Simulations of chemotaxis and random motility in 2D random porous domains

A Rheological Study on the Effect of Tethering Pro- and Anti-Inflammatory Cytokines into Hydrogels on Human Mesenchymal Stem Cell Migration, Degradation, and Morphology

Polymer-peptide hydrogels are being designed as implantable materials that deliver human mesenchymal stem cells (hMSCs) to treat wounds. Most wounds can progress through the healing process without intervention. During the normal healing process, cytokines are released from the wound to create a concentration gradient, which causes directed cell migration from the native niche to the wound site. Our work takes inspiration from this process and uniformly tethers cytokines into the scaffold to measure changes in cell-mediated degradation and motility. This is the first step in designing cytokine concentration gradients into the material to direct cell migration. We measure changes in rheological properties, encapsulated cell-mediated pericellular degradation and migration in a hydrogel scaffold with covalently tethered cytokines, either tumor necrosis factor-α (TNF-α) or transforming growth factor-β (TGF-β). TNF-α is expressed in early stages of wound healing causing an inflammatory response. TGF-β is released in later stages of wound healing causing an anti-inflammatory response in the surrounding tissue. Both cytokines cause directed cell migration. We measure no statistically significant difference in modulus or the critical relaxation exponent when tethering either cytokine in the polymeric network without encapsulated hMSCs. This indicates that the scaffold structure and rheology is unchanged by the addition of tethered cytokines. Increases in hMSC motility, morphology and cell-mediated degradation are measured using a combination of multiple particle tracking microrheology (MPT) and live-cell imaging in hydrogels with tethered cytokines. We measure that tethering TNF-α into the hydrogel increases cellular remodeling on earlier days postencapsulation and tethering TGF-β into the scaffold increases cellular remodeling on later days. We measure tethering either TGF-β or TNF-α enhances cell stretching and, subsequently, migration. This work provides rheological characterization that can be used to design new materials that present chemical cues in the pericellular region to direct cell migration.

A multiple-relaxation-time lattice-boltzmann model for bacterial chemotaxis: effects of initial concentration, diffusion, and hydrodynamic dispersion on traveling bacterial bands

Bacterial chemotaxis can enhance the bioremediation of contaminants in aqueous and subsurface environments if the contaminant is a chemoattractant that the bacteria degrade. The process can be promoted by traveling bands of chemotactic bacteria that form due to metabolism-generated gradients in chemoattractant concentration. We developed a multiple-relaxation-time (MRT) lattice-Boltzmann method (LBM) to model chemotaxis, because LBMs are well suited to model reactive transport in the complex geometries that are typical for subsurface porous media. This MRT-LBM can attain a better numerical stability than its corresponding single-relaxation-time LBM. We performed simulations to investigate the effects of substrate diffusion, initial bacterial concentration, and hydrodynamic dispersion on the formation, shape, and propagation of bacterial bands. Band formation requires a sufficiently high initial number of bacteria and a small substrate diffusion coefficient. Uniform flow does not affect the bands while shear flow does. Bacterial bands can move both upstream and downstream when the flow velocity is small. However, the bands disappear once the velocity becomes too large due to hydrodynamic dispersion. Generally bands can only be observed if the dimensionless ratio between the chemotactic sensitivity coefficient and the effective diffusion coefficient of the bacteria exceeds a critical value, that is, when the biased movement due to chemotaxis overcomes the diffusion-like movement due to the random motility and hydrodynamic dispersion.

Multiscale models of angiogenesis

Vascular disease, cancer, stroke, neurodegeneration, diabetes, inflammation, asthma, obesity, arthritis--the list of conditions that involve angiogenesis reads like main chapters in a book on pathology. Angiogenesis, the growth of capillaries from preexisting vessels, also occurs in normal physiology, in response to exercise or in the process of wound healing.Why and when is angiogenesis prevalent? What controls the process? How can we intelligently control it? These are the key questions driving researchers in fields as diverse as cell biology, oncology, cardiology, neurology, biomathematics, systems biology, and biomedical engineering. As bioengineers, we approach angiogenesis as a complex, interconnected system of events occurring in sequence and in parallel, on multiple levels, triggered by a main stimulus, e.g., hypoxia.

Cell population-based model of dermal wound invasion with heterogeneous intracellular signaling properties

A deterministic model of dermal wound invasion, which accounts for the platelet-derived growth factor (PDGF) gradient sensing mechanism in fibroblasts mediated by cell surface receptors and the phosphoinositide 3-kinase (PI3K) signal transduction pathway, was previously described (Biophys J 2006; 90:2297-308). Here, we extend that work and implement a hybrid modeling strategy that treats fibroblasts as discrete entities endowed with heterogeneous properties, namely receptor, PI3K and 3' phosphoinositide phosphatase expression levels. Analysis of the model suggests that the wound environment fosters the advancement of cells within the population that are better fit to migrate and/or proliferate in response to PDGF stimulation. Thus, cell-to-cell variability results in a significantly higher rate of wound invasion as compared with the deterministic model, in a manner that depends on the way in which individual cell properties are sampled or inherited upon cell division.

Strategies to enhance capillary formation inside biomaterials: a computational study

Control over angiogenesis (formation of new capillaries from preexisting vessels) is often a crucial requirement for implantable porous biomaterials serving as scaffolds for tissue regeneration. Angiogenesis is influenced by the transport of chemoattractants such as vascular endothelial growth factor (VEGF) through the implant. To investigate this influence, we developed a computational model of capillary formation based on endothelial cell migration by modeling the random motion of sprout tips biased along spatially and temporally evolving concentration gradients of VEGF. The model focuses on the effect of diffusive VEGF transport inside a 2D domain on the directed migration of sprouts to test several chemical and physical strategies to stimulate and control angiogenesis. We considered a 2D porous membrane that is located between the primary vessel and a line source of VEGF. We assess the vascular network formed in 2 cases of a high and zero VEGF degradation rates applying 3 strategies of VEGF production: (1) only a line source; (2) a line source plus controlled release from a small number of VEGF sources that are randomly dispersed on the pore boundaries; and (3) a line source plus controlled release of VEGF from the pore boundaries themselves. Results show that in the limiting cases where VEGF degradation rate is relatively high, strategies 2 and 3 lead to a substantial increase in the number of vessels. This increase depends on the relative rates at which the line source and embedded sources or solid boundaries produce VEGF. Using strategy 2 results in a newly formed capillary network that is highly localized around the embedded sources. However, using strategy 3 leads to a more uniformly distributed vessel network and a higher degree of vessel ingrowth inside the porous membrane. In addition, the duration at which we engineer the embedded sources or pore boundaries to release VEGF determines the morphology of the capillary network. Although a higher release duration leads to a dense network of newly formed vessels near the primary vessel, it hinders further vessel penetration inside the porous membrane. Therefore, in applying both strategies 2 and 3, there is an optimum release duration that leads to a deeper penetration of vessels inside the membrane. It is hoped that insights from this study will aid in the design of materials with optimal structural and chemical properties to facilitate controlled angiogenesis.