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Mathematical model for a Herschel-Bulkley fluid flow in an elastic tube

100%
Vajravelu K., Sreenadh S., Devaki P., Prasad K.
Open Physics
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2011
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vol. 9
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issue 5
1357-1365
EN
The constitution of blood demands a yield stress fluid model, and among the available yield stress fluid models for blood flow, the Herschel-Bulkley model is preferred (because Bingham, Power-law and Newtonian models are its special cases). The Herschel-Bulkley fluid model has two parameters, namely the yield stress and the power law index. The expressions for velocity, plug flow velocity, wall shear stress, and the flux flow rate are derived. The flux is determined as a function of inlet, outlet and external pressures, yield stress, and the elastic property of the tube. Further when the power-law index n = 1 and the yield stress τ 0 → 0, our results agree well with those of Rubinow and Keller [J. Theor. Biol. 35, 299 (1972)]. Furthermore, it is observed that, the yield stress and the elastic parameters (t 1 and t 2) have strong effects on the flux of the non-Newtonian fluid flow in the elastic tube. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.
2
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The influence of high tone power therapy on the peripheral microcirculation in the lower limbs

86%
Nowakowska I., Szymańska J., Witkoś J., Wodarska M., Kucharzewski M., Dembkowski M.
Physiotherapy
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2009
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vol. 17
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issue 4
10-18
PL
Jedną z najnowszych metod wspomagania leczenia wielu schorzeń jest terapia energotonowa. Jest ona nowoczesnym sposobem terapii, powstałym na bazie badań naukowych na polu różnych dziedzin: medycyny, fizyki, matematyki, fizjologii, biochemii i innych. Dzięki tak rozległej płaszczyźnie badań nad High Tone Power Therapy (HiToP) można mówić o niej jako o zjawisku interdyscyplinarnym. Celem pracy była ocena wpływu terapii energotonowej na mikrokrążenie obwodowe kończyn dolnych. Materiał i metoda: badaniami objęto grupę 30 osób w wieku od 20 do 60 lat. W pierwszej podgrupie znalazły się osoby leczone z powodu chorób naczyń obwodowych w zakresie tętniczym i żylnym kończyn dolnych, odpowiednio 4 i 12 osób, a w drugiej osoby zdrowe (14 osób). Wszystkim badanym wykonano serię 10 zabiegów terapii energotonowej w okolicy kończyn dolnych stosując metodę SimulFAMx. Bezpośrednio przed, jak i po serii zabiegów dokonano pomiaru przepływu krwi metodą Laser-Doppler. Wyniki: u wszystkich badanych po wykonanych zabiegach zaobserwowano zwiększenie dynamiki przepływu w mikrokrążeniu obwodowym kończyn dolnych. Wyniki te wykazały pewne zróżnicowanie, aczkolwiek nie całkiem jednoznacznie. Pod wpływem zabiegów stwierdzono wyraźny wzrost przepływu u osób leczonych z powodu zaburzeń naczyniowych, w porównaniu do osób zdrowych, u których zanotowano znaczny wzrost tylko wartości minimalnych. Wnioski: wstępne wyniki wskazują, że terapia energotonowa może być cenną pomocą w leczeniu zaburzeń obwodowego krążenia krwi.
EN
One of the basic diagnostic methods of evaluating the microcirculation vessels is the Laser-Doppler examination which makes it possible to determine the dynamics of the flow and to evaluate the level of blood supply. Among the newest methods of adjunct treatment for various diseases is energotonic therapy which is a modern therapy based on researches carried out in various fields of science: medicine, physics, mathematics, physiology, biochemistry and other. Due to such a wide range of research fields the high tone power therapy may be said to be an interdisciplinary phenomenon. The aim of the research was to evaluate the effects of the high tone power therapy on peripheral microcirculation in the lower limbs. Material and Methods: the research group consisted of 30 people aged from 20 to 60 which was divided into two subgroups. The first subgroup included 16 people treated for peripheral vascular disease in the area of arteries and veins of the lower limbs - 4 and 12 people respectively - and the second subgroup included 14 healthy people. All the examined were undergone a series of 10 procedures of energotonic therapy in the lower limbs by means of the SimulFAMx method. In all the examined before and after the therapy the blood flow was measured using the Laser-Doppler method. Results: an increase in the dynamics of the blood flow in peripheral microcirculation in the lower limbs was observed in all the examined. The results showed certain diversification, yet it was not entirely clear. After the therapy there was a significant increase of the blood flow in patients treated for vascular disorders in comparison with the group of healthy people in which only the minimal values increased significantly. Conclusions: initial results indicate that the high tone energy therapy may be a valuable aid in treating disorders of the peripheral blood circulation.
3
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Viscoelastic changes in the blood and vascular wall in a pulsating circular flow

86%
Beraia M., Todua F., Khomeriki I.
Polish Journal of Medical Physics And Engineering
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2010
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vol. 16
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issue 1
43-53
EN
Altered flow conditions, such as separation and recirculationg zones, low and oscillatory shear stress, play an important role in the development of arterial disease. Endothelial denudation by the blood flow is the first step in atherosclerosis. The description of blood flow in vivo is complicated due to the viscoelasticity of vessel walls. However, conventional researches of the effect of the blood vessel viscoelasticity on the blood pressure wave propagation using non-linear one-dimensional models do not take into account the viscoelasticity, despite it being importance in the analysis of pulse wave propagation in arteries.The purpose of this paper is to study the impact of the arterial pulse wave on the viscoelastic blood flow and initial factors of atherosclerosis.In 12 healthy men (25-39 years of age) peak velocity, mean velocity, mean flow and net flow in the aorta have been investigated by MR angiography.Initial velocity was registered after 43msec of the ECG-R wave, and it differed from zero at all sites of the aorta, although net flow was equal to zero. Womersley's number from the ascending to the thoracic aorta decreased from 12.5 ± 1.5 to 7.3 ± 1.2; flow modified from inertio-elastic to viscous. Pulse pressure wave move on artery walls fifteen or more times more rapidly than the blood flow. In the aortic arch in protodiastole blood flow separated into the opposite directed streams resulting in wave superposition with the high net flow. At the isthmus area separated waves interferences and reflects to anterograde direction.Pulse oscillation increases strain rate to the contiguous vessel wall flow layers. At the sites with the flow wave negative interference vessel pulse oscillation attenuates and at the boundary reflection flow wave can shift the vessel wall.
4
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Effects of treadmill training on walking distance and lower limb blood flow in patients with intermittent claudication

72%
Mika P., Cencora A.
Medical Rehabilitation
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2005
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vol. 9(1)
3-9
PL
Cel: U pacjentów z chromaniem przestankowym regularnie prowadzony trening marszowy na bieżni prowadzi do wzrostu dystansu marszu. Mechanizm tej poprawy jest wieloczynnikowy a jedną z prawdopodobnych przyczyn może być wzrost przepływu tętniczego w kończynach dolnych. Przedmiotem badań była ocena zmian dystansu marszu oraz przepływu tętniczego w kończynach dolnych podczas treningu marszowego na bieżni u pacjentów z chromaniem przestankowym. Metoda: 80 pacjentów z miażdżycą zarostową kończyn dolnych (II stopień według Fontaine) było randomizowanych do programu treningowego lub do grupy kontrolnej. Pacjenci z grupy badawczej przez okres 3 miesięcy uczestniczyli 3 razy tygodniowo w treningu marszowym. Sesje składały się z wysiłków marszowych powtarzanych 3-krotnie, każdy o dystansie marszu wynoszącym 85% indywidualnie określonego dystansu chromania. Przed rozpoczęciem programu i po jego zakończeniu w obu grupach oceniano dystans pojawienia się chromania oraz zmiany w prędkości przepływu tętniczego w kończynach dolnych (pomiar indeksu pulsacji metodą dopplerowską). Wyniki: Po 12 tygodniach programu w grupie badawczej zaobserwowano wzrost indeksu pulsacji mierzony na tętnicy podkolanowej (43%), piszczelowej tylnej (59%) i grzbietowej stopy (78,8%). W grupie kontrolnej niewielki wzrost (11,4%) odnotowano na tętnicy podkolanowej. Towarzyszyła temu poprawa dystansu pojawienia się chromania – 119,6% w grupie badawczej i 16,9% w grupie kontrolnej. Zmiany były istotne statystycznie (p< 0,05). Wnioski: Wyniki badań wskazują, że trening marszowy prowadzony u pacjentów z chromaniem przestankowym prowadzi do korzystnych zmian przepływu tętniczego w kończynach dolnych w zakresie poprawy jego prędkości oraz znacznej poprawy dystansu marszu pokonywanego bez bólu.
EN
Background: In patients with intermittent claudication treadmill training improves their walking ability. While the benefits of an exercise rehabilitation programme are recognized, the mechanisms involved are not completely appreciated. The improvement in lower limb blood flow may by one of the mechanisms leading to the increase in walking distance. In the present study arterial blood flow in lower limb as well as walking distance were assessed before and after supervised pain-free treadmill training. Methods: Eighty patients with peripheral arterial occlusive disease (stage II according to Fontaine) were randomised into the treadmill program or to the control group. Patients in the exercising group participated for 3 months 3 times a week in supervised treadmill trainings. Each session consisted of 3 cycles, each amounting to 85% of the pain-free walking distance. Changes in arterial blood flow and the onset of claudication pain were assessed in both groups.Results: After 12 weeks of the treadmill training lower limb blood flow in exercising group significantly improved (p<0.05). Painfree walking distance was prolonged by 119,6% in the exercising group and only 16.9% in the control group. Those changes were statistically significant in both groups (p<0.05).Conclusion: The results indicate that exercise training program using intermittent walking to 85% of the onset of claudication pain leads to a significant improvement in lower limb blood velocity and increase in pain-free walking distance.
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