Mathematical Modeling of Cardiovascular System Dynamics Using a Lumped Parameter Method

Shim, Eun Bo; Sah, Jong Youb; Youn, Chan Hyun

doi:10.2170/jjphysiol.54.545

Cited by 33 publications

(21 citation statements)

References 44 publications

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“…For the vascular system electrical circuit analogue models (sometimes called lumped, or distributed, parameter models) have been developed. These models exploit an analogy between fluid flow through a compliant pipe network, and electrical circuits 164. The fluid flow, pressure and tube compliance correspond respectively to current, voltage and capacitance in the electrical circuit.…”

Section: Interaction With the Cardiovascular Systemmentioning

confidence: 99%

The use of computational fluid dynamics in the development of ventricular assist devices

Fraser

Taşkın

Griffith

et al. 2011

Medical Engineering & Physics

227

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Progress in the field of prosthetic cardiovascular devices has significantly contributed to the rapid advancements in cardiac therapy during the last four decades. The concept of mechanical circulatory assistance was established with the first successful clinical use of heart-lung machines for cardiopulmonary bypass. Since then a variety of devices have been developed to replace or assist diseased components of the cardiovascular system. Ventricular assist devices (VADs) are basically mechanical pumps designed to augment or replace the function of one or more chambers of the failing heart.Computational Fluid Dynamics (CFD) is an attractive tool in the development process of VADs, allowing numerous different designs to be characterized for their functional performance virtually, for a wide range of operating conditions, without the physical device being fabricated. However, VADs operate in a flow regime which is traditionally difficult to simulate; the transitional region at the boundary of laminar and turbulent flow. Hence different methods have been used and the best approach is debatable. In addition to these fundamental fluid dynamic issues, blood consists of biological cells. Device-induced biological complications are a serious consequence of VAD use. The complications include blood damage (haemolysis, blood cell activation), thrombosis and emboli. Patients are required to take anticoagulation medication constantly which may cause bleeding. Despite many efforts blood damage models have still not been implemented satisfactorily into numerical analysis of VADs, which severely undermines the full potential of CFD. This paper reviews the current state of the art CFD for analysis of blood pumps, including a practical critical review of the studies to date, which should help device designers choose the most appropriate methods; a summary of blood damage models and the difficulties in implementing them into CFD; and current gaps in knowledge and areas for future work.

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Section: Interaction With the Cardiovascular Systemmentioning

confidence: 99%

The use of computational fluid dynamics in the development of ventricular assist devices

Fraser

Taşkın

Griffith

et al. 2011

Medical Engineering & Physics

227

236

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“…But for limited data in an ICU setting, unique parameter identification would only be obtained if a small subset of the parameter set is optimized. Thus, the majority of parameters have to be fixed at generic values which are only ever known on a population level, not for individual patients [43][44][45]. Therefore, pre-determined dynamics would be assumed, which are likely wrong in fast changing critical care patients.…”

Section: Discussionmentioning

confidence: 99%

“…The identified parameter changes can then be analyzed as time progresses, and trends and variations can be compared between patients. For example, population assumptions on reflex response [41,45] could be characterized within known bounds, and included in the model. Thus, the concept is to let the clinical data itself guide the modelling, with only basic model structures initially assumed in the process.…”

Section: Discussionmentioning

confidence: 99%

Unique parameter identification for cardiac diagnosis in critical care using minimal data sets

Hann

Chase

Desaive

et al. 2010

Computer Methods and Programs in Biomedicine

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Lumped parameter approaches for modelling the cardiovascular system typically have many parameters of which a significant percentage are often not identifiable from limited data sets. Hence, significant parts of the model are required to be simulated with little overall effect on the accuracy of data fitting, as well as dramatically increasing the complexity of parameter identification. This separates sub-structures of more complex cardiovascular system models to create uniquely identifiable simplified models that are one to one with the measurements. In addition, a new concept of parameter identification is presented where the changes in the parameters are treated as an actuation force into a feed back control system, and the reference output is taken to be steady state values of measured volume and pressure. The major advantage of the method is that when it converges, it must be at the global minimum so that the solution that best fits the data is always found.By utilizing continuous information from the arterial/pulmonary pressure waveforms and the end-diastolic time, it is shown that potentially, the ventricle volume is not required in the data set, which was a requirement in earlier published work. The simplified models can also act as a bridge to identifying more sophisticated cardiac models, by providing an initial set of patient specific parameters that can reveal trends and interactions in the data over time. The goal is to apply the simplified models to retrospective data on groups of patients to help characterize population trends or un-modelled dynamics within known bounds. These trends can assist in improved prediction of patient responses to cardiac disturbance and therapy intervention with potentially smaller and less invasive data sets. In this way a more complex model that takes into account individual patient variation can be developed, and applied to the improvement of cardiovascular management in critical care. Keywords :Model-based cardiac diagnosis ; Cardiovascular system ; Integral-based parameter identification ; Pressure waveform ; ECG ; Intensive care unit IntroductionIn critical care, cardiovascular dysfunction can be easily misdiagnosed due to incomplete information and the complexities involved, leading to premature discharge or non-optimal treatment [1][2][3]. It is also a major cause of increased length of stay and death [4,5]. Demand for critical care is growing dramatically severely affecting healthcare delivery [6][7][8]. The overall goal of this research is to use computational cardiac models to better aggregate available clinical data in an intensive care unit (ICU) into a more readily understood physiological context for clinicians. The computational models can be used to reveal non-linear dynamics and interactions that are not readily apparent in the data.A major difficulty faced with cardiovascular modelling in general, is the level of detail these models typically include. For example multi-scale modelling approaches utilizing finite elements have successfully expl...

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“…However, because the transmission speed differs between the 2, the stimulus-reaction curves also differ, such that the response time of the parasympathetic nerve is fast (0.5 - 1 s) and that of the sympathetic nerve is slow (3 - 10 s). This model, developed by DeBoer et al6 for the command transmission of autonomic control function, was successfully introduced in studies by Heldt et al7 and Shim et al8 The ganglion transmission model and autonomic control function used here have thoroughly been discussed in a review by Shim et al9…”

Section: Methodsmentioning

confidence: 99%

Numerical Simulation of the Effect of Sodium Profile on Cardiovascular Response to Hemodialysis

et al. 2008

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PurposeWe developed a numerical model that predicts cardiovascular system response to hemodialysis, focusing on the effect of sodium profile during treatment.Materials and MethodsThe model consists of a 2-compartment solute kinetics model, 3-compartment body fluid model, and 12-lumped-parameter representation of the cardiovascular circulation model connected to set-point models of the arterial baroreflexes. The solute kinetics model includes the dynamics of solutes in the intracellular and extracellular pools and a fluid balance model for the intracellular, interstitial, and plasma volumes. Perturbation due to hemodialysis treatment induces a pressure change in the blood vessels and the arterial baroreceptors then trigger control mechanisms (autoregulation system). These in turn alter heart rate, systemic arterial resistance, and cardiac contractility. The model parameters are based largely on the reported values.ResultsWe present the results obtained by numerical simulations of cardiovascular response during hemodialysis with 3 different dialysate sodium concentration profiles. In each case, dialysate sodium concentration profile was first calculated using an inverse algorithm according to plasma sodium concentration profiles, and then the percentage changes in each compartment pressure, heart rate, and systolic ventricular compliance and systemic arterial resistance during hemodialysis were determined. A plasma concentration with an upward convex curve profile produced a cardiovascular response more stable than linear or downward convex curves.ConclusionBy conducting numerical tests of dialysis/cardivascular models for various treatment profiles and creating a database from the results, it should be possible to estimate an optimal sodium profile for each patient.

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Mathematical Modeling of Cardiovascular System Dynamics Using a Lumped Parameter Method

Cited by 33 publications

References 44 publications

The use of computational fluid dynamics in the development of ventricular assist devices

The use of computational fluid dynamics in the development of ventricular assist devices

Unique parameter identification for cardiac diagnosis in critical care using minimal data sets

Numerical Simulation of the Effect of Sodium Profile on Cardiovascular Response to Hemodialysis

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