An Introductory Overview of Image-Based Computational Modeling in Personalized Cardiovascular Medicine.

Cardiovascular diseases account for the number one cause of deaths in the world. Part of the reason for such grim statistics is our limited understanding of the underlying mechanisms causing these devastating pathologies, which is made difficult by the invasiveness of the procedures associated with their diagnosis (e.g., inserting catheters into the coronal artery to measure blood flow to the heart). Likewise, it is also difficult to design and test assistive devices without implanting them in vivo. However, with the recent advancements made in biomedical scanning technologies and computer simulations, image-based modeling (IBM) has arisen as the next logical step in the evolution of non-invasive patient-specific cardiovascular medicine. Yet, due to its novelty, it is still relatively unknown outside of the niche field. Therefore, the goal of this manuscript is to review the current state-of-the-art and the limitations of the methods used in this area of research, as well as their applications to personalized cardiovascular investigations and treatments. Specifically, the modeling of three different physics - electrophysiology, biomechanics and hemodynamics - used in the cardiovascular IBM is discussed in the context of the physiology that each one of them describes and the mechanisms of the underlying cardiac diseases that they can provide insight into. Only the "bare-bones" of the modeling approaches are discussed in order to make this introductory material more accessible to an outside observer. Additionally, the imaging methods, the aspects of the unique cardiac anatomy derived from them, and their relation to the modeling algorithms are reviewed. Finally, conclusions are drawn about the future evolution of these methods and their potential toward revolutionizing the non-invasive diagnosis, virtual design of treatments/assistive devices, and increasing our understanding of these lethal cardiovascular diseases.

Is the endothelial cell responsible for the thrombus core and shell architecture?

Ischemia leading to heart attacks and strokes is the major cause of deaths in the world. This report explores the possibility that intracellular material from ruptured endothelial cells is partially responsible for the heterogeneous core-and-shell blood clot architecture, typically observed using intravital microscopy. As evidence, we present a fluid dynamic argument that platelet agonists emanating from the injury cannot activate platelets in the thrombus core, given that they would have to travel against flow of blood escaping into the extravascular. Furthermore, we demonstrate visual evidence that the core material appears to be continuous and originating from the damaged endothelium. Finally, we present a mechanism, illustrating the steps of platelet recruitment into the thrombus and sealing of the injury. If correct, the model presented herein will be beneficial to the understanding and treatment of heart attacks, strokes and hemophilia.

Ranking migration cue contributions to guiding individual fibroblasts faced with a directional decision in simple microfluidic bifurcations.

Directed cell migration in complex micro-environments, such as in vivo pores, is important for predicting locations of artificial tissue growth and optimizing scaffold architectures. Yet, the directional decisions of cells facing multiple physiochemical cues have not been characterized. Hence, we aim to provide a ranking of the relative importance of the following cues to the decision-making of individual fibroblast cells: chemoattractant concentration gradient, channel width, mitosis, and contact-guidance. In this study, bifurcated micro-channels with branches of different widths were created. Fibroblasts were then allowed to travel across these geometries by following a gradient of platelet-derived growth factor-BB (PDGF-BB) established inside the channels. Subsequently, a combination of statistical analysis and image-based diffusion modeling was used to report how the presence of multiple complex migration cues, including cell-cell influences, affect the fibroblast decision-making. It was found that the cells prefer wider channels over a higher chemoattractant gradient when choosing between asymmetric bifurcated branches. Only when the branches were symmetric in width did the gradient become predominant in directing which path the cell will take. Furthermore, when both the gradient and the channels were symmetric, contact guidance became important for guiding the cells in making directional choices. Based on these results we were able to rank these directional cues from most influential to the least as follows: mitosis > channel width asymmetry > chemoattractant gradient difference > and contact-guidance. It is expected that these results will benefit the fields of regenerative medicine, wound healing and developmental biology.

In vivo measurement of blood clot mechanics from computational fluid dynamics based on intravital microscopy images.

Ischemia which leads to heart attacks and strokes is one of the major causes of death in the world. Whether an occlusion occurs or not depends on the ability of a growing thrombus to resist flow forces exerted on its structure. This manuscript provides the first known in vivo measurement of how much stress a clot can withstand, before yielding to the surrounding blood flow. Namely, Lattice-Boltzmann Method flow simulations are performed based on 3D clot geometries, which are estimated from intravital microscopy images of laser-induced injuries in cremaster microvasculature of live mice. In addition to reporting the blood clot yield stresses, we also show that the thrombus "core" does not experience significant deformation, while its "shell" does. This indicates that the shell is more prone to embolization. Therefore, drugs should be designed to target the shell selectively, while leaving the core intact to minimize excessive bleeding. Finally, we laid down a foundation for a nondimensionalization procedure which unraveled a relationship between clot mechanics and biology. Hence, the proposed framework could ultimately lead to a unified theory of thrombogenesis, capable of explaining all clotting events. Thus, the findings presented herein will be beneficial to the understanding and treatment of heart attacks, strokes and hemophilia.

Numerical accuracy comparison of two boundary conditions commonly used to approximate shear stress distributions in tissue engineering scaffolds cultured under flow perfusion.

INTRODUCTION: Flow-induced shear stresses have been found to be a stimulatory factor in pre-osteoblastic cells seeded in 3D porous scaffolds and cultured under continuous flow perfusion. However, due to the complex internal structure of the scaffolds, whole scaffold calculations of the local shear forces are computationally intensive. Instead, representative volume elements (RVEs), which are obtained by extracting smaller portions of the scaffold, are commonly used in literature without a numerical accuracy standard. OBJECTIVE: Hence, the goal of this study is to examine how closely the whole scaffold simulations are approximated by the two types of boundary conditions used to enable the RVEs: "wall boundary condition" (WBC) and "periodic boundary condition" (PBC). METHOD: To that end, lattice Boltzmann method fluid dynamics simulations were used to model the surface shear stresses in 3D scaffold reconstructions, obtained from high-resolution microcomputed tomography images. RESULTS: It was found that despite the RVEs being sufficiently larger than 6 times the scaffold pore size (which is the only accuracy guideline found in literature), the stresses were still significantly under-predicted by both types of boundary conditions: between 20% and 80% average error, depending on the scaffold's porosity. Moreover, it was found that the error grew with higher porosity. This is likely due to the small pores dominating the flow field, and thereby negating the effects of the unrealistic boundary conditions, when the scaffold porosity is small. Finally, it was found that the PBC was always more accurate and computationally efficient than the WBC. Therefore, it is the recommended type of RVE.

Cell Sequence and Mitosis Affect Fibroblast Directional Decision-Making During Chemotaxis in Microfluidic Mazes.

INTRODUCTION: Directed fibroblast migration is central to highly proliferative processes in regenerative medicine and developmental biology. However, the mechanisms by which single fibroblasts affect each other's directional decisions, while chemotaxing in microscopic pores, are not well understood. METHODS: We explored effects of cell sequence and mitosis on fibroblast platelet-derived growth factor-BB (PDGF-BB)-induced migration in microfluidic mazes with two possible through paths: short and long. Additionally, image-based modeling of the chemoattractant's diffusion, consumption and decay, was used to explain the experimental observations. RESULTS: It both cases, the cells displayed behavior that is contradictory to expectation based on the global chemoattractant gradient pre-established in the maze. In case of the sequence, the cells tend to alternate when faced with a bifurcation: if a leading cell takes the shorter (steeper gradient) path, the cell following it chooses the longer (weaker gradient) path, and vice versa. Image-based modeling of the process showed that the local PDGF-BB consumption by the individual fibroblasts may be responsible for this phenomenon. Additionally, it was found that when a mother cell divides, its two daughters go in opposite directions (even if it means migrating against the chemoattractant gradient and overcoming on-going cell traffic). CONCLUSIONS: It is apparent that micro-confined fibroblasts modify each other's directional decisions in a manner that is counter-intuitive to what is expected from classical chemotaxis theory. Consequently, accounting for these effects could lead to a better understanding of tissue generation in vivo, and result in more advanced engineered tissue products in vitro.

Bulk stress distributions in the pore space of sphere-packed beds under Darcy flow conditions.

In this paper, bulk stress distributions in the pore space of columns packed with spheres are numerically computed with lattice Boltzmann simulations. Three different ideally packed and one randomly packed configuration of the columns are considered under Darcy flow conditions. The stress distributions change when the packing type changes. In the Darcy regime, the normalized stress distribution for a particular packing type is independent of the pressure difference that drives the flow and presents a common pattern. The three parameter (3P) log-normal distribution is found to describe the stress distributions in the randomly packed beds within statistical accuracy. In addition, the 3P log-normal distribution is still valid when highly porous scaffold geometries rather than sphere beds are examined. It is also shown that the 3P log-normal distribution can describe the bulk stress distribution in consolidated reservoir rocks like Berea sandstone.

Simulation of intrathrombus fluid and solute transport using in vivo clot structures with single platelet resolution.

The mouse laser injury thrombosis model provides up to 0.22 µm-resolved voxel information about the pore architecture of the dense inner core and loose outer shell regions of an in vivo arterial thrombus. Computational studies were conducted on this 3D structure to quantify transport within and around the clot: Lattice Boltzmann method defined vessel hemodynamics, while passive Lagrangian Scalar Tracking with Brownian motion contribution simulated diffusive-convective transport of various inert solutes (released from lumen or the injured wall). For an input average lumen blood velocity of 0.478 cm/s (measured by Doppler velocimetry), a 0.2 mm/s mean flow rate was obtained within the thrombus structure, most of which occurred in the 100-fold more permeable outer shell region (calculated permeability of the inner core was 10(-11) cm(2)). Average wall shear stresses were 80-100 dyne/cm(2) (peak values >200 dyne/cm(2)) on the outer rough surface of the thrombus. Within the thrombus, small molecule tracers (0.1 kDa) experienced ~70,000 collisions/s and penetrated/exited it in about 1 s, whereas proteins (~50 kDa) had ~9000 collisions/s and required about 10 s (tortuosity ~2-2.5). These simulations help define physical processes during thrombosis and constraints for drug delivery to the thrombus.

3D tissue-engineered construct analysis via conventional high-resolution microcomputed tomography without X-ray contrast.

As the field of tissue engineering develops, researchers are faced with a large number of degrees of freedom regarding the choice of material, architecture, seeding, and culturing. To evaluate the effectiveness of a tissue-engineered strategy, histology is typically done by physically slicing and staining a construct (crude, time-consuming, and unreliable). However, due to recent advances in high-resolution biomedical imaging, microcomputed tomography (µCT) has arisen as a quick and effective way to evaluate samples, while preserving their structure in the original state. However, a major barrier for using µCT to do histology has been its inability to differentiate between materials with similar X-ray attenuation. Various contrasting strategies (hardware and chemical staining agents) have been proposed to address this problem, but at a cost of additional complexity and limited access. Instead, here we suggest a strategy for how virtual 3D histology in silico can be conducted using conventional µCT, and we provide an illustrative example from bone tissue engineering. The key to our methodology is an implementation of scaffold surface architecture that is ordered in relation to cells and tissue, in concert with straightforward image-processing techniques, to minimize the reliance on contrasting for material segmentation. In the case study reported, µCT was used to image and segment porous poly(lactic acid) nonwoven fiber mesh scaffolds that were seeded dynamically with mesenchymal stem cells and cultured to produce soft tissue and mineralized tissue in a flow perfusion bioreactor using an osteogenic medium. The methodology presented herein paves a new way for tissue engineers to identify and distinguish components of cell/tissue/scaffold constructs to easily and effectively evaluate the tissue-engineering strategies that generate them.

Predicting the stress distribution within scaffolds with ordered architecture.

Current tissue engineering technologies involve the seeding of cells on porous scaffolds, within which the cells can proliferate and differentiate, when cultured in bioreactors. The flow of culture media through the scaffolds generates stresses that are important for both cell differentiation and cell growth. A recent study [Appl. Phys. Lett. 97 (2010), 024101] showed that flow-induced stresses inside highly porous and randomly structured scaffolds follow a three-point gamma probability density function (p.d.f.). The goal of the present study is to further investigate whether the same p.d.f. can also describe the distribution of stresses in structured porous scaffolds, what is the range of scaffold porosity for which the distribution is valid, and what is the physical reason for such behavior. To do that, the p.d.f. of flow-induced stresses in different scaffold geometries were calculated via flow dynamics simulations. It was found that the direction of flow relative to the internal architecture of the scaffolds is important for stress distributions. The stress distributions follow a common distribution within statistically acceptable accuracy, when the flow direction does not coincide with the direction of internal structural elements of the scaffold.

Boundary slip and wetting properties of interfaces: correlation of the contact angle with the slip length.

Correlations between contact angle, a measure of the wetting of surfaces, and slip length are developed using nonequilibrium molecular dynamics for a Lennard-Jones fluid in Couette flow between graphitelike hexagonal-lattice walls. The fluid-wall interaction is varied by modulating the interfacial energy parameter epsilonr=epsilonsfepsilonff and the size parameter sigmar=sigmasfsigmaff, (s=solid, f=fluid) to achieve hydrophobicity (solvophobicity) or hydrophilicity (solvophilicity). The effects of surface chemistry, as well as the effects of temperature and shear rate on the slip length are determined. The contact angle increases from 25 degrees to 147 degrees on highly hydrophobic surfaces (as epsilonr decreases from 0.5 to 0.1), as expected. The slip length is functionally dependent on the affinity strength parameters epsilonr and sigmar: increasing logarithmically with decreasing surface energy epsilonr (i.e., more hydrophobic), while decreasing with power law with decreasing size sigmar. The mechanism for the latter is different from the energetic case. While weak wall forces (small epsilonr) produce hydrophobicity, larger sigmar smoothes out the surface roughness. Both tend to increase the slip. The slip length grows rapidly with a high shear rate, as wall velocity increases three decades from 100 to 10(5) ms. We demonstrate that fluid-solid interfaces with low epsilonr and high sigmar should be chosen to increase slip and are prime candidates for drag reduction.