Novel nonlinear models for microvascular tree of heart tissue

V.Kardashov, Sh.Einav

Israel

 

It is well known that micro-circulation presents the very important component of the systemic cardiovascular activity.љ The interaction of the micro-circulation with activity of the heart and large arteries mainly determines the dynamics of the important cardiovascular parameters: blood pressure, cardiac output, heart rate variability, etc. It implies the importance of designing of micro-and-nano-sensors and related diagnostic and clinical tools for noninvasive control and stimulation of the microcirculation. In the present paper the computer assisted and model based approach for possible revascularization of the ischemic heart tissue by application of theљљ regulating ultrasound is considered.

љThe main object of the paper is development of the mathematical software for computer assisted revascularization or angiogenesis in the ischemic regions of the heart under resonant ultrasound subjection. Angiogenesis is the proliferation of endothelial and smooth muscle cells to form a new blood vessels. Researchers now recognize that stimulation of angiogenesis may have a place in the treatment of cardiovascular diseases. Reestablishing blood flow to ischemic tissue through angiogenesis may provide a biologic "bypass" for patients with ischemic heart disease. The same applies to the treatment of peripheral vascular disease. Our main hypothesis is that the resonant focused or delivered subjection of the medical ultrasound can create the optimal bio-mechanical and bio-chemical conditions for angiogenesis.

The novel nonlinear reaction-diffusion model with external control term among with known simple linear models is proposed. Possible coupling of these models with recently treated computer algorithms for micro-vascular tree reconstruction in the ischemic heart tissue is discussed. On the other hand, taking into account the micro and nano-dimension of the heart fibers and capillaries, the possible application of the micro-and nano-technologies via reaction-diffusion is considered.

Regulation of vascular growth is a very complex problem. Research based on morphological methods and research based on the methods of molecular biology should complement each other, creating mutual influences. It implies that application of the modern nonlinear dynamics, for instance, Turing model of the morphogenesis, coupled with nano-scale bio-molecular approaches to angiogenesis, can be used, from our point of view, for construction of the realistic mathematical, biophysical and medical engineering background for designing of the micro -andљ nano-sensors. In this context, it isљ importantљ development of the so hybrid models that also can be coupled with computer signal processing of biomedical data and application of the different physical fields ( ultrasound, infra-red and laser subjection).