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Mathematical model > Vascular model
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Vascular model
The modelling object can be represented as a ring system of compartments: left ventricle (HL), systemic artery (AL), capillaryvenous systemic compartment (systemic vein) (VL), right ventricle (HR), pulmonary artery (AR), capillaryvenous pulmonary compartment (pulmonary vein) (VR). Aortic, tricupsid, pulmonary and mitral valves provide direct blood flow through this ring system.
The blood pressure Pi in i-section of vascular system is determined by this function of blood volume Vi on this section:
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(7) |
In the formula (7) 
, volumetric elasticity Gi describes rigidity properties of a vascular wall, ωi - stressless volume of a vascular section. Values of volumetric elasticity and non-intense volume characterize a vascular tone and nonlinearly depend on a condition vector x and vector A of dynamic system parameters:
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(8) |
The change speed of blood volume Vi in i -section of vascular system is determined by the difference between the input and output blood flows, i.e. the differential equation takes place:
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(9) |
where Fki – the value of input blood flow, Fij – the value of output blood flow, k - index of upstream compartment, j - index of downstream compartment.
The value of blood flow Fij in the section between i- and j-compartments is determined by the difference between pressures in these compartments:
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(10) |
Conductivity values Yij of vascular sections are determined by nonlinear functions of condition vector x and parametres vector A :
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(11) |
System of correlations (7) - (11) with concrete expressions for functions (8) è (11) is given in subthemes.
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Contents sectionMathematical model > Vascular model
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