Numerical investigation of LDL nanoparticle collision in coronary artery grafts with porous wall and different implantation angles and two state of inlet velocity.

This study aimed to reduce the risk of graft occlusion by evaluating the two-phase flow of blood and LDL nanoparticles in coronary artery grafts. The study considered blood as an incompressible Newtonian fluid, with the addition of LDL nanoparticles, and the artery wall as a porous medium. Two scenarios were compared, with constant inlet velocity (CIV) and other with pulsatile inlet velocity (PIV), with LDL nanoparticles experiencing drag, wall-induced lift, and induced Saffman lift forces, or drag force only. The study also evaluated the concentration polarization of LDLs (CP of LDLs) near the walls, by considering the artery wall with and without permeation. To model LDL nanoparticles, the study randomly injected 100, 500, and 1000 nanoparticles in three release states at each time step, using different geometries. Numerical simulations were performed using COMSOL software, and the results were presented as relative collision of nanoparticles to the walls in tables, diagrams, and shear stress contours. The study found that a graft implantation angle of 15° had the most desirable conditions compared to larger angles, in terms of nanoparticle collision with surfaces and occlusion. The nanoparticle release modes behaved similarly in terms of collision with the surfaces. A difference was observed between CIV and PIV. Saffman lift and wall-induced lift forces having no effect, possibly due to the assumption of a porous artery wall and perpendicular outlet flow. In case of permeable artery walls, relative collision of particles with the graft wall was larger, suggesting the effect of CP of LDLs.

Investigating the temperature distribution behavior and flow parameters of argon fluid in a nanochannel with changing dimensions of the obstacle using the molecular dynamics (MD) method.

This article, examines the flow of argon inside a nanochannel with respect to the molecular dynamics (MD) in the free molecular flow regime using LAMMPS software. The nanochannel is made of copper featuring a square cross-section and obstacles of varying dimensions and values. In this study, the flow of argon fluid is three-dimensional. To gain a deeper understanding of the effect of solid walls within the nanochannel and their influence on flow behavior, the research is simulated in a nanochannel with all side walls for the 3D model and without side walls for the 2D model. This research assesses the effect of the obstacles' dimensions and values on the nanochannel wall surface and areas above the wall surface. The total dimensions of all simulated two- and three-dimensional atomic structures with a square cross-section are assumed to be 60 × 60 × 100 Å3. and the presence of square obstacles (with dimensions of 8 × 8 × 8 Å3) and rectangular obstacles (with dimensions of 8 × 18 × 8 Å3) is examined. This study seeks to understand the influence on flow behavior, temperature distribution, density, heat flux, velocity, and thermal conductivity coefficient. This study is simulated using a time step of 1 fs for 10,000 time steps, involving approximately 10,000-15,000 argon and copper atoms. The results of this research indicate that obstacles with structures of P and R and larger dimensions increase the number of solid atoms exhibiting stronger attractive forces. Compared to a smooth nanochannel, the thermal exchange between fluid and solid atoms results in a density increase of 17.5 % and 17.3 %, respectively. On the other hand, in the 3D nanochannel, the sidewalls of the nanochannel have reduced the effect of the presence of R and P obstacles with larger dimensions, which comparing to a smooth nanochannel, have increased the density by 8.21 % and 7.53 %, respectively. The obstacles with different spatial positions (P and R structures) in the two-dimensional nanochannel cause a rise in the thermal conductivity coefficient. The P structure obstacles have a better effect on the thermal conductivity coefficient in the 2D nanochannel compared to the R structure. In the three-dimensional nanochannel, utilizing smaller obstacles proves to be more effective because it results in better atom distribution or temperature distribution due to increased atomic collisions in the central region compared to the wall regions.

A multiscale cell-based model of tumor growth for chemotherapy assessment and tumor-targeted therapy through a 3D computational approach.

OBJECTIVES: Computational modeling of biological systems is a powerful tool to clarify diverse processes contributing to cancer. The aim is to clarify the complex biochemical and mechanical interactions between cells, the relevance of intracellular signaling pathways in tumor progression and related events to the cancer treatments, which are largely ignored in previous studies. MATERIALS AND METHODS: A three-dimensional multiscale cell-based model is developed, covering multiple time and spatial scales, including intracellular, cellular, and extracellular processes. The model generates a realistic representation of the processes involved from an implementation of the signaling transduction network. RESULTS: Considering a benign tumor development, results are in good agreement with the experimental ones, which identify three different phases in tumor growth. Simulating tumor vascular growth, results predict a highly vascularized tumor morphology in a lobulated form, a consequence of cells' motile behavior. A novel systematic study of chemotherapy intervention, in combination with targeted therapy, is presented to address the capability of the model to evaluate typical clinical protocols. The model also performs a dose comparison study in order to optimize treatment efficacy and surveys the effect of chemotherapy initiation delays and different regimens. CONCLUSIONS: Results not only provide detailed insights into tumor progression, but also support suggestions for clinical implementation. This is a major step toward the goal of predicting the effects of not only traditional chemotherapy but also tumor-targeted therapies.

Multiscale modeling of tumor growth and angiogenesis: Evaluation of tumor-targeted therapy.

The dynamics of tumor growth and associated events cover multiple time and spatial scales, generally including extracellular, cellular and intracellular modifications. The main goal of this study is to model the biological and physical behavior of tumor evolution in presence of normal healthy tissue, considering a variety of events involved in the process. These include hyper and hypoactivation of signaling pathways during tumor growth, vessels' growth, intratumoral vascularization and competition of cancer cells with healthy host tissue. The work addresses two distinctive phases in tumor development-the avascular and vascular phases-and in each stage two cases are considered-with and without normal healthy cells. The tumor growth rate increases considerably as closed vessel loops (anastomoses) form around the tumor cells resulting from tumor induced vascularization. When taking into account the host tissue around the tumor, the results show that competition between normal cells and cancer cells leads to the formation of a hypoxic tumor core within a relatively short period of time. Moreover, a dense intratumoral vascular network is formed throughout the entire lesion as a sign of a high malignancy grade, which is consistent with reported experimental data for several types of solid carcinomas. In comparison with other mathematical models of tumor development, in this work we introduce a multiscale simulation that models the cellular interactions and cell behavior as a consequence of the activation of oncogenes and deactivation of gene signaling pathways within each cell. Simulating a therapy that blocks relevant signaling pathways results in the prevention of further tumor growth and leads to an expressive decrease in its size (82% in the simulation).

Thermally induced stress in a nanoconfined gas medium.

Molecular dynamics simulations of static argon gas at three different levels of rarefaction are conducted for a channel of 5.4 nm height to investigate the simultaneous effect of the wall force field and the gas temperature on the stress distribution along the channel height. Using the interactive thermal wall model, different temperatures are applied on the channel walls to be able to investigate the effect of the wall temperature and the induced heat flux through the gas medium on the stress distribution. Considering the monoatomic neutral argon gas, the kinetic, particle-particle virial, and surface-particle virial are considered for computing the stress distribution along the channel height. The normal stress components in the bulk gas region are distributed isotropically regardless of the gas density, temperature, and induced heat flux through the domain, while an anisotropy is observed due to the presence of the surface-particle virial. As the gas becomes hotter, the velocity of the gas atoms increases, and thus the kinetic stress component also increases. Besides, the gas density in the wall force field region reduces which eventually attenuates the surface-particle and particle-particle virial stress within 1 nm from each wall. This effect was also observed as the gas becomes cooler. It is shown that the combination of gas density, wall temperature, and induced heat flux are the main parameters which determine the distribution of stress within the gas medium especially in the wall force field region where repulsive and attractive interactions exist.

Scaling Laws of Flow Rate, Vessel Blood Volume, Lengths, and Transit Times With Number of Capillaries.

The structure-function relation is one of the oldest hypotheses in biology and medicine; i.e., form serves function and function influences form. Here, we derive and validate form-function relations for volume, length, flow, and mean transit time in vascular trees and capillary numbers of various organs and species. We define a vessel segment as a "stem" and the vascular tree supplied by the stem as a "crown." We demonstrate form-function relations between the number of capillaries in a vascular network and the crown volume, crown length, and blood flow that perfuses the network. The scaling laws predict an exponential relationship between crown volume and the number of capillaries with the power, λ, of 4/3 < λ < 3/2. It is also shown that blood flow rate and vessel lengths are proportional to the number of capillaries in the entire stem-crown systems. The integration of the scaling laws then results in a relation between transit time and crown length and volume. The scaling laws are both intra-specific (i.e., within vasculatures of various organs, including heart, lung, mesentery, skeletal muscle and eye) and inter-specific (i.e., across various species, including rats, cats, rabbits, pigs, hamsters, and humans). This study is fundamental to understanding the physiological structure and function of vascular trees to transport blood, with significant implications for organ health and disease.

Analytical expressions for estimating endurance time and glove thermal resistance related to human finger in cold conditions.

Frostbite is considered the severest form of cold injury and can lead to necrosis and loss of peripheral appendages. Therefore, prediction of endurance time of limb's tissue in cold condition is not only necessary but also crucial to estimate cold injury intensity and to choose appropriate clothing. According to the previous work which applied a 3-D thermal model for human finger to analyze cold stress, in this study, an expression is presented for endurance time in cold conditions to prevent cold injury. A formula is also recommended to select a proper glove with specific thermal resistance based on the ambient situation and cold exposure time. By employing linear extrapolation and real physical conditions, the proposed formulas were drawn out from numerical simulation. Analytical results show good agreement with numerical data. The used numerical data had been also validated with experimental data existed in the literature. Furthermore, the effect of different parameters such as glove thermal resistance and ambient temperature is investigated analytically.

A 3D thermal model to analyze the temperature changes of digits during cold stress and predict the danger of frostbite in human fingers.

The existing computational models of frostbite injury are limited to one and two dimensional schemes. In this study, a coupled thermo-fluid model is applied to simulate a finger exposed to cold weather. The spatial variability of finger-tip temperature is compared to experimental ones to validate the model. A semi-realistic 3D model for tissue and blood vessels is used to analyze the transient heat transfer through the finger. The effect of heat conduction, metabolic heat generation, heat transport by blood perfusion, heat exchange between tissues and large vessels are considered in energy balance equations. The current model was then tested in different temperatures and air speeds to predict the danger of frostbite in humans for different gloves. Two prevalent gloves which are commonly used in cold climate are considered for investigation. The endurance time and the fraction of necrotic tissues are two main factors suggested for obtaining the response of digit tissues to different environmental conditions.

Heat transfer analysis of skin during thermal therapy using thermal wave equation.

Specifying exact geometry of vessel network and its effect on temperature distribution in living tissues is one of the most complicated problems of the bioheat field. In this paper, the effects of blood vessels on temperature distribution in a skin tissue subjected to various thermal therapy conditions are investigated. Present model consists of counter-current multilevel vessel network embedded in a three-dimensional triple-layered skin structure. Branching angles of vessels are calculated using the physiological principle of minimum work. Length and diameter ratios are specified using length doubling rule and Cube law, respectively. By solving continuity, momentum and energy equations for blood flow and Pennes and modified Pennes bioheat equations for the tissue, temperature distributions in the tissue are measured. Effects of considering modified Pennes bioheat equation are investigated, comprehensively. It is also observed that blood has an impressive role in temperature distribution of the tissue, especially at high temperatures. The effects of different parameters such as boundary conditions, relaxation time, thermal properties of skin, metabolism and pulse heat flux on temperature distribution are investigated. Tremendous effect of boundary condition type at the lower boundary is noted. It seems that neither insulation nor constant temperature at this boundary can completely describe the real physical phenomena. It is expected that real temperature at the lower levels is somewhat between two predicted values. The effect of temperature on the thermal properties of skin tissue is considered. It is shown that considering temperature dependent values for thermal conductivity is important in the temperature distribution estimation of skin tissue; however, the effect of temperature dependent values for specific heat capacity is negligible. It is seen that considering modified Pennes equation in processes with high heat flux during low times is significant.

Constructal law of vascular trees for facilitation of flow.

Diverse tree structures such as blood vessels, branches of a tree and river basins exist in nature. The constructal law states that the evolution of flow structures in nature has a tendency to facilitate flow. This study suggests a theoretical basis for evaluation of flow facilitation within vascular structure from the perspective of evolution. A novel evolution parameter (Ev) is proposed to quantify the flow capacity of vascular structures. Ev is defined as the ratio of the flow conductance of an evolving structure (configuration with imperfection) to the flow conductance of structure with least imperfection. Attaining higher Ev enables the structure to expedite flow circulation with less energy dissipation. For both Newtonian and non-Newtonian fluids, the evolution parameter was developed as a function of geometrical shape factors in laminar and turbulent fully developed flows. It was found that the non-Newtonian or Newtonian behavior of fluid as well as flow behavior such as laminar or turbulent behavior affects the evolution parameter. Using measured vascular morphometric data of various organs and species, the evolution parameter was calculated. The evolution parameter of the tree structures in biological systems was found to be in the range of 0.95 to 1. The conclusion is that various organs in various species have high capacity to facilitate flow within their respective vascular structures.

Development of a general method for designing microvascular networks using distribution of wall shear stress.

In the present study, theoretical formulations for calculation of optimal bifurcation angle and relationship between the diameters of mother and daughter vessels using the power law model for non-Newtonian fluids are developed. The method is based on the distribution of wall shear stress in the mother and daughter vessels. Also, the effect of distribution of wall shear stress on the minimization of energy loss and flow resistance is considered. It is shown that constant wall shear stress in the mother and daughter vessels provides the minimum flow resistance and energy loss of biological flows. Moreover, the effects of different wall shear stresses in the mother and daughter branches, different lengths of daughter branches in the asymmetric bifurcations and non-Newtonian effect of biological fluid flows on the bifurcation angle and the relationship between the diameters of mother and daughter branches are considered. Using numerical simulations for non-Newtonian models such as power law and Carreau models, the effects of optimal bifurcation angle on the pressure drop and flow resistance of blood flow in the symmetric bifurcation are investigated. Numerical simulations show that optimal bifurcation angle decreases the pressure drop and flow resistance especially for bifurcations at large Reynolds number.