We all know, while medical professionals know the most, that Medicine IS a Hierarchical, Heterogeneous, Multiscale Science. Most of us, meanwhile, don't know that these are just words in Medicine, in spite that the mountains of studies were published on this point of view. The deficiency is that, of course, the mathematical, physical models, mathematics of that modeling are in all those studies that use the Homogeneous GO theorem. The consecutive development models are of one scale. That is the starting point for not only the verbal presentation of models in medicine, but everything else - understanding of disease, healing methods, policies, etc. That's strange for medical professionals - the mathematics, physics and disease treatments? Meanwhile, the digital graphical images usage, that now is in the core of medicine practices (and was), is all due to the math application in medicine.
As it is established in HSP-VAT the mathematical formulation, statements, and modeling of physical processes occurring in strongly heterogeneous media results on the whole in the necessity for the particular medium scaled characteristics development, and accordingly, for process governing equations. This is all applicable to the Heterogeneous Scaled nature of assignments within the Biology/Medicine disciplines.
We have developed concepts, theoretical presentations, and methods to address a number of bio-medical type processes along with our development of general theories for transport phenomena in hierarchical, heterogeneous, and scaled media. The basic methodology allows us to treat multiple scale transport processes ranging from the nano-, microscopic to the macroscopic. Some of the phenomena we can model with a little enhancement of our present already developed basic theories.
Among major aims of the HSP-VAT application to Biological/Medicine issues/problems are the following:
1) Provide theoretical derivation of main sets of governing equations (GE) on each level of the hierarchy and estimate feasibility of closure developments.
2) Develop theoretical mechanisms and varieties of closure approaches for each specific biological or/and medicine system hierarchical level.
3) Estimate the feasibility of theoretical procedures for the development of numerical convergent algorithms for solution evaluations of the equations governing the process.
Among other areas of interests for us in the Ht Biology/Medicine we have been treating the issues related to blood circulation in the variety of human tissues.
Since no single model exists at the present time that could account for multiscaling and consider the actual blood transport within the tissue or organ morphology, (well, the methods using not proper mathematics we are not able to consider seriously), we have been working over the suggested earlier by us the development which treats the blood flow in at least four scale heterogeneous systems, including: 1- separate cells (red and white) and dispersed cell medium modeling as well as capillary and arteriole wall scale modeling; 2 - single blood vessel models including previous multiphase scale governing equation statements; 3 - single tissue sample capillary network scale modeling; 4 - finally the three phase blood transport modeling in the tissue morphological vessel networks in conjugation with the soft tissue's phases. Here could be mentioned:
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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
vessels wall permeability.
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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 have made some contribution 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 for Artificial Kidney Membranes"
To give a better idea how it might be procurable, the contribution to following project 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.
"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 based on 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 latter project had been formed even into the proposal to NIH in 1994 - see the sub-section here.
It is of great interest to us the questions related to the functionality and physical and mathematical formulation of the drug development altogether with the disease modeling in vivo. As long as these are profoundly the Heterogeneous Multiscaled Multiphysics and Multiphase tasks then that all is in the area of only treatable character while with the HSP-VAT approach. Few commonly important diseases are within our development procedure.