By Charles E. Taylor, Virginia Commonwealth University
Mock circulatory loops (MCLs) simulate the human circulatory system to enable testing of ventricular assist devices and other cardiac assist technologies. When conducting tests using an MCL, investigators must adjust the settings on each component in the loop. Components typically include a mechanical pump, a compliance chamber, and a peripheral resistance valve (Figure 1). In the past, these setting adjustments were performed manually, a method that was imprecise, time-consuming, and susceptible to human error.
Using Simulink® and Simscape™, I modeled a fully automated MCL in which the heart pump, compliance chamber, and peripheral resistance valve are controlled via microprocessors. With this setup, researchers can accurately simulate a wider range of the cardiac conditions and dynamics needed to evaluate the performance of cardiac assist devices.
MCLs typically employ a lumped parameter model for arterial compliance and peripheral resistance. In a lumped parameter model, the entire resistance to flow experienced by the ventricle or ventricular assist device is combined into a single resistance value. In an MCL, this value is controlled via the peripheral resistance valve (Figure 2). As a result, this valve must have an operating range that spans the resistance produced by all arterial vasculature for any condition that the MCL will simulate.
Because commercially available valves did not provide the required operating range and resolution, I had to create my own. As part of this process, I modeled the valve using Simulink, Simscape, and SimHydraulics® (Figure 3a). The primary purpose of this model was to characterize key valve parameters that could not be measured directly, including the valve’s coefficient of discharge and its critical Reynolds number. This model was integrated into a larger Simulink model of the entire MCL for system-level simulations.
I then compared the pressure produced by the numerical model and the physical system (Figure 3b). The experimental data set was used as the training set for determining the parameters in the numerical model; the degree of correlation indicated the performance of the parameter estimation routines employed.
After constructing a valve prototype, I measured the upstream and downstream pressure as I varied the flow rate and position of the valve actuator, which determines the valve orifice area. The data set, which included the flow rate and resistor position input variables, was used to validate the parameter estimation results from Figure 3b at a different operating state. I then used this experimental data in Simulink and Simulink Design Optimization™ to find values for the valve’s coefficient of discharge and critical Reynolds number.
After characterizing the valve parameters, I integrated the valve model into a larger Simulink model of the MCL and ran simulations to determine whether the valve’s operating range met requirements. The initial valve prototype did not, so I machined it to increase the orifice size and reran the experiments and parameter estimation. After two iterations, I had the valve I needed. As a final step, I connected the valve to a stepper motor to enable precise, automated opening and closing.
The Harvard Apparatus pulsatile blood pump (model 1423) is the gold standard for producing flow conditions within an MCL. By setting the heart rate, stroke volume, and percent systole (the fraction of each stroke in which blood flows out of the pump) on this device, researchers can reproduce output similar to that of a human’s left ventricle. As with the peripheral resistance valve, however, all setting changes must be made manually by adjusting dials and cranks on the device.
To automate this process, I wanted to bypass the dials and other manual controls with an embedded controller that would enable the heart rate, stroke volume, and percent systole to be adjusted programmatically and remotely. I began by creating a model of the device driveline in SolidWorks®. I then used SimMechanics Link to import this model into SimMechanics™ (Figure 4).
I incorporated the driveline model into a complete model of the pump, created using Simulink, Simscape, SimElectronics®, and SimMechanics. This larger model included the device’s voltage supply, piston, electric motor, and gear box, as well as the hydromechanical interface on the pump head (Figure 5). As with the peripheral resistance valve, I used parameter estimation to characterize several of the model's parameters that were not directly measurable: motor damping, motor inertia, and pump piston friction. The complete plant model helped me better understand how the pump worked, and was vital to the development and tuning of the pump controller software, which I deployed to a Microchip Technology PIC18F2550 microcontroller.
The compliance chamber in my MCL includes a circular elastic membrane separating the fluid below from the air above. Compliance is controlled by changing the air pressure in the upper compartment of the chamber. With older, manual compliance chambers, the pressure setting is changed manually, and there is no way to determine the system’s compliance in real time. The compliance chamber that I designed includes a real-time controller that uses input from a pressure sensor and a laser displacement sensor to monitor compliance (Figure 6). The controller can maintain a set point and simulate dynamic changes in arterial compliance.
As with the peripheral resistance valve and heart pump, I began by developing a physical model of the plant. This model, developed using Simulink, Simscape, and SimHydraulics, incorporated several initially unknown parameter values, including membrane elasticity; I had to test numerous materials before finding a membrane with the appropriate stiffness and durability. Using parameter estimation in Simulink Design Optimization, I identified these model parameters based on experimental data. Once the Simulink model accurately reflected the performance of my custom-built compliance chamber, I used it to tune the discrete proportional integral (PI) controller gains, enabling the controller to maintain system compliance at a set point specified by the researcher. The controller tuning was performed automatically with Control Design Toolbox™. Automated controller design and stability verification enabled me to deploy a control architecture with minimal programming effort.
The assembled numerical model of the mock circulatory loop was completed by connecting up the subsystems. I then reevaluated the initial steady-state condition values for the components in each of these subsystems to ensure the cohesiveness of the entire model at the start of the simulation.
The mock circulatory loop model enables the user to control the set points of the various subsystems to orchestrate conditions of interest. The complete Simulink model of the system also enables the user to apply parameter estimation routines to patient data to determine the settings needed to replicate human pressure and flow waveforms. The model can also be used to rapidly evaluate a medical device's safety under a large number of conditions. Event sequences can be used to determine whether any of these conditions would send a device into failure.
My current work focuses on simulating pulmonary circulation characteristics in the MCL using a centrifugal pump. For this project I used Embedded Coder® to generate code for the control system from a Simulink model, and xPC Target™ to perform hardware-in-the-loop testing of the controller. At each step of MCL development, the ability to simulate a device in Simulink has deepened my understanding of the device’s operating characteristics and accelerated the development of the control software.
Dr. Charles E. Taylor completed this work as part of his doctoral dissertation in the Artificial Heart Laboratory at Virginia Commonwealth University, under the direction of Dr. Gerald E. Miller. Dr. Taylor is continuing this research as an assistant professor in the mechanical engineering department at the University of Louisiana at Lafayette.
Published 2013 - 92147v00