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1

Dialysis therapies: Investigation of transport and regulatory processes using mathematical modelling

Pstras Leszek, Stachowska-Pietka Joanna, Debowska Malgorzata, Pietribiasi Mauro, Poleszczuk Jan, Waniewski Jacek

Biocybernetics and Biomedical Engineering

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2022

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Vol. 42, no. 1

60--78

EN

Haemodialysis (HD) and peritoneal dialysis (PD) are the main kidney replacement therapies for patients with end-stage renal disease. Both of these life-sustaining therapies replace the key functions of the failing kidneys, i.e. the removal of the excess body water and waste products of metabolism as well as the restoration of fluid-electrolyte and acid-base balance. The dialysis-induced multi-scale transport and regulatory processes are complex and difficult to analyse or predict without the use of mathematical and computational models. Here, following a brief introduction to renal replacement therapies, we present an overview of the most important aspects and challenges of HD and PD, indicating the types and examples of mathematical models that are used to study or optimize these therapies. We discuss various compartmental models used for the study of intra- and interdialytic fluid and solute kinetics as well as distributed models of water and solute transport taking place across the peritoneal tissue or in the dialyzer. We also discuss models related to blood volume changes and cardiovascular stability during HD, including models of the thermal balance, likely related to intradialytic hypotension. A short overview of models of acid-base equilibration during HD and mineral metabolism in dialysis patients is also provided, along with a brief outline of models related to blood flow in arteriovenous fistulas and cardiovascular adaptations following the fistula creation. Finally, we discuss the model-based methods of assessment of dialysis adequacy in both HD and PD.

2

Segmentary strategy in modeling of cardiovascular system with blood supply to regional skin

Li Zhongyou, Jiang Wentao, Diao Junjie, Chen Chong, Xu Kairen, Fan Haidong, Yan Fei

Biocybernetics and Biomedical Engineering

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2021

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Vol. 41, no. 4

1505--1517

EN

Objective: The focus of this study is to model the cardiovascular system (CS) involving regional skin blood flow (SBF) to gain new insights into the skin-CS relationship. Methods: A lumped parameter model with a series of electrical components was developed to model the CS involving SBF. Four parts were considered: the heart, arterial circulation, microcirculation (including the skin and other tissues), and the venous system. The model was validated based on previous publications. Additionally, the body surface was divided into seven blocks replaced by lumped resistances in this model, including the head, upper limbs and neck, chest and back, anterolateral abdomen, posterior abdomen, lower limbs, and buttocks. The SBF of each block was described using a weighted average method (relative ratio of cutaneous blood perfusion and regional body surface area) Results: Cardiodynamics characterized the properties of cardiac cycles, including isovolumic contraction, accelerated ejection, decelerated ejection, isovolumic diastole, and filling phases. Blood flow and pulse pressure in the arterial trunk declined and increased, respectively, from the aorta root to the distal portion, exhibiting normal cardiovascular properties. Accordingly, the blood pressure of the arterial branches attached to the arterial trunk also satisfied normal physiological characteristics; the blood flow of all the arterial branches exhibited good agreement with previous studies. Additionally, the modeled SBF of each region was consistent with the data from the weighted average method. Conclusion: This model effectively demonstrates the normal properties of the CS that involves regional SBF and may be promising in the prediction of the skin-CS relationship.

3

Numerical and experimental investigation on nonlinear dynamic characteristics of planetary gear train

Zhang Jianwu, Guo Han, Yu Haisheng, Zhang Tong

Journal of Theoretical and Applied Mechanics

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2020

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Vol. 58 nr 4

1009--1022

EN

A deep hybrid electric vehicle (DHEV) equipped with a Ravigneaux compound planetary gear train (PGT) encounters severe gear whine noises during acceleration in the EV drive mode. For the analysis of vibro-acoustic sources, a 5DOF lumped-parameter vibration model for the PGT dynamic system is established as well as sound pressures radiated from the transmission on a test bench are measured for data processing and recognition. By comparison between numerical and experimental analyses, natural vibration modes of the PGT are examined and high frequency modal resonances in association with the planetary gears are observed only to cause narrow band whine noises. Furthermore, a 2DOF reduced dynamic model for the planetary gears with consideration of nonlinearities such as time-varying mesh stiffness and backlash is proposed, and numerical solutions to bifurcations and dynamic instabilities of the two sets of planetary gears are obtained. It is found that nonlinear vibration behaviour of the long and short planets are major causes of shock and vibration of the hybrid transmission. Severe vibro-acoustic noises excited dominantly by the planetary gears are alleviated after implementing micro-geometry modifications to the PGT.

4

Numerical study of a two-way MR mount in squeeze-mode

Gołdasz J., Sapiński B.

Czasopismo Techniczne. Elektrotechnika

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2016

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Y. 113, iss. 2-E

29--40

EN

In the paper, the authors present the results of a numerical study of a magnetorheological (MR) damper prototype operating in the so-called squeeze mode. The analyzed prototype allows achieving a symmetrical response in both directions of piston motion. The authors show the results of magnetostatic analyses of the electro-magnetic circuit of the device and lumped parameter model using calculations of the control circuit and the damping force output.

PL

W artykule przedstawiono wyniki obliczeń prototypowej konstrukcji tłumika z cieczą MR działającej w trybie ściskania. Analizowany prototyp pozwala uzyskać identyczny zakres sił tłumienia w obu kierunkach ruchu. Autorzy prezentują osiągi tłumika oszacowane na podstawie obliczeń polowych oraz obliczeń z wykorzystaniem modelu o parametrach skupionych.

5

Theoretical study of a twin-tube magnetorheological damper concept

Gołdasz J.

Journal of Theoretical and Applied Mechanics

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2015

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Vol. 53 nr 4

885—894

EN

In this study, the author presents a theoretical model of a semi-active magnetorheological (MR) twin-tube damper concept. The model relies on geometric variables and material properties and can be used in engineering and research studies on damper structures. Other non-linear characteristics, namely, the fluid chamber compressibility, fluid inertia, cylinder elasticity, friction, one-way check valves are included into the model as well. The author studies the performance of the damper model as design variables are varied, and the results are analysed and discussed.

6

Zmodyfikowana metoda potencjałów węzłowych w analizach energetycznych budynków

Narowski P.

Fizyka Budowli w Teorii i Praktyce

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2015

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T. 7, nr 3

35--48

PL

W artykule przedstawiono metodę wyznaczania ilości ciepła do ogrzewania i chłodzenia budynku, wykorzystującą model budynku w postaci sieci przepływu ciepła z elementami gałęzi o skupionych parametrach pojemności i przewodności cieplnej. Analogia matematyczna sieci przepływu ciepła i sieci elektrycznych pozwala na zastosowanie podobnych metod rozwiązywania tych układów. W artykule opisano metodę potencjałów węzłowych oraz wskazano jej wady, które często uniemożliwiają zastosowanie tej metody do opisu sieci przepływu ciepła w budynku. W dalszej części przedstawiono modyfikację metody potencjałów węzłowych, która usuwa wykazane wady metody klasycznej, pozwalając na opis sieci przepływu ciepła w budynku z wykorzystaniem sieci z węzłami w których zadane są wartości temperatury. Przedstawiona metoda pozwala na automatyczne, komputerowe, formułowanie układu równań opisujących sieć przepływu energii w budynku umożliwiając szybkie modyfikowanie schematów modeli budynku używanych do analiz energetycznych. W przeciwieństwie do równań podanych w normie PN EN ISO 13790, opisana metoda nie wymaga wyprowadzania nowych równań opisujących uproszczony godzinowy model dynamiki cieplnej budynku. Układ równań zmodyfikowanego modelu godzinowego budynku może być automatycznie generowany na podstawie topologii schematu modelu przyjętego do obliczeń. Na końcu artykułu w dodatku przedstawiono przykładowe macierze składowe gałęzi oraz macierz główną i wektor wyrazów wolnych dla modelu 5R1C wyznaczony zmodyfikowaną metodą potencjałów węzłowych.

EN

This paper presents principles of modified nodal analysis used to solve lumped parameters networks which model whole building heat exchange. The lumped capacitance and resistance 5R1C or 6R1C method used for whole building modelling with simple hourly method utilize predefined equations presented in PN EN ISO 13790 standard. Modification of building energy network model causes that the model equations have to be determined again. The problem can be solved with graph theory and classic nodal analysis used for determining node potentials, which are in the case of building energy analysis, nodes temperature. This method whatever is very useful, cannot be used for networks containing branches with ideal potential sources. Modified nodal analysis combines dual graph topology with network admittance branches classified for the first group, and impedance branches classified for second group. Branch elements can be presented as stamp matrices which are used for define main matrix and right hand side vector of network equation system. Modified nodal analysis can be used for automatic formulation of equation set which then can be solved with any efficient numerical method. This approach allows to quickly modify building model and provide energy analysis without deriving new equations for that model as presented in PN EN ISO 13790 standard.

7

Study of flow-induced vibration phenomena in automotive shock absorbers

Sikora M.

Mechanics and Control

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2014

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Vol. 33, no. 2

58--64

EN

The purpose of this study was to develop a model of the dynamic behavior of a hydraulic vehicle double-tube shock absorber. The model accounts for the effects of compressibility, valve stiction, inertia, etc. and can be suitable for use in the analysis on flow-induced pressure fluctuations in the device. The author highlights all major variables to influence the output of the shock absorber, and then proceeds by performing a series of simulations using the developed model. The model is demonstrated to operate well in the large amplitude and low frequency range as well as the small amplitude and high frequency excitation operation regimes. The results are presented in the form of time histories of pressures in each fluid volume of the damper, flow rates through the valves, piston rod acceleration and force. Fast Fourier Transform (FFT) graphs are presented, too, in order to identify the major components of the pressure fluctuation phenomena in the frequency domain.

PL

Celem niniejszej pracy jest zbudowanie modelu dwururowego tłumika hydraulicznego odzwierciedlającego dynamiczne zachowanie zaworu. Stworzony model uwzględnia szereg zjawisk takich jak ściśliwość cieczy, bezwładność, siłę potrzebną do rozsunięcia dwóch równoległych płaszczyzn, pomiędzy którymi znajduje się olej (tzw. siła lepienia) i inne. Pozwala to na symulacje zjawisk dynamicznych i badanie drgań wywołanych przepływem oleju. Zostały uwzględnione wszystkie najważniejsze zmienne wpływające na generowanie drgań. Model działa poprawnie zarówno w niskich, jak i wysokich częstotliwościach. Rezultaty przeprowadzonych symulacji zostały przedstawione w postaci przebiegów czasowych ciśnienia, natężenia przepływu przez zawory oraz przyśpieszenia tłoczyska tłumika. Na wykresach częstotliwościowych widoczne są najważniejsze składowe obserwowanych drgań.

8

Analiza cieplna silnika PMSM za pomocą metody elementów skończonych oraz schematów cieplnych

Mynarek P., Kowol M.

Maszyny Elektryczne : zeszyty problemowe

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2014

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Nr 4(104)

49--54

PL

Silniki synchroniczne z magnesami trwałymi dzięki dużej gęstości mocy coraz chętnie wykorzystywane są w motoryzacji. Nowe zastosowanie silników elektrycznych skutkuje zwiększonymi wymaganiami odnośnie układu chłodzenia. Zbyt duże nagrzewanie silnika PMSM może wpływać negatywnie na pracę magnesów trwałych oraz spowodować skrócenie czasu życia maszyny w wyniku termicznego starzenia się izolacji. Dlatego też niezmiernie ważna jest dokładna znajomość rozkładu temperatury w poszczególnych częściach maszyny elektrycznej, w różnych jej stanach pracy. W artykule przedstawiono analizę cieplną silnika synchronicznego z magnesami trwałymi przeprowadzoną w oparciu o metodę schematów cieplnych jak również o metodę elementów skończonych (MES). Zaprezentowane podejście wykorzystujące obydwie metody i pozwala na skuteczną analizę maszyny. Opisano także metodę homogenizacji uzwojeń wsypywanych. Wyniki symulacji komputerowych zostały zweryfikowane pomiarowo na obiekcie rzeczywistym silnika.

EN

Permanent magnet synchronous motor due to the high power density are often used in hybryd electric vehicles. New application of electric motors results in increased demands on the cooling system. Too high heating in a PMSM motor can cause negative effects on the work of permanent magnets and a significant shortening of the life of the machine due to the phenomenon of thermal aging of insulation. Therefore, it is extremely important to know the exact temperature distribution in different parts of the electrical machine In its various operating conditions. The paper presents lumped parameter thermal model and FE model of permanent magnet synchronous motor. A method for homogenization of a winding stator is also described. In order to validate correctness of the calculation results, measurements on the physical model of the machine are carried out.

9

Role and applications of circulatory models in cardiovascular pathophysiology

Ferrari G., Kozarski M., De Lazzari C., Górczyńska K., Pałko K. J., Zieliński K., Di Molfetta A., Darowski M.

Biocybernetics and Biomedical Engineering

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2009

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Vol. 29, no. 4

3-24

EN

Circulatory models are relevant for research, education and testing of prosthetic devices/components. Independently of its structure that can be numerical, physical or hybrid the models can be used in different areas of cardiovascular pathophysiology. However, the models are often used to reproduce specific circulatory conditions instead of being used as 'systemic' tools. That is to say, the models are used to evaluate the global effects of external disturbances such as pathologies, therapies, special environments or surgery on the circulatory system. Aim of this paper is to illustrate a family of circulatory models developed to represent the whole circulatory system in pathophysiological conditions describing some of the possible applications.

10

Open loop hybrid circulatory model: the effect of the arterial lumped parameter loading structure on selected ventricular and circulatory variables

Kozarski M., Ferrari G., Zieliński K., Górczyńska K., Pałko K. J., Tokarz A., Darowski M.

Biocybernetics and Biomedical Engineering

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2008

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Vol. 28, no. 1

17-27

EN

Different combinations of the artero-ventricular coupling design (numerical, physical and hybrid) and the arterial system structure (four-element standard, simplified, modified and three-element three-lump "ladder" Windkessel) have been applied in an open loop circulatory model to test their influence on selected ventricular and circulatory variables. Numerical investigations have shown that a four-element Windkessel with an introduced in series lumped inertance can evoke some numerical problems e.g. when combined with the simplified ventricular model containing "ideal" zero switching time heart valves or constant valve resistance during opening. The four-element Windkessel structure modification i.e. replacing the in series inertance by the parallel one, considerably improves the network match. Also the three-element three-lump "ladder" Windkessel has been found very useful in the blood circulation modelling thanks to relatively small input inertance and high input capacitance of its first lump.

11

Development of hybrid (numerical-physical) models of the cardiovascular system: numerical-electrical and numerical hydraulic applications

Ferrari G., Kozarski M., De Lazzari C., Górczyńska K., Darowski M., Tosti G.

Biocybernetics and Biomedical Engineering

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2005

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Vol. 25, no. 4

3-15

EN

Circulatory models are relevant to research, education and prosthetic devices/components testing. Their structure can be both numerical and physical, according to the specific needs. Numerical models are often developed first and then followed or accompanied by physical models. This approach is associated with higher costs, less accuracy and time-consuming development. Circulatory models defined as hybrid (merger of numerical and physical sections) can solve these problems. This paper presents two applications of the hybrid model with the physical section based on two different structures (electrical and hydraulic). The results show that the model can represent hemodynamic relationships in different circulatory conditions, including IABP assistance.

12

Physical modelling of the cardiovascular system : development of a new simulation system based on hybrid (numerical-hydraulic) components

Ferrari G., De Lazzari C., Kozarski M., Clemente F., Górczyńska K., Mimmo R., Tosti G., Guaragno M.

Biocybernetics and Biomedical Engineering

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2003

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Vol. 23, no. 2

3-15

EN

Research, education, testing of assist devices and training are among the applications of physical models of the circulation. Unfortunately, they are rather expensive and the scope of their use is structure-dependent as it is not easy to modify them. As numerical models do not have these limitations, our aim is to develop a physical model of the circulation limited to the sections of interest merging them with numerical models representing the remaining parts of the circulatory system. The system under development is therefore a hybrid where physical and numerical sections, merged together, represent the circulatory system. The sections developed till now represent one of the ventricles and part of the arterial tree. This paper is devoted to the description of the hybrid ventricular model and its first applications.