Finite state machine implementation for left ventricle modeling and control

Figures

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  Fig. 1. Left Ventricular Pressure–Volume Relationship (Stouffer [30]). a Schematic of LV pressure–volume loop in a normal heart. In Phase I, preceding the opening of the mitral valve, ventricular filling occurs with only a small increase in pressure and a large increase in volume, guided along the EDPVR curve. Phase II constitutes the first segment of systole called isovolumetric contraction. Phase III begins with the opening of the aortic valve; ejection initiates and LV volume falls as LV pressure continues to increase. Isovolumetric relaxation begins after the closure of the aortic valve constituting Phase IV. b Effects of increasing preload on a LV-PV loop with afterload and contractility remaining constant. Loop 2 has an increased preload compared to loop 1 by rolling the arterial elastance (Ea) line parallel while keeping the slope (Ea) constant, resulting in an increase in SV. c Effects of increasing afterload on a LV-PV loop with preload and contractility held constant. This consists of increasing the slope of the Ea line. d Effects of increasing contractility on a LV-PV loop with preload and afterload remaining constant. This consists of increasing the slope (Ees) of the ESPVR…

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  Fig. 2. Computational model of example PV loop developed in Simulink™ to reflect Eqs. 4, 5, 6, 7, and 8, to be utilized to find the critical points which define the initiation of phases 1, 2, and 4. a reflects the system of equations in this example, capable of solving in real-time. b presents a graph of these equations with critical points annotated. The driving values can be interchanged with clinical values for individualized PV assessment, as well as can be controlled over time for determining the effects of preload, afterload, and contractility changes. These values are presented in Tables 1 and 2

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  Fig. 3. State transition diagram of sequential decision-based control logic represented in Mealy machine structure form was developed to control the transition between left ventricular PV phases. The Variables, parameters that are held constant, are Piston cross-sectional area (A), b3, b2, b1, b0, Isovolumetric Contraction Offset, Systolic Ejection Rate, and Systolic Ejection Offset. The Inputs, parameters that can change with time, are \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{LV}}_{\text{ESP}}$$\end{document}LVESP, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{LV}}_{\text{ESV}}$$\end{document}LVESV, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}…

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  Fig. 4. Presented is the hydraulic testing model developed utilizing Simulink® and Simscape™. This system was designed to replicate the dynamics of a force-based piston pump model that drives the pressure within a chamber between two opposing check valves, conditions reflected within the left ventricular portion of an MCS. All block element parameter values that were modified are noted in the diagram, while any parameters not noted were left standard to the block’s original parameter values. Additionally, for any element parameter denoted as ‘Variable’, these values were not left constant for all simulations presented. The hydraulic testing model is a one-input, four-output system. The input is the force [N] applied to the piston and is regulated by means of the Stateflow® control architecture. The outputs are simulated LVV [mL], simulated LVP [mmHg], simulated AoP [mmHg], and LAP [mmHg]

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  Fig. 5. The outlined approach was effective at simulating the characteristic LV-PV relationship. Preload, afterload, and contractility changes in time were simulated by means of manipulating the input variables of the computational model via evenly-spaced discrete increments that change per cycle count. The LV-PV loop, pressure versus time, and volume versus time graphs are presented for each simulation. Displayed in a is the derived LV-PV loop, based on the computational model parameters determined using DataThief on loop 1 of Fig. 1b and presented in Fig. 2. The parameters for this LV-PV loop constitutes the initial conditions for the subsequent simulations. b presents the system correctly responding to a discrete change in preload. c reveals the correct afterload change response to the PV relationship. d displays the correct system response to contractility change. Each simulation was run for a total simulation time of 10 s and the system takes one cycle before it settles. The system functions consistently for every preceding cycle. The heart rate begins at approximately 60 bpm for each simulation. The reference force [N] produced by the FSM as well as the piston position [cm] can be…

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  Fig. 6. The outlined approach was effective at simulating Heart Failure with Normal Ejection Fraction (HFNEF) and the Control developed by means of a preload reduction analysis conducted in 2008 by Westermann et al. [50] and presented in Fig. 1 of their investigation. The ESPVR, Ea, and EDPVR curve coefficients were developed utilizing DataThief to find the associated LVESP, LVESV, LVEDP, and LVEDV for the initial and final loops, as well as evaluate the EDPVR curve. These datasets were analyzed over a 10 s total simulation time and for each simulation is the LV-PV loop; LVP, LAP, and AoP versus time; and volume versus time graphs. a presents the Control where the slope and y-intercept of Ea was divided into evenly-spaced increments to constitute 4 intermediate discrete steps between the initial and final cycle parameters. HFNEF is presented in b. The slope and y-intercept of Ea was also divided into evenly-spaced increments to constitute 4 intermediate discrete steps between the initial and final cycle parameters. For both simulations, the results produced an error of less than 1 mmHg and 1 mL for all targeted datasets and reflect a mean heart rate [bpm] within the range of mean values…