Numerical study of the effect of vascular bed on heat transfer during high intensity focused ultrasound (HIFU) ablation of the liver tumor.

In this study, the influence of vascular bed comprising terminal arterial branches on heat transfer in a liver tumor exposed to high intensity focused ultrasound (HIFU) is studied numerically. Also, the effect of vascular density on temperature distribution is investigated. A coupled set of acoustics, thermal, and fluid models is used to calculate the temperature distribution in the liver. The numerical model is established based on the Westervelt and bioheat equations along with the Navier-Stokes equations. Moreover, the acoustic streaming effect is included with Newtonian and non-Newtonian flow assumptions. It is found that in a vascular bed comprising terminal arterial branches, the effect of acoustic streaming is negligible because of the small diameter of these vessels, and the non-Newtonian behavior of blood flow reduces the peak streaming velocity. It is also shown that the vascular density (amount of tissue vascular content) has a considerable cooling effect on peak temperature and hence lesion volume in the liver and, by increasing the vascular density, the treatment duration is prolonged. Results show that when the tumor is embedded in the vascular bed, the cancer cells near the vessels walls remain viable. Some approaches are proposed and compared to improve the efficacy of HIFU in a tumor located in the vascular bed. These approaches include increasing the source pressure or transducer gain. It is concluded that for the assumed configuration of the vascular bed, adjusting the transducer gain is preferred to increase the lesion size and to prevent the problems related to skin burns simultaneously.

Fully-coupled mathematical modeling of actomyosin-cytosolic two-phase flow in a highly deformable moving Keratocyte cell.

Interaction between intracellular dynamics and extracellular matrix (ECM) generally occurred into very thin fragment of moving cell, namely lamellipodia, enables all movable cells to crawl on ECM. In fast-moving cells such as fish Keratocytes, Lamellipodia including most cell area finds a fan-like shape during migration, with a variety of aspect ratio function of fish type. In this work, our purpose is to present a novel and more complete two-dimensional continuum mathematical model of actomyosin-cytosolic two-phase flow of a self-deforming Keratocyte with circular spreaded to steady fan-like shape. In the new approach, in addition to the two-phase flow of the F-actin and cytosol, the G-actin transport was spatiotemporally modeled. We also for the first time modeled the effect of variable volume fraction of the moving F-actin porous network on solute transport in the cytosolic fluid. Our novel fully-coupled mathematical model provides a better understanding of intracellular dynamics of fast-migrating Keratocytes; such as the F-actin centripetal and cytosolic fountain-like flows, free-active myosin distribution, distribution sequence of the G-actin, F-actin, and myosin, and myosin-induced pressure flied of cytoplasm as well as the map of intracellular forces like myosin contraction and adhesion traction. All these results are qualitatively and quantitatively in good agreement with experimental observations. According to a range of value of parameters used in this model, our steady state of moving Keratocyte finds fan-like shape with the same aspect ratio as wide category of fish Keratocytes. This new model can predict shape of Keratocytes in other range of parameter values.

Theoretical modeling of actin-retrograde-flow passing clusters of confined T cell receptors.

Through the activation process of T cells, actin filaments move from the cell periphery toward the cell center. The moving filaments engage with T cell receptors and thus contribute to transportation of the signaling molecules. To study the connection between the moving actin filaments and T cell receptors, an experiment available in the literature has measured filaments flow velocity passing over a region of confined clusters of receptors. It shows that flow velocity decreases in the proximity of the receptors, and then regains its normal value after traversing the region, suggesting a dissipative friction-like connection. In this work, we develop a minimal theoretical model to re-examine this experiment. The model brings the insight that, in contrast to the first impression that the experiment gives, the direct necessity of having a minimum in the velocity profile is not the locally high friction region, but a combined driving force of push from upstream and pull from within and downstream of the system. The predicted driving force integrates our current understanding of the spatially dependent role of the myosin motor proteins and the actin-polymerization-machinery, which make the pulling and pushing forces, respectively.

A mechanical model for morphological response of endothelial cells under combined wall shear stress and cyclic stretch loadings.

The shape and morphology of endothelial cells (ECs) lining the blood vessels are a good indicator for atheroprone and atheroprotected sites. ECs of blood vessels experience both wall shear stress (WSS) and cyclic stretch (CS). These mechanical stimuli influence the shape and morphology of ECs. A few models have been proposed for predicting the morphology of ECs under WSS or CS. In the present study, a mathematical cell population model is developed to simulate the morphology of ECs under combined WSS and CS conditions. The model considers the cytoskeletal filaments, cell-cell interactions, and cell-extracellular matrix interactions. In addition, the reorientation and polymerization of microfilaments are implemented in the model. The simulations are performed for different conditions: without mechanical stimuli, under pure WSS, under pure CS, and under combined WSS and CS. The results are represented as shape and morphology of ECs, shape index, and angle of orientation. The model is validated qualitatively and quantitatively with several experimental studies, and good agreement with experimental studies is achieved. To the best of our knowledge, it is the first model for predicting the morphology of ECs under combined WSS and CS condition. The model can be used to indicate the atheroprone regions of a patient's artery.

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

The F-actin network and cytosol in the lamellipodia of crawling cells flow in a centripetal pattern and spout-like form, respectively. We have numerically studied this two-phase flow in the realistic geometry of a moving keratocyte. Cytosol has been treated as a low viscosity Newtonian fluid flowing through the high viscosity porous medium of F-actin network. Other involved phenomena including myosin activity, adhesion friction, and interphase interaction are also discussed to provide an overall view of this problem. Adopting a two-phase coupled model by myosin concentration, we have found new accurate perspectives of acto-cytosolic flow and pressure fields, myosin distribution, as well as the distribution of effective forces across the lamellipodia of a keratocyte with stationary shape. The order of magnitude method is also used to determine the contribution of forces in the internal dynamics of lamellipodia.

Analytical solutions of actin-retrograde-flow in a circular stationary cell: a mechanical point of view.

The network of actin filaments in the lamellipodium (LP) of stationary and migrating cells flows in a retrograde direction, from the membrane periphery toward the cell nucleus. We have theoretically studied this phenomenon in the circular stationary (fully spread) cells. Adopting a continuum view on the LP actin network, new closed-form solutions are provided for the actin-retrograde-flow (ARF) in a polar coordinate system. Due to discrepancy in the mechanical models of the actin network in the ARF regime, solutions are provided for both assumptions of solid and fluid behavior. Other involved phenomena, including polymerizing machine at the membrane periphery, cytosol drag, adhesion friction, and membrane tension, are also discussed to provide an overall quantitative view on this problem.