Velibor Isailovic

A computational study of circulating large tumor cells traversing microvessels

Circulating tumor cells (CTCs) are known to be a harbinger of cancer metastasis. The CTCs are known to circulate as individual cells or as a group of interconnected cells called CTC clusters. Since both single CTCs and CTC clusters have been detected in venous blood samples of cancer patients, they needed to traverse at least one capillary bed when crossing from arterial to venous circulation. The diameter of a typical capillary is about 7µm, whereas the size of an individual CTC or CTC clusters can be greater than 20µm and thus size exclusion is believed to be an important factor in the capillary arrest of CTCs - a key early event in metastasis. To examine the biophysical conditions needed for capillary arrest, we have developed a custom-built viscoelastic solid-fluid 3D computational model that enables us to calculate, under physiological conditions, the maximal CTC diameter that will pass through the capillary. We show that large CTCs and CTC clusters can successfully cross capillaries if their stiffness is relatively small. Specifically, under physiological conditions, a 13µm diameter CTC passes through a 7µm capillary only if its stiffness is less than 500Pa and conversely, for a stiffness of 10Pa the maximal passing diameter can be as high as 140µm, such as for a cluster of CTCs. By exploring the parameter space, a relationship between the capillary blood pressure gradient and the CTC mechanical properties (size and stiffness) was determined. The presented computational platform and the resulting pressure-size-stiffness relationship can be employed as a tool to help study the biomechanical conditions needed for capillary arrest of CTCs and CTC clusters, provide predictive capabilities in disease progression based on biophysical CTC parameters, and aid in the rational design of size-based CTC isolation technologies where CTCs can experience large deformations due to high pressure gradients.

Multiscale Modeling of Circular and Elliptical Particles in Laminar Shear Flow

Drug delivery systems for cancer prevention and pain management have been improved related to classical cancer chemotherapy. Nanotechnology with nanoparticles offers new ways in transport of drug molecules and contrast agents by the blood flow through the circulatory system. In this study, we use multiscale mesoscopic bridging procedure of the finite elements (FE) coupled with dissipative particle dynamics (DPD) and lattice Boltzmann (LB) method to model the motion of circular and elliptical particles in a 2-D laminar flow. Four examples are considered: 1) one sedimenting cylinder in a channel, 2) two sedimenting cylinders in a channel, 3) motion of four elliptical particles in a linear shear flow, and 4) motion of circular and elliptical particle in the arterial bifurcation geometry. A good agreement with solution from the literature available was found. These results show that the multiscale approach with coupled FE and DPD/LB methods can effectively be applied to model motion of micro/nanoparticles for a drug delivery system.

SIFEM project: Finite element modeling of the cochlea

The cochlea is a very interesting part of the body. There are several investigations of experiments on the real cochlea and mathematical models. The cochlea works on the basis of a vibrating system. SIFEM project focuses on the development the multi-scale modelling of the inner-ear with regard to the sensorineural hearing loss. In this study we focused on the finite element model of the cochlea. The first approximation is straight box model where both domain basilar membrane and surrounding fluid are modeled. Fluid-structure interaction problem was implemented. The basilar membrane was modeled as structural plate with 3D brick finite element and fluid domain around the basilar membrane was modeled as full 3D Navier-Stokes equations. ALE formulation was employed for fluid domain and mesh moving algorithm for motion of the membrane and fluid mesh. The results for different frequencies for 3D box and spiral model are presented. It can be observed that viscous fluid allow a sharper response of the membrane, because the viscous fluid would quickly damp out the vibratory motion.

Transport Phenomena: Computational Models for Convective and Diffusive Transport in Capillaries and Tissue

A review of computational procedures for convective and diffusive transport, developed by the authors, is presented in this chapter. The presented finite element computational framework is directed to transport within capillaries and tissue. The convective transport includes modeling of motion of deformable bodies within fluid flow. It is based on a strong coupling concept and remeshing procedure. It was found by the authors that this approach has advantages in reliability and accuracy with respect to others available in literature, although it is not computationally efficient. A hierarchical multiscale model for diffusion couples molecular dynamics and continuum FE method by evaluating equivalent continuum diffusive parameters; these parameters include commonly used diffusion coefficients, but also parameters which account for physicochemical interactions between diffusing molecules and microstructural solid surfaces. A numerical homogenization is used in this multiscale model. Coupled convective and diffusive transport is also considered. A number of typical solved examples illustrate generality, robustness, and accuracy of the presented computational methodology.

Mapping cyclic stretch in the postpneumonectomy murine lung

In many mammalian species, the removal of one lung [pneumonectomy (PNX)] is associated with the compensatory growth of the remaining lung. To investigate the hypothesis that parenchymal deformation may trigger lung regeneration, we used respiratory-gated micro-computed tomography scanning to create three-dimensional finite-element geometric models of the murine cardiac lobe with cyclic breathing. Models were constructed of respiratory-gated micro-computed tomography scans pre-PNX and 24 h post-PNX. The computational models demonstrated that the maximum stretch ratio map was patchy and heterogeneous, particularly in subpleural, juxta-diaphragmatic, and cephalad regions of the lobe. In these parenchymal regions, the material line segments at peak inspiration were frequently two- to fourfold greater after PNX; some regions of the post-PNX cardiac lobe demonstrated parenchymal compression at peak inspiration. Similarly, analyses of parenchymal maximum shear strain demonstrated heterogeneous regions of mechanical stress with focal regions demonstrating a threefold increase in shear strain after PNX. Consistent with previously identified growth patterns, these subpleural regions of enhanced stretch and shear strain are compatible with a mechanical signal, likely involving cyclic parenchymal stretch, triggering lung growth.

Numerical Model Assessment of Radial-Well Aging

There are 99 radial wells at Belgrades groundwater source which lies along the banks of the Sava River. The capacity of this source has been declining over time due to two dominant processes: riverbed colmation and well aging. Both have resulted in substantial additional well-maintenance costs. Aging of radial-well laterals is a result of physical, chemical, and biochemical processes which depend on a number of parameters. The objective of the study presented in this paper was to assess changes in hydraulic losses at the entrance to the laterals due to colmation (clogging) of screen slots of the laterals in order to define the well-aging process and take timely action. Groundwater flow to a single well was numerically simulated using a three-dimensional model. Special software was developed for this purpose; in addition to standard groundwater flow calculations, it allows for geometry and spatial positions of well laterals to be specified in a user-friendly manner. This paper highlights reasons for developing the software and its special features. Model application and results are illustrated using a case study of a well which taps the alluvial aquifer of the Sava River and is part of Belgrades water supply system.

Finite element coiled cochlea model

Cochlea is important part of the hearing system, and thanks to special structure converts external sound waves into neural impulses which go to the brain. Shape of the cochlea is like snail, so geometry of the cochlea model is complex. The simplified cochlea coiled model was developed using finite element method inside SIFEM FP7 project. Software application is created on the way that user can prescribe set of the parameters for spiral cochlea, as well as material properties and boundary conditions to the model. Several mathematical models were tested. The acoustic wave equation for describing fluid in the cochlea chambers – scala vestibuli and scala timpani, and Newtonian dynamics for describing vibrations of the basilar membrane are used. The mechanical behavior of the coiled cochlea was analyzed and the third chamber, scala media, was not modeled because it does not have a significant impact on the mechanical vibrations of the basilar membrane. The obtained results are in good agreement with experiment...

3D Modeling of Plaque Progression in the Human Coronary Artery

The inflammation and lipid accumulation in the arterial wall represents a progressive disease known as atherosclerosis. In this study, a numerical model of atherosclerosis progression was developed. The wall shear stress (WSS) and blood analysis data have a big influence on the development of this disease. The real geometry of patients, and the blood analysis data (cholesterol, HDL, LDL, and triglycerides), used in this paper, was obtained within the H2020 SMARTool project. Fluid domain (blood) was modeled using Navier-Stokes equations in conjunction with continuity equation, while the solid domain (arterial wall) was modeled using Darcy’s law. For the purpose of modeling low-density lipoprotein (LDL) and oxygen transport, convection-diffusion equations were used. Kedem-Katchalsky equations were used for coupling fluid and solid dynamics.

Computational modeling of plaque development in the coronary arteries

Computational study for plaque formation and development for the patient specific coronary arteries was performed. Transport of macrophages and oxidized LDL distribution for the initial plaque grow model inside the intimal area was implemented. Mass transport of LDL through the wall and the simplified inflammatory process was firstly solved. The Navier-Stokes equations govern the blood motion in the lumen, the Darcy law is used for model blood filtration, Kedem-Katchalsky equations for the solute and flux exchanges between the lumen and the intima. The system of three additional reaction-diffusion equations that models the inflammatory process and lesion growth model in the intima was used. Some examples of computer simulation for plaque formation and progression for the specific patient for left and right coronary arteries are presented. Determination of plaque location and plaque volume with computer simulation for a specific patient shows a potential benefit for prediction of disease progression.

Prediction of Coronary Plaque Progression Using Data Driven Approach

Coronary artery disease or coronary atherosclerosis (CATS) is the most common type of cardiovascular disease and the number one cause of death worldwide. Early identification of patients who will develop progression of disease is beneficial for treatment planning and adopting the strategy for reduction of risk factors that could cause future cardiac events. In this paper, we propose the data mining model for prediction of CATS progression. We exploit patient’s health record by using various machine learning methods. Predictor variables, including heterogenious data from cellular to the whole organism level, are initially preprocessed by feature selection approaches to select only the most informative features as inputs to machine learning algorithms. Results obtained and features selected within this study indicate the high potential of machine learning to be used in clinical practice as well as that specific monocytes are important markers impacting the plaque progression.