We have developed methods to address a number of bio-medical type processes along with our development of general theories for transport phenomena in heterogeneous media. The basic methodology allows us to treat multiple scale transport processes ranging from the microscopic to the macroscopic. Some of the phenomena we could model with a little enhancement of our present already developed basic theories are:

       interaction between overall bulk blood perfusion in brain matter and vascular morphology characteristics such as diameter of vessels ( capillaries and arterioles), cerebral vascular tree morphometry and vessel wall permeability.

       mathematical models for Cerebral Blood Flow (CBF) could be developed and will constitute the significant improvements to those used at present time and described, for example, in "Textbook of Head Injury" (Muizelaar, J.P., pp. 221-240). The scaled VAT introduction to the CBF would lead to a much more accurate calculation of CBF characteristics in normal and posttraumatic intracranial medium.

Few projects we have some involvement in and could contribute to are:


"Cerebral Blood Flow Models for Normal and with Acute Disorders Brain Intracranial Medium"


"Cerebral Blood Flow Extracranial Thermal Diffusion Measurement Technique"


"Noninvasive Transcranial High Resolution Doppler Ultrasonography Improvement"


"Optimization of Filter's Morphology in Artificial Kidney Membranes"



To give a better idea how it might be procurable, the contribution to following projects titled


"Multiscale Modeling of Brain Blood Supply System"


A biomechanical model of the brain blood supply system, beginning with the major blood input arteries and extending through a consequent networks of arterioles, capillaries, venules and sinuses,could be developed. The first step would be to create a mathematical model of the brain vessel network morphology suitable for the scaled modeling and then map and develop a data base for the brain vessel network morphology (BVNM). A detailed map of BVNM and a database with morphometrical data would be used in subsequent steps of the simulation, starting with the development of a theoretical, physical and mathematical basis to simulate the flow of a non-Newtonian blood medium with species exchange in at least three morphologically different brain blood networks. A thorough morphometrical investigation of the BVNM would be undertaken, accompanied by a numerical network simulation. A specific theoretical biomechanical approach, database and software for the BVNM map would be the result of this project. The database and BVNM map would have independent market value and could be the basis for distinct improvement of medical service and research.


had been made basically combining the respected brain tissue engineering morphology and scaling consideration of the processes.

Another project comfortably came into an envelope as the one naturally treatable with the VAT scaling methodology:


"Hierarchical Multiphase Muscle Blood System Simulation"


This project would be aimed at developing a physically based methodology for modeling and simulating transport phenomena is a multiphase healthy blood medium within a muscle tissue blood vessel network. Since no one model exists at the present time that can treat the multiple scales that are present in actual blood vessel morphology, the suggested development would treat the blood flow as a four scale heterogeneous system where the four scales are:

1) dispersed cell medium modeling of separate cells (red and white) including capillary and arteriole wall scale modeling,

2) single blood vessel models that are based on from the first multiphase scale governing equation statements,

3) single muscle fiber capillary network scale modeling, and

4) three phase blood transport modeling in a muscle fiber bundle capillary network.

To create these kinds of models, the present nonlinear multiscale morphological modeling approach will be used and significantly oriented toward the biomedical improvements. The modeling procedures will provide a more accurate physical model enabling considering the transport of blood constituents at each level of the hierarchy. After being developed, these models would offer significant advantages over existing one-phase-one-vessel models, due to their multilevel description and the direct dependence on given specific muscle morphology.




This later project had been formed even into the proposal to NIH in 1994 -