Numerical simulation of a compound capsule in a constricted microchannel

Investigating the Influence of Heterogeneity Within Cell Types on Microvessel Network Transport

Background

Current research on the biophysics of circulating tumor cells often overlooks the heterogeneity of cell populations, focusing instead on average cellular properties. This study aims to address the gap by considering the diversity of cell biophysical characteristics and their implications on cancer spread.

Methods

We utilized computer simulations to assess the influence of variations in cell size and membrane elasticity on the behavior of cells within fluid environments. The study controlled cell and fluid properties to systematically investigate the transport of tumor cells through a simulated network of branching channels.

Results

The simulations revealed that even minor differences in cellular properties, such as slight changes in cell radius or shear elastic modulus, lead to significant changes in the fluid conditions that cells experience, including velocity and wall shear stress (p < 0.001).

Conclusion

The findings underscore the importance of considering cell heterogeneity in biophysical studies and suggest that small variations in cellular characteristics can profoundly impact the dynamics of tumor cell circulation. This has potential implications for understanding the mechanisms of cancer metastasis and the development of therapeutic strategies.

Enhancing Adaptive Physics Refinement Simulations Through the Addition of Realistic Red Blood Cell Counts

Simulations of cancer cell transport require accurately modeling mm-scale and longer trajectories through a circulatory system containing trillions of deformable red blood cells, whose intercellular interactions require submicron fidelity. Using a hybrid CPU-GPU approach, we extend the advanced physics refinement (APR) method to couple a finely-resolved region of explicitly-modeled red blood cells to a coarsely-resolved bulk fluid domain. We further develop algorithms that: capture the dynamics at the interface of differing viscosities, maintain hematocrit within the cell-filled volume, and move the finely-resolved region and encapsulated cells while tracking an individual cancer cell. Comparison to a fully-resolved fluid-structure interaction model is presented for verification. Finally, we use the advanced APR method to simulate cancer cell transport over a mm-scale distance while maintaining a local region of RBCs, using a fraction of the computational power required to run a fully-resolved model.

Distributed Acceleration of Adhesive Dynamics Simulations

Cell adhesion plays a critical role in processes ranging from leukocyte migration to cancer cell transport during metastasis. Adhesive cell interactions can occur over large distances in microvessel networks with cells traveling over distances much greater than the length scale of their own diameter. Therefore, biologically relevant investigations necessitate efficient modeling of large field-of-view domains, but current models are limited by simulating such geometries at the sub-micron scale required to model adhesive interactions which greatly increases the computational requirements for even small domain sizes. In this study we introduce a hybrid scheme reliant on both on-node and distributed parallelism to accelerate a fully deformable adhesive dynamics cell model. This scheme leads to performant system usage of modern supercomputers which use a many-core per-node architecture. On-node acceleration is augmented by a combination of spatial data structures and algorithmic changes to lessen the need for atomic operations. This deformable adhesive cell model accelerated with hybrid parallelization allows us to bridge the gap between high-resolution cell models which can capture the sub-micron adhesive interactions between the cell and its microenvironment, and large-scale fluid-structure interaction (FSI) models which can track cells over considerable distances. By integrating the sub-micron simulation environment into a distributed FSI simulation we enable the study of previously unfeasible research questions involving numerous adhesive cells in microvessel networks such as cancer cell transport through the microcirculation.

High Performance Adaptive Physics Refinement to Enable Large-Scale Tracking of Cancer Cell Trajectory

The ability to track simulated cancer cells through the circulatory system, important for developing a mechanistic understanding of metastatic spread, pushes the limits of today's supercomputers by requiring the simulation of large fluid volumes at cellular-scale resolution. To overcome this challenge, we introduce a new adaptive physics refinement (APR) method that captures cellular-scale interaction across large domains and leverages a hybrid CPU-GPU approach to maximize performance. Through algorithmic advances that integrate multi-physics and multi-resolution models, we establish a finely resolved window with explicitly modeled cells coupled to a coarsely resolved bulk fluid domain. In this work we present multiple validations of the APR framework by comparing against fully resolved fluid-structure interaction methods and employ techniques, such as latency hiding and maximizing memory bandwidth, to effectively utilize heterogeneous node architectures. Collectively, these computational developments and performance optimizations provide a robust and scalable framework to enable system-level simulations of cancer cell transport.

The role of adhesive receptor patterns on cell transport in complex microvessels

Cell transport is governed by the interaction of fluid dynamic forces and biochemical factors such as adhesion receptor expression and concentration. Although the effect of endothelial receptor density is well understood, it is not clear how the spacing and local spatial distribution of receptors affect cell adhesion in three-dimensional microvessels. To elucidate the effect of vessel shape on cell trajectory and the arrangement of endothelial receptors on cell adhesion, we employed a three-dimensional deformable cell model that incorporates microscale interactions between the cell and the endothelium. Computational cellular adhesion models are systematically altered to assess the influence of receptor spacing. We demonstrate that the patterns of receptors on the vessel walls are a key factor guiding cell movement. In straight microvessels, we show a relationship between cell velocity and the spatial distribution of adhesive endothelial receptors, with larger receptor patches producing lower translational velocities. The joint effect of the complex vessel topology seen in microvessel shapes such as curved and bifurcated vessels when compared to straight tubes is explored with results which showed the spatial distribution of receptors affecting cell trajectory. Our findings here represent demonstration of the previously undescribed relationship between receptor pattern and geometry that guides cellular movement in complex microenvironments.

A data-driven approach to modeling cancer cell mechanics during microcirculatory transport

In order to understand the effect of cellular level features on the transport of circulating cancer cells in the microcirculation, there has been an increasing reliance on high-resolution in silico models. Accurate simulation of cancer cells flowing with blood cells requires resolving cellular-scale interactions in 3D, which is a significant computational undertaking warranting a cancer cell model that is both computationally efficient yet sufficiently complex to capture relevant behavior. Given that the characteristics of metastatic spread are known to depend on cancer type, it is crucial to account for mechanistic behavior representative of a specific cancer's cells. To address this gap, in the present work we develop and validate a means by which an efficient and popular membrane model-based approach can be used to simulate deformable cancer cells and reproduce experimental data from specific cell lines. Here, cells are modeled using the immersed boundary method (IBM) within a lattice Boltzmann method (LBM) fluid solver, and the finite element method (FEM) is used to model cell membrane resistance to deformation. Through detailed comparisons with experiments, we (i) validate this model to represent cancer cells undergoing large deformation, (ii) outline a systematic approach to parameterize different cell lines to optimally fit experimental data over a range of deformations, and (iii) provide new insight into nucleated vs. non-nucleated cell models and their ability to match experiments. While many works have used the membrane-model based method employed here to model generic cancer cells, no quantitative comparisons with experiments exist in the literature for specific cell lines undergoing large deformation. Here, we describe a phenomenological, data-driven approach that can not only yield good agreement for large deformations, but explicitly detail how it can be used to represent different cancer cell lines. This model is readily incorporated into cell-resolved hemodynamic transport simulations, and thus offers significant potential to complement experiments towards providing new insights into various aspects of cancer progression.

Numerical simulation of intracellular drug delivery via rapid squeezing

Intracellular drug delivery by rapid squeezing is one of the most recent and simple cell membrane disruption-mediated drug encapsulation approaches. In this method, cell membranes are perforated in a microfluidic setup due to rapid cell deformation during squeezing through constricted channels. While squeezing-based drug loading has been successful in loading drug molecules into various cell types, such as immune cells, cancer cells, and other primary cells, there is so far no comprehensive understanding of the pore opening mechanism on the cell membrane and the systematic analysis on how different channel geometries and squeezing speed influence drug loading. This article aims to develop a three-dimensional computational model to study the intracellular delivery for compound cells squeezing through microfluidic channels. The Lattice Boltzmann method, as the flow solver, integrated with a spring-connected network via frictional coupling, is employed to capture compound capsule dynamics over fast squeezing. The pore size is proportional to the local areal strain of triangular patches on the compound cell through mathematical correlations derived from molecular dynamics and coarse-grained molecular dynamics simulations. We quantify the drug concentration inside the cell cytoplasm by introducing a new mathematical model for passive diffusion after squeezing. Compared to the existing models, the proposed model does not have any empirical parameters that depend on operating conditions and device geometry. Since the compound cell model is new, it is validated by simulating a nucleated cell under a simple shear flow at different capillary numbers and comparing the results with other numerical models reported in literature. The cell deformation during squeezing is also compared with the pattern found from our compound cell squeezing experiment. Afterward, compound cell squeezing is modeled for different cell squeezing velocities, constriction lengths, and constriction widths. We reported the instantaneous cell center velocity, variations of axial and vertical cell dimensions, cell porosity, and normalized drug concentration to shed light on the underlying physics in fast squeezing-based drug delivery. Consistent with experimental findings in the literature, the numerical results confirm that constriction width reduction, constriction length enlargement, and average cell velocity promote intracellular drug delivery. The results show that the existence of the nucleus increases cell porosity and loaded drug concentration after squeezing. Given geometrical parameters and cell average velocity, the maximum porosity is achieved at three different locations: constriction entrance, constriction middle part, and outside the constriction. Our numerical results provide reasonable justifications for experimental findings on the influences of constriction geometry and cell velocity on the performance of cell-squeezing delivery. We expect this model can help design and optimize squeezing-based cargo delivery.

Computational models of cancer cell transport through the microcirculation

The transport of cancerous cells through the microcirculation during metastatic spread encompasses several interdependent steps that are not fully understood. Computational models which resolve the cellular-scale dynamics of complex microcirculatory flows offer considerable potential to yield needed insights into the spread of cancer as a result of the level of detail that can be captured. In recent years, in silico methods have been developed that can accurately and efficiently model the circulatory flows of cancer and other biological cells. These computational methods are capable of resolving detailed fluid flow fields which transport cells through tortuous physiological geometries, as well as the deformation and interactions between cells, cell-to-endothelium interactions, and tumor cell aggregates, all of which play important roles in metastatic spread. Such models can provide a powerful complement to experimental works, and a promising approach to recapitulating the endogenous setting while maintaining control over parameters such as shear rate, cell deformability, and the strength of adhesive binding to better understand tumor cell transport. In this review, we present an overview of computational models that have been developed for modeling cancer cells in the microcirculation, including insights they have provided into cell transport phenomena.

Investigating the Interaction Between Circulating Tumor Cells and Local Hydrodynamics via Experiment and Simulations

Introduction

The biological and mechanical properties of circulating tumor cells (CTCs) in combination with the hemodynamics affect the preference of metastatic sites in the vasculature. Despite the extensive literature on the effects of biological properties on cell adhesion, the effects of hydrodynamic forces on primary attachment remains an active area of research. Using simulations in conjunction with experimentation, we provide new insight into the interplay of CTCs dynamics and local hydrodynamics.

Methods

A flow experiment of CTC attachment was performed within a bioprinted, double branching endothelialized vessel. Simulations of fluid flow and CTC transport in the reconstructed and idealized bifurcated vessel were respectively performed by HARVEY, our in-house massively parallel computational fluid dynamics solver. HARVEY is based on the lattice Boltzmann and finite element methods to model the fluid and cells dynamics. The immersed boundary method is employed for resolving the fluid-structure interaction.

Results

CTC attachment was quantified experimentally at all regions of the complex vessel. The results demonstrate a clear preference for CTCs to attach at the branch points. To elucidate the effect of the vessel topology on the location of attachment, a fluid-only simulation was performed assessing the differences in the hydrodynamics along the vessel. CTC transport in idealized bifurcated vessels was subsequently studied to examine the effects of cell deformability on the local hydrodynamics patterns and, thus, the preference of attachment sites.

Conclusions

The current work provides evidence on the correlation of the hydrodynamics forces arising from the vessel topology and CTC properties on the attachment regions.

Multi-GPU Immersed Boundary Method Hemodynamics Simulations

Large-scale simulations of blood flow that resolve the 3D deformation of each comprising cell are increasingly popular owing to algorithmic developments in conjunction with advances in compute capability. Among different approaches for modeling cell-resolved hemodynamics, fluid structure interaction (FSI) algorithms based on the immersed boundary method are frequently employed for coupling separate solvers for the background fluid and the cells within one framework. GPUs can accelerate these simulations; however, both current pre-exascale and future exascale CPU-GPU heterogeneous systems face communication challenges critical to performance and scalability. We describe, to our knowledge, the largest distributed GPU-accelerated FSI simulations of high hematocrit cell-resolved flows with over 17 million red blood cells. We compare scaling on a fat node system with six GPUs per node and on a system with a single GPU per node. Through comparison between the CPU- and GPU-based implementations, we identify the costs of data movement in multiscale multi-grid FSI simulations on heterogeneous systems and show it to be the greatest performance bottleneck on the GPU.

Localization of Rolling and Firm-Adhesive Interactions Between Circulating Tumor Cells and the Microvasculature Wall

INTRODUCTION

The adhesion of tumor cells to vessel wall is a critical stage in cancer metastasis. Firm adhesion of cancer cells is usually followed by their extravasation through the endothelium. Despite previous studies identifying the influential parameters in the adhesive behavior of the cancer cell to a planer substrate, less is known about the interactions between the cancer cell and microvasculature wall and whether these interactions exhibit organ specificity. The objective of our study is to characterize sizes of microvasculature where a deformable circulating cell (DCC) would firmly adhere or roll over the wall, as well as to identify parameters that facilitate such firm adherence and underlying mechanisms driving adhesive interactions.

METHODS

A three-dimensional model of DCCs is applied to simulate the fluid-structure interaction between the DCC and surrounding fluid. A dynamic adhesion model, where an adhesion molecule is modeled as a spring, is employed to represent the stochastic receptor-ligand interactions using kinetic rate expressions.

RESULTS

Our results reveal that both the cell deformability and low shear rate of flow promote the firm adhesion of DCC in small vessels ( < 10 μ m ). Our findings suggest that ligand-receptor bonds of PSGL-1-P-selectin may lead to firm adherence of DCC in smaller vessels and rolling-adhesion of DCC in larger ones where cell velocity drops to facilitate the activation of integrin-ICAM-1 bonds.

CONCLUSIONS

Our study provides a framework to predict accurately where different DCC-types are likely to adhere firmly in microvasculature and to establish the criteria predisposing cancer cells to such firm adhesion.

Multivascular networks and functional intravascular topologies within biocompatible hydrogels

Solid organs transport fluids through distinct vascular networks that are biophysically and biochemically entangled, creating complex three-dimensional (3D) transport regimes that have remained difficult to produce and study. We establish intravascular and multivascular design freedoms with photopolymerizable hydrogels by using food dye additives as biocompatible yet potent photoabsorbers for projection stereolithography. We demonstrate monolithic transparent hydrogels, produced in minutes, comprising efficient intravascular 3D fluid mixers and functional bicuspid valves. We further elaborate entangled vascular networks from space-filling mathematical topologies and explore the oxygenation and flow of human red blood cells during tidal ventilation and distension of a proximate airway. In addition, we deploy structured biodegradable hydrogel carriers in a rodent model of chronic liver injury to highlight the potential translational utility of this materials innovation.

Suitability of lattice Boltzmann inlet and outlet boundary conditions for simulating flow in image-derived vasculature

The lattice Boltzmann method (LBM) is a popular alternative to solving the Navier-Stokes equations for modeling blood flow. When simulating flow using the LBM, several choices for inlet and outlet boundary conditions exist. While boundary conditions in the LBM have been evaluated in idealized geometries, there have been no extensive comparisons in image-derived vasculature, where the geometries are highly complex. In this study, the Zou-He (ZH) and finite difference (FD) boundary conditions were evaluated in image-derived vascular geometries by comparing their stability, accuracy, and run times. The boundary conditions were compared in four arteries: a coarctation of the aorta, dissected aorta, femoral artery, and left coronary artery. The FD boundary condition was more stable than ZH in all four geometries. In general, simulations using the ZH and FD method showed similar convergence rates within each geometry. However, the ZH method proved to be slightly more accurate compared with experimental flow using three-dimensional printed vasculature. The total run times necessary for simulations using the ZH boundary condition were significantly higher as the ZH method required a larger relaxation time, grid resolution, and number of time steps for a simulation representing the same physiological time. Finally, a new inlet velocity profile algorithm is presented for complex inlet geometries. Overall, results indicated that the FD method should generally be used for large-scale blood flow simulations in image-derived vasculature geometries. This study can serve as a guide to researchers interested in using the LBM to simulate blood flow.

Role of deformable cancer cells on wall shear stress-associated-VEGF secretion by endothelium in microvasculature

Endothelial surface layer (glycocalyx) is the major physiological regulator of tumor cell adhesion to endothelium. Cancer cells express vascular endothelial growth factor (VEGF) which increases the permeability of a microvessel wall by degrading glycocalyx. Endothelial cells lining large arteries have also been reported, in vitro and in vivo, to mediate VEGF expression significantly under exposure to high wall shear stress (WSS) > 0.6 Pa. The objective of the present study is to explore whether local hemodynamic conditions in the vicinity of a migrating deformable cancer cell can influence the function of endothelial cells to express VEGF within the microvasculature. A three-dimensional model of deformable cancer cells (DCCs) migrating within a capillary is developed by applying a massively parallel hemodynamics application to simulate the fluid-structure interaction between the DCC and fluid surrounding the DCC. We study how dynamic interactions between the DCC and its local microenvironment affect WSS exposed on endothelium, under physiological conditions of capillaries with different diameters and flow conditions. Moreover, we quantify the area of endothelium affected by the DCC. Our results show that the DCC alters local hemodynamics in its vicinity up to an area as large as 40 times the cancer cell lateral surface. In this area, endothelium experiences high WSS values in the range of 0.6–12 Pa. Endothelial cells exposed to this range of WSS have been reported to express VEGF. Furthermore, we demonstrate that stiffer cancer cells expose higher WSS on the endothelium. A strong impact of cell stiffness on its local microenvironment is observed in capillaries with diameters <16 μm. WSS-induced-VEGF by endothelium represents an important potential mechanism for cancer cell adhesion and metastasis in the microvasculature. This work serves as an important first step in understanding the mechanisms driving VEGF-expression by endothelium and identifying the underlying mechanisms of glycocalyx degradation by endothelium in microvasculature. The identification of angiogenesis factors involved in early stages of cancer cell-endothelium interactions and understanding their regulation will help, first to develop anti-angiogenic strategies applied to diagnostic studies and therapeutic interventions, second to predict accurately where different cancer cell types most likely adhere in microvasculature, and third to establish accurate criteria predisposing the cancer metastasis.

Off-center motion of a trapped elastic capsule in a microfluidic channel with a narrow constriction

Owing to their significance in capsule-related engineering and biomedical applications, a number of studies have considered the dynamics of elastic capsules flowing in constricted microchannels. However, these studies have focused on capsules moving along the channel centerline. In the present study, we numerically investigate the transient motion of an elastic capsule in a microfluidic channel with a rectangular constriction, which is initially trapped at the constriction inlet while off the channel centerline (i.e., on the channel bottom-wall). Under the push of the surrounding flow, the capsule can squeeze into the constriction, but only if the capsule deformability or the constriction size is sufficiently large. We find that the critical capillary number leading to the penetration of the capsule into the constriction is larger for off-centerline capsules compared to centered capsules. The centered capsule is stationary at the steady state when it remains stuck at the constriction; in contrast, the off-centerline capsule is not stationary but exhibits a tank-treading motion, i.e., its overall shape maintains a nonspherical shape with a protrusion into the constriction while its membrane exhibits a continuous rotation. Further, we examine the dependence of the capsule motion type, capsule deformation degree and membrane tension distribution on the capillary number (measuring the effects of flow strength and membrane mechanics) and constriction geometries (including the constriction height and width). Finally, we discuss the mechanism governing the capsule motion by analyzing the hydrodynamic forces acting on the capsule. The shear force acting on the capsule top owing to the fluid flow in the gap between the capsule top and the channel top-wall is the main source inducing the membrane tank-treading rotation.