Two-Phase Acto-Cytosolic Fluid Flow in a Moving Keratocyte: A 2D Continuum Model

Simulation of a Free Boundary Cell Migration Model through Physics Informed Neural Networks

Understanding the complexities of single-cell migration is facilitated by computational modeling, which provides important insights into the physiological processes that underlie migration mechanisms. This study developed a computational model for one-dimensional actomyosin flow in a migrating cell with moving boundaries. The model incorporates the complex interplay of actin polymerization, substrate adhesion, and actomyosin dynamics through a system of coupled nonlinear partial differential equations. A physics-informed neural network is designed to understand the dynamic behavior of actin flow and actin concentration within the cell along with the unknown moving boundaries, taking into account the computational cost of solving a dynamic model with a deformable domain. The model's capacity to depict the complex interaction between biological and physical processes within the cell is demonstrated by the numerical results, which qualitatively agree with experimental and computational data available in the literature. This study demonstrates the application of a deep learning method to simulate a challenging biophysical problem with moving boundaries. The model does not require synthetic data for training and accurately reflects the intricate biophysics of cell migration.

Computational simulations of tumor growth and treatment response: Benefits of high-frequency, low-dose drug regimens and concurrent vascular normalization

Implementation of effective cancer treatment strategies requires consideration of how the spatiotemporal heterogeneities within the tumor microenvironment (TME) influence tumor progression and treatment response. Here, we developed a multi-scale three-dimensional mathematical model of the TME to simulate tumor growth and angiogenesis and then employed the model to evaluate an array of single and combination therapy approaches. Treatments included maximum tolerated dose or metronomic (i.e., frequent low doses) scheduling of anti-cancer drugs combined with anti-angiogenic therapy. The results show that metronomic therapy normalizes the tumor vasculature to improve drug delivery, modulates cancer metabolism, decreases interstitial fluid pressure and decreases cancer cell invasion. Further, we find that combining an anti-cancer drug with anti-angiogenic treatment enhances tumor killing and reduces drug accumulation in normal tissues. We also show that combined anti-angiogenic and anti-cancer drugs can decrease cancer invasiveness and normalize the cancer metabolic microenvironment leading to reduced hypoxia and hypoglycemia. Our model simulations suggest that vessel normalization combined with metronomic cytotoxic therapy has beneficial effects by enhancing tumor killing and limiting normal tissue toxicity.

Investigation of cancer response to chemotherapy: a hybrid multi-scale mathematical and computational model of the tumor microenvironment

Tumor microenvironment (TME) is a multi-scale biological environment that can control tumor dynamics with many biomechanical and biochemical factors. Investigating the physiology of TME with a heterogeneous structure and abnormal functions not only can achieve a deeper understanding of tumor behavior but also can help develop more efficient anti-cancer strategies. In this work, we develop a hybrid multi-scale mathematical model of TME to simulate the progression of a three-dimensional tumor and elucidate its response to different chemotherapy approaches. The chemotherapy approaches include multiple low dose (MLD) of anti-cancer drug, maximum tolerated dose (MTD) of anti-cancer drug, combination therapy of MLD and anti-angiogenic drug, and combination therapy of MTD and anti-angiogenic drug. The results show that combining anti-angiogenic agent with anti-cancer drug increases the performance of cancer treatment and decreases side effects for normal tissue. Indeed, the vascular normalization caused by anti-angiogenic therapy improves anti-cancer drug delivery for both MLD and MTD approaches. The results show that anti-cancer drug administered in a lower dose than the maximum tolerated dose repetitively over a long period treats cancer with a considerable performance and fewer side effects. We also show that tumor morphology and distribution of cancer cell phenotypes can be considered as the characteristics to distinguish different chemotherapy approaches. This robust model can be applied to predict the behavior of any type of cancer and quantify cancer response to different chemotherapy approaches. The computational results of cancer response to chemotherapy are in good agreement with experimental measurements.

A multi-scale model for determining the effects of pathophysiology and metabolic disorders on tumor growth

The search for efficient chemotherapy drugs and other anti-cancer treatments would benefit from a deeper understanding of the tumor microenvironment (TME) and its role in tumor progression. Because in vivo experimental methods are unable to isolate or control individual factors of the TME and in vitro models often do not include all the contributing factors, some questions are best addressed with systems biology mathematical models. In this work, we present a new fully-coupled, agent-based, multi-scale mathematical model of tumor growth, angiogenesis and metabolism that includes important aspects of the TME spanning subcellular-, cellular- and tissue-level scales. The mathematical model is computationally implemented for a three-dimensional TME, and a double hybrid continuous-discrete (DHCD) method is applied to solve the governing equations. The model recapitulates the distinct morphological and metabolic stages of a solid tumor, starting with an avascular tumor and progressing through angiogenesis and vascularized tumor growth. To examine the robustness of the model, we simulated normal and abnormal blood conditions, including hyperglycemia/hypoglycemia, hyperoxemia/hypoxemia, and hypercarbia/hypocarbia - conditions common in cancer patients. The results demonstrate that tumor progression is accelerated by hyperoxemia, hyperglycemia and hypercarbia but inhibited by hypoxemia and hypoglycemia; hypocarbia had no appreciable effect. Because of the importance of interstitial fluid flow in tumor physiology, we also examined the effects of hypo- or hypertension, and the impact of decreased hydraulic conductivity common in desmoplastic tumors. The simulations show that chemotherapy-increased blood pressure, or reduction of interstitial hydraulic conductivity increase tumor growth rate and contribute to tumor malignancy.