor growth.