Multifractality through Non-Markovian Stochastic Processes in the Scale Relativity Theory. Acute Arterial Occlusions as Scale Transitions
Nicolae Dan Tesloianu,
Lucian Dobreci,
Vlad Ghizdovat,
Andrei Zala,
Adrian Valentin Cotirlet,
Alina Gavrilut,
Maricel Agop,
Decebal Vasincu,
Igor Nedelciuc,
Cristina Marcela Rusu,
Irina Iuliana Costache
Affiliations
Nicolae Dan Tesloianu
Cardiology Department, “Sf. Spiridon” University Hospital, 700111 Iasi, Romania
Lucian Dobreci
Department of Physical and Occupational Therapy, “VasileAlecsandri” University of Bacau, 600115 Bacau, Romania
Vlad Ghizdovat
Biophysics and Medical Physics Department, Faculty of Medicine, “Grigore T. Popa” University of Medicine and Pharmacy, 16 University Str., 700115 Iasi, Romania
Andrei Zala
Municipal Emergency Hospital Moineşti, 1 Zorilor Street, 605400 Moinești, Romania
Adrian Valentin Cotirlet
Department of Physical and Occupational Therapy, “VasileAlecsandri” University of Bacau, 600115 Bacau, Romania
Alina Gavrilut
Faculty of Mathematics, “Alexandru Ioan Cuza” University, Carol I Bd., No. 11, 700506 Iasi, Romania
Maricel Agop
Physics Department, “Gheorghe Asachi” Technical University, Prof. dr. docent Dimitrie Mangeron Rd., No. 59A, 700050 Iasi, Romania
Decebal Vasincu
Biophysics Department, Faculty of Dental Medicine, “Grigore T. Popa” University of Medicine and Pharmacy, 16 University Str., 700115 Iasi, Romania
Igor Nedelciuc
Institute of Cardiovascular Disease “G.I.M. Georgescu”, 700503 Iasi, Romania
Cristina Marcela Rusu
Physics Department, “Gheorghe Asachi” Technical University, Prof. dr. docent Dimitrie Mangeron Rd., No. 59A, 700050 Iasi, Romania
Irina Iuliana Costache
Cardiology Department, “Sf. Spiridon” University Hospital, 700111 Iasi, Romania
By assimilating biological systems, both structural and functional, into multifractal objects, their behavior can be described in the framework of the scale relativity theory, in any of its forms (standard form in Nottale’s sense and/or the form of the multifractal theory of motion). By operating in the context of the multifractal theory of motion, based on multifractalization through non-Markovian stochastic processes, the main results of Nottale’s theory can be generalized (specific momentum conservation laws, both at differentiable and non-differentiable resolution scales, specific momentum conservation law associated with the differentiable–non-differentiable scale transition, etc.). In such a context, all results are explicated through analyzing biological processes, such as acute arterial occlusions as scale transitions. Thus, we show through a biophysical multifractal model that the blocking of the lumen of a healthy artery can happen as a result of the “stopping effect” associated with the differentiable-non-differentiable scale transition. We consider that blood entities move on continuous but non-differentiable (multifractal) curves. We determine the biophysical parameters that characterize the blood flow as a Bingham-type rheological fluid through a normal arterial structure assimilated with a horizontal “pipe” with circular symmetry. Our model has been validated based on experimental clinical data.
