Developing mathematical models for cardiovascular system functional assessments

E A Rzaev; S R Rasulov; A G Rzaev

doi:10.17750/KMJ2015-681

Kazan medical journal ›› 2015, Vol. 96 ›› Issue (4) : 681 -685. DOI: 10.17750/KMJ2015-681

Medical cybernetics

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Developing mathematical models for cardiovascular system functional assessments

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Abstract

Aim. Development of mathematical models of circulation (considering anomaly in hemorheology) allowing to diagnose functional condition of vessels/cardiovascular system.

Methods. Echocardiography, mathematical modeling, sedimentation and rheology laws, human mechanics and physiology methods were used for developing mathematical models.

Results. The following mathematical models were obtained: for determination of colloid dispersive blood system viscosity, considering concentration of dispersive phase (blood cells) and blood structure formation; velocity of inconvenient blood cells sedimentation depending on flow velocity of sediment and cell concentration; parameters of blood elasticity and viscosity as a connection between the velocity change and blood viscosity, Young`s elasticity and change tension; blood filtration in vessels (modified form of Darcy`s law) considering tension and changes of destroyed and undestroyed colloid blood system structure velocity. It was shown that impairments of blood flow velocity leads to blood cells sedimentation and thrombus structure formation, which is not moving according to Newton’s law. New indicators for diagnosing functional condition of vessels and estimating the severity of vascular insufficiency are introduced.

Conclusion. Developed hemorheologic models allow to adequately estimate human cardiovascular bloodflow.

Keywords

viscosity / pressure change / blood / serum / microvasculature

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E A Rzaev, S R Rasulov, A G Rzaev. Developing mathematical models for cardiovascular system functional assessments. Kazan medical journal, 2015, 96(4): 681-685 DOI:10.17750/KMJ2015-681

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