S. Simakov

Computational study of blood flow in lower extremities under intense physical load

Abstract This work is aimed at computational study of the blood flow in lower extremities under intense physical load. We present a modified 1D cardiovascular system model describing skeletal-muscle pumping and autoregulation effects on the blood flow in lower extremities. Skeletal-muscle pump effect is introduced as an external time-periodical pressure function applied to a group of veins. The period of this function is associated with the two-stride period during running. The computational study reveals the explicit optimal stride frequency providing the maximum blood flow through the lower extremities. It is shown that the optimal stride frequency depends on personal parameters. The model is validated by a comparison to the stride frequencies of a number of top-level athletes, therefore, providing a method to assess the level of physical conditioning.

Numerical issues of modelling blood flow in networks of vessels with pathologies

The synthesis of the blood circulation model and the elastic fiber model of the vessel wall allows us to take into account the influence of possible vessel pathologies on the global blood flow. The interaction is based on the state equation representing the dependence of the transmural pressure on the cross-section of the vessel. Numerical properties of both models are considered in the paper. The mathematical modelling of blood circulation is a fundamental problem lying at the junction of several disciplines, such as differential equations, numerical analysis, elasticity theory, and physiology. Several numerical implementations of blood circu- lation models taking into account elastic properties of blood vessels were created in the last decade (6,9,10,14,21,22). Previously we proposed an approach to synthesis of the blood circulation model and the elastic model of the vessel wall (24) taking into account the influence of possible vessel pathologies on the global blood flow. The distinctive feature of the approach is the use of merely one-dimensional dif- ferential operators, which provided us with an efficient numerical simulation tech- nology. The mathematical blood flow model is a system of differential equations for each vessel linked by boundary conditions at the points of vessel junctions (22). The mathematical model of the elastic vessel wall is based on the fiber approach (17,18) to the calculation of the reaction force as a response to the deformation of a fiber. The representation of an elastic body by sets of fibers of different configurations was successfully used for simulation of cardiac work (13) and collapsed veins (18). In our model we used the same types of fibers as in (18). The synthesis of both models is based on the state equation representing the dependence of the transmural pressure on the cross-section area of the vessel. This

Virtual fractional flow reserve assessment in patient-specific coronary networks by 1D hemodynamic model

Abstract Atherosclerotic diseases of coronary vessels are the main reasons of myocardial ischemia. The value of the fractional flow reserve (FFR) factor is the golden standard for making decision on coronary network surgical treatment. The FFR measurements require expensive endovascular diagnostics. We propose a noninvasive method of the virtual FFR assessment in patient-specific coronary network based on angiography and computer tomography data. Also we analyze sensitivity of the model to the heart stroke volume.

Patient-specific anatomical models in human physiology

Abstract Patient-specific simulations of human physiological processes remain the challenge for many years. Detailed 3D reconstruction of body anatomical parts on the basis of medical images is an important stage of individualized simulations in physiology. In this paper we present and develop the methods and algorithms for construction of patient-specific discrete geometric models. These models are represented by anatomically correct computational meshes. Practical use of these methods is demonstrated for two important medical applications: numerical evaluation of fractional flow reserve in coronary arteries and electrocardiography simulation

Computational Study of the Vibrating Disturbances to the Lung Function

Frequently during its lifetime a human organism is subjected to the acoustical and similar to them vibrating impacts. Under the certain conditions such influence may cause physiological changes in the organs functioning. Thus the study of the oscillatory mechanical impacts to the organism is very important task of the numerical physiology. It allows to investigate the endurance limits of the organism and to develop protective measures in order to extend them. The noise nuisances affects to the most parts of the organism disrupting their functions. The vibrating disturbances caused to the lung function as one of the most sensitive to the acoustical impacts is considered in this work. The model proposed to describe the air motion in trachea-bronchial tree is based on the one dimensional no-linear theory including mass and momentum conservation for the air flow in flexible tubes similar to the model of blood flow in large vessels [1]. It combined with the single-component model of alveole [1], [2]. Two types of vibrating impacts were simulated that affect the thorax and the nasopharynx. The conducted simulations allowed us to detect two resonance frequencies that lay in the ranges from 3 Hz to 8 Hz and from 40 to 70 Hz when the thorax was affected (fig.1). For the nasopharynx disturbances no resonance states were found. Open image in new window Fig. 1. Dependencies of the integral volume and pressure of the lungs from oscillatory impacts.

Computational Simulations of Fractional Flow Reserve Variability

Fractional flow reserve (FFR) is the golden standard for making decision on surgical treatment of coronary vessels with multiple stenosis. Clinical measurements of FFR require expensive invasive procedure with endovascular ultrasound probe. In this work a method of FFR simulation is considered. It is based on modelling 1D haemodynamics in patient-specific coronary vessels network reconstructed from CT scans. In contrast to our previous studies we used explicit minimum oscillating 2nd order characteristic method for internal nodes and 2nd order approximation of compatibility conditions for discretization of boundary conditions in junctions. The model is applied for simulating the change of FFR due to variability of the vessels elasticity and autoregulation response rate.

Global Dynamical Model of the Cardiovascular System

Blood system functions are very diverse and important for most processes in human organism. One of its primary functions is matter transport among different parts of the organism including tissue supplying with oxygen, carbon dioxide excretion, drug propagation etc. Forecasting of these processes under normal conditions and in the presence of different pathologies like atherosclerosis, loss of blood, anatomical abnormalities, pathological changing in chemical transformations and others is significant issue for many physiologists. In this connection should be pointed out that global processes are of special interest as they include feedbacks and interdependences among different regions of the organism. At the modern level of computer engineering the most adequate physical model for the dynamical description of cardiovascular system is the model of non-stationary flow of incompressible fluid through the system of elastic tubes. Mechanics of such flow is described by nonlinear set of hyperbolic equations including mass and momentum conservation joined with equation of state that determines elastic properties of the tube [1]. As we interested in global processes the models of the four vascular trees (arterial and venous parts of systemic and pulmonary circulation) must be closed with heart and peripheral circulation models. Heart operation is described by the model of fluid flow averaged by volume through the system of extensible chambers that results in the set of stiff ordinary differential equations [1]. When combined these models allow us to consider functional changes and responses as during one cardiac cycle and at a longer periods upon 10 minutes that Open image in new window Fig. 1. Pressure wave propagation through the large pulmonary arteries during one cardiac cycle. Grayscale designates divergence from the minimum pressure in each vessel.

Computational Models on Graphs for Nonlinear Hyperbolic and Parabolic System of Equations

For each graph edge with length X k we consider 1D nonlinear hyperbolic system of equations \( \overrightarrow \nu _t + \overrightarrow F _{x_k } \left( {\overrightarrow \nu } \right) = \overrightarrow f ,\overrightarrow \nu = \left\{ {\nu _1 , \ldots ,\nu _1 } \right\},t \geqslant 0,0 \leqslant x_k \leqslant X_k ,k = 1, \ldots ,K \) (1) with initial conditions \( \overrightarrow \nu \left( {0,x_k } \right) = \overrightarrow \nu ^0 \left( {x_k } \right),k = 1, \ldots ,K \) and the next boundary conditions: for graph enters \( \left( {l^0 = 1, \ldots L^0 ,x_{k_ * } = 0} \right)\varphi _{li}^0 \left( {t,\overrightarrow \nu \left( {t,0} \right)} \right) = 0,i = 1, \ldots r_k^0 \leqslant I \) (2), for graph exits \( \left( {l^ * = 1, \ldots L^ * ,x_k = X_k } \right)\varphi _{li} \left( {t,\overrightarrow \nu \left( {t,X_k } \right)} \right) = 0,i = 1, \ldots ,r_k^ * \leqslant I \) (3) and for graph branchpoints \( l^ * = 1, \ldots L\psi _{lm} \left( {t,w_l ,\overrightarrow \nu _{l1} , \ldots \overrightarrow \nu _{lM_1 } } \right) = 0m = 1, \ldots M_l \) (4). Here K is the number of graph edges, LO - enters, LO - exits, L - branchpoints, M l - incoming and outgoing graph edges for the lth branchpoint, \( \overrightarrow \nu _{l1} , \ldots \overrightarrow \nu _{lM_l } \) - required vectors in the ends of edges adjoining to branchpoin l, W l - required vector for the branchpoint l. The matrix \( {{\partial \overrightarrow F } \mathord{\left/ {\vphantom {{\partial \overrightarrow F } {\partial \overrightarrow \nu }}} \right. \kern-\nulldelimiterspace} {\partial \overrightarrow \nu }} = A = \left\{ {a_{ij} } \right\}i,j = 1, \ldots ,I \) is Jacobi matrix and we can apply the identity \( A = \Omega ^{ - 1} \Lambda \Omega \), where \( \Lambda = \left\{ {\lambda _i } \right\} \) is the diagonal matrix of the matrix A eigenvalues, Ώ is the nonsingular matrix whose rows are linearly independent left-hand eigenvectors of the matrix A \( \left( {Det\Omega \ne 0} \right) \) and Ώ −1 is the matrix inverse to Ώ.

Multiscale CT-Based Computational Modeling of Alveolar Gas Exchange during Artificial Lung Ventilation, Cluster (Biot) and Periodic (Cheyne-Stokes) Breathings and Bronchial Asthma Attack

An airflow in the first four generations of the tracheobronchial tree was simulated by the 1D model of incompressible fluid flow through the network of the elastic tubes coupled with 0D models of lumped alveolar components, which aggregates parts of the alveolar volume and smaller airways, extended with convective transport model throughout the lung and alveolar components which were combined with the model of oxygen and carbon dioxide transport between the alveolar volume and the averaged blood compartment during pathological respiratory conditions. The novel features of this work are 1D reconstruction of the tracheobronchial tree structure on the basis of 3D segmentation of the computed tomography (CT) data; 1D−0D coupling of the models of 1D bronchial tube and 0D alveolar components; and the alveolar gas exchange model. The results of our simulations include mechanical ventilation, breathing patterns of severely ill patients with the cluster (Biot) and periodic (Cheyne-Stokes) respirations and bronchial asthma attack. The suitability of the proposed mathematical model was validated. Carbon dioxide elimination efficiency was analyzed in all these cases. In the future, these results might be integrated into research and practical studies aimed to design cyberbiological systems for remote real-time monitoring, classification, prediction of breathing patterns and alveolar gas exchange for patients with breathing problems.

The Model of Global Blood Circulation and Applications

1D model of global blood circulation describes hemodynamics of healthy vascular system very well. Real applications demand considerations of vascular pathologies, implants and influence of external effects. In this paper we discuss how to do it on the basis of the model. The first approach is to update the state equation of the model. This equation describes elastic properties of the vessel wall. The second approach is to use a 3D model of the blood flow in the region of interest. The 3D model should be coupled with the 1D model of global blood circulation.