In response to the growing shortage of donor organs and the success of ventricular assist devices (VADs) as a bridge-to-transplant therapy, the role of VADs has expanded to long-term support in patients with end-stage heart failure.1–3 Widespread clinical acceptance of VADs as “destination therapy” (or permanent support) will require safe and effective VAD support for a minimum of 5 years with patient outcomes comparable with heart transplantation. To achieve this objective, VADs require in-use device monitoring and longterm reliability.4,5 In the benchmark Randomized Evaluation of Mechanical Assistance for the Treatment of Congestive Heart Failure (REMATCH) study for VAD destination therapy, device failure was reported to be 35% after 2 years,6 falling well short of acceptable performance criteria. Despite recent engineering improvements, device failures or malfunctions are still a major concern.7–9
Early investigation of second-generation continuous flow pumps, such as axial flow (AF) and centrifugal flow (CF) VADs, has demonstrated improved reliability and durability compared with previous devices.10,11 However, the probability of VAD failure may be underestimated for destination therapy because the majority of reported studies did not anticipate long-term VAD support, and study end-points were often only reported for support up to 24 months.6,10,11 Computational reliability analysis has indicated that continuous flow VAD reliability decreases precipitously after 4 years of use.12,13 Furthermore, AF and CF VADs have no valves to prevent retrograde flow, which may increase the risk of patient mortality in the event of device failure.8,9 Even if VAD stoppage is detected, emergency responses may be challenging, invasive, and must be accomplished quickly for patient survival.14,15 Although VAD failure is still a significant concern, methods for early fault detection can assist in mitigating the challenges associated with catastrophic VAD events.
Despite the critical need and potentially fatal consequences of VAD failure, development of safe and effective fault detection system(s) has been limited. Because of redundant device design, catastrophic failures are typically caused by multiple subsystem faults, which may lead to eventual catastrophic failure.13 Current methods to detect various subsystem VAD faults use multiple sensors and complex analysis techniques.4 However, monitoring VAD with implanted sensors during long-term support will increase the complexity of the overall system. Fault detection systems that do not rely on additional sensors or blood-contacting sensors minimize additional complications, such as sensor drift, thrombosis, and infection. Conversely, limiting the number of sensors may result in a loss of system monitoring accuracy, which is required for typical parameter estimation methods for fault detection.16,17 Therefore, a VAD fault detection algorithm based on direct analysis of a single intrinsic or noninvasive sensor measurement may solve many of these limitations.
In this study, a robust VAD fault detection algorithm was developed to meet the design criteria of minimal, nonblood-contacting sensors, and direct signal analysis. The fault detection strategy uses VAD motor speed characteristics in response to an input step change in motor current. A significant change in initial mean VAD speed, settling time, and final mean VAD speed was observed during fault conditions. Importantly, the VAD faults could be detected even with 10% revolutions per minute (rpm) measurement noise with both axial and centrifugal VADs. The VAD fault detection algorithm is device independent and may deliver a robust, reliable, nonintrusive means to minimize catastrophic VAD failures.
Model of the Circulatory System
The proposed VAD fault detection algorithm was tested using computer simulation of the human cardiovascular system in heart failure during AF and CF VAD support. The computer simulation model was validated over a range of clinically equivalent test conditions and has been used to develop and test physiologic control algorithms for mechanical circulatory support devices.18–21 In brief, the computer model subdivides the human circulatory system into four valves and eight blocks (left ventricle [LV], right ventricle, pulmonary arterial and venous circulations, systemic circulation, coronary circulation, vena cava, and aorta). Each block is characterized by its resistance, compliance, pressure, and blood volume. The right and LV blocks were characterized with time-varying compliance. The coronary block was modeled with time-varying compliance and resistance. The remaining blocks were characterized by constant resistances and compliances. The volume of blood in each block is described by an expression for the macroscopic material balance, which is a function of volume (V), pressure (P), compliance (C), and resistance (R), given by:
where dV n /dt is the rate of change of volume in block n, F in is the blood flow rate into the block, and F out is the blood flow rate out of the block. Models of AF or CF VADs were integrated into the cardiovascular simulation model, and tested during normal and fault test conditions as described below.
Model of the Axial Flow Ventricular Assist Device
A parameter-based AF VAD model developed by Choi et al. 22 was used in this fault detection study. The AF VAD was driven by a brushless direct current (DC) motor, described by the equation23:
where J is the inertia of the rotor, ω is the rotor speed in rad/s, T e is the motor torque, T p is the load torque, and B is the damping coefficient. The motor torque can be related to the amplitude of the phase current, I, and the back EMF constant, K B, through the equation:
In addition, the load torque can be calculated as a function of pump rotational speed and VAD-generated flow, F p, with the following equation:
where a 0 and a 1 are correlation constants. To obtain a closed cardiovascular system-VAD model, an equation for pump flow rate in terms of pump rotational speed and pressure difference across the pump, ΔP, was used22,24:
where b 0, b 1, and b 2 are experimental constants. The AF VAD was integrated with the circulatory system model as a parallel flow path from the LV to the aorta blocks. The normal parameters were experimentally identified and are given as: J = 9.16 × 10−7 kg m2, B = 6.6 × 10−7 kg m2/s, a 0 = 7.38 × 10−13 kg m2 s/ml3, a 1 = 1.98 × 10−11 kg m2 s/ml, b 0 = −0.296 mm Hg s/ml, b 1 = −0.027 mm Hg s2/ml, and b 2 = 9.33 × 10−5 mm Hg s2.22
Model of the Centrifugal Flow Ventricular Assist Device
A parameter-based model for a CF VAD, developed by Kitamura et al.,25 was used to test the fault detection algorithm. The equations for the CF VAD model are:
where F p, ω, and ΔP are as defined above, φ is the total inertance of the inlet and outlet cannulas, J 1 is the inertia of the rotor, T R is the kinetic friction coefficient, ωfull is the rotor speed at full support, K 1 is the torque constant of the DC motor, I is the pump current, and c 1, c 2, c 3, c 4, and K 2 are viscosity-dependent parameters. The CF VAD was integrated with the circulatory system model as a parallel flow path from the LV to the aorta blocks. The normal parameters were determined experimentally and are given as c 1 = 6.841 × 104 mm Hg s2/ml, c 2 = 4.718 × 10−3 mm Hg s2/ml2, c 3 = 2.636 × 10−4 kg m2/s, c 4 = 1.012 × 10−6 kg m2/ml, J 1 = 4.756 × 10−6 kg m2, K 1 = 0.0051 kg m2/(s2 A), K 2 = 4.7664 × 10−3 mm Hg s2, φ = 2 mm Hg s2/ml, and T R = 1.9992 × 10−3 kg m2/s2.25
Modeling VAD Faults and Measurement Errors
The limit cycle input currents, I, required to achieve full (5.0 L/min) and partial (2.5 L/min) support with normal AF and CF VAD function were determined. The parameters of the AF and CF VAD equations were altered to simulate faults (Table 1). For the AF VAD, three groups of parameter variations were tested: 1) K B\J\B, 112 variations; 2) a 0\a 1, 25 variations; and 3) b 0\b 1\b 2, 125 variations. Three comparable groups of parameter variations were also tested for CF VAD: 1) K 1\J 1\T R, 112 variations; 2) c 3\c 4, 25 variation; and 3) φ\K 2\c 1\c 2, 375 variations. Earlier studies of DC motor faults17,26,27 were referenced to select the variation range for the parameters (Table 1). The variation ranges for the experimentally determined constants were set at −20% to +20%. Measurement errors in VAD rpm were modeled as uniformly distributed noise of 1%, 5%, and 10% of the rpm magnitude. Ten simulations at each measurement noise level were performed to test the robustness and accuracy of the VAD fault detection algorithm.
VAD Fault Test Algorithm
VAD fault test simulations were initiated with the previously determined full-support input current and initial conditions for normal AF and CF VAD. The VAD fault detection algorithm developed in this study was a motor current step-down test, from full-flow support motor current levels to partial flow-support motor current levels. A partial support step down was chosen to avoid retrograde flow through the VAD and to maintain some level of support, thus minimizing the risk to patients with heart failure. The motor current step down was initiated after 150 seconds of simulated VAD support. For fault detection, the mean limit cycle VAD rpm before and after the step test (initial and final rpm), and the settling time to reach the final rpm (t s) were measured. To determine the rpm settling time, the rpm measurements were smoothed using a low-pass filter to minimize the pressure-dependent rpm oscillations generated by the native heartbeat. The t s was defined as the time required for the rpm to remain within 98% of the total rpm change after the motor current step down.
The effect of blood viscosity on VAD rpm dynamics was tested using viscosity-dependent parameters (c 1, c 2, c 3, c 4, and K 2) for the CF VAD. The viscosity-dependent parameters were experimentally determined at fluid viscosities of 3.5, 4.2, 5.1, and 6.2 cP.25 Responses with blood viscosity of 3.5 cP were used as the basis for comparison to responses with the higher blood viscosities. The tests and analyses aforementioned were applied to measure the effect of blood viscosity on VAD fault detection.
Data were analyzed off-line with MATLAB (MathWorks, Natick, MA) and PRISM (GraphPad, La Jolla, CA) data analysis software. A value of p < 0.05 was considered statistically significant. N-way ANOVA was used to compare the VAD speed responses between the fault modes per variation group. For each fault condition with random measurement noise, 10 simulations were performed per noise level (n = 10). Statistical analysis for variance of fault conditions with measurement noise was performed using a one-sample Student’s t-test. The hypothetical values for comparison were derived from the normal VAD condition responses calculated without measurement noise. For the viscosity dependence test comparisons, the hypothetical values were derived from the 3.5 cP condition responses without measurement noise. Mean initial rpm, mean final rpm, and t s response overlaps were determined by comparing the minimum and maximum values of VAD response ranges for each fault condition with those of the normal VAD condition. If any overlap occurred in the rpm or settling time ranges, the fault was considered to be undetectable using the fault detection algorithm.
Failure Modes, Model Parameters, and Step Response
All simulated failure modes produced significant and observable changes in settling time (t s), the initial mean VAD rpm, and the final mean VAD rpm in response to the motor current step down (Figure 1). As an example, the t s increased by 10.7 seconds when the b 0\b 1\b 2 parameters were increased by 20% for AF VAD. Similarly, the t s increased by 22.0 seconds, a nearly fourfold increase from the normal condition, when c 3\c 4 parameters were both changed −20% for the CF VAD. In addition, rpm changes of up to 1,760 and 310 rpm were generated for AF and CF VADs, respectively. These results demonstrate that various VAD faults can produce detectable changes in ts, the initial mean rpm, and the final mean rpm in response to motor current step changes.
An analysis was performed to identify which VAD parameter changes were the significant sources of variation for the measured rpm responses and which of the measured speed responses were the most sensitive. The majority of model parameters were significant sources of variation for initial mean rpm, final mean rpm, and t s in response to the motor current step (Table 2). In our simulations, the rotor inertia of both AF and CF VADs had the least impact on the measured rpm responses (AF: initial mean rpm and ts, p > 0.05; CF: all measured responses, p > 0.05). The CF VAD cannula inertance parameter, φ, does not produce variation for initial mean rpm and less significant variation for final mean rpm. For the tested fault modes of the AF VAD, the initial mean rpm was the least sensitive to changes in AF VAD parameters. For the CF VAD, t s was the least sensitive measured response. The final mean rpm was the most sensitive to parameter changes with both VAD models (AF: all parameters, p < 0.01; CF: all parameter expect J, p < 0.05).
Fault Mode with Measurement Error
The effects of measurement error on the VAD speed responses were assessed by introducing uniformly distributed 1%, 5%, and 10% rpm noise (n = 10 simulations per noise level; Figure 2). The theoretical speed responses were defined from the normal VADs without applied measurement noise. Most of the tested fault modes with applied measurement noise produced significantly different rpm responses when compared with the theoretical normal VAD responses (Figure 3). Even if 10% measurement noise was applied and only one of the three responses (initial rpm, final rpm, or settling time) was observed, VAD faults were detected in 96.5% and 87.8% of simulated AF and CF VAD faults, respectively (Figure 3, C and F). If all the three responses were considered and if a significant change in one of the responses per VAD condition would identify a fault, then the fault detection rate with 10% noise improved to 99.6% for AF VAD and 97.2% for CF VAD (Figure 3, G and H).
Overlap of Normal and Fault Mode Responses
In practice, the theoretical VAD speed responses would not be known a priori. Thus, it would be advantageous to characterize and compare measured ranges of speed responses for each individual pump. Ranges of VAD speed responses for the normal and fault conditions were measured with 1%, 5%, and 10% measurement noise (n = 10 simulations per noise level). The simulated fault was assumed to be detected when the VAD rpm and t s ranges of the fault condition did not overlap with the normal condition ranges (Figure 4). Using this criterion, 95.4% of AF VAD faults and 89.6% of CF VAD faults were identified, even with 10% measurement noise (Figure 4, G and H).
Step Response Dependence on Viscosity
The VAD speed responses to motor current changes may be significantly affected by blood viscosity. The CF VAD model with experimentally determined viscosity-dependent parameters for four different fluid viscosities (3.5, 4.2, 5.1, and 6.2 cP) was used to test the effect of viscosity on the fault detection step test. Viscosity has a large effect on the measured rpm responses and t s (Figure 5). The t s decreased by 32% when blood viscosity was increased from 3.5 to 4.2 cP. All the response changes were attenuated at the higher viscosities, with the smallest response changes occurring between the 5.1 and 6.2 cP conditions. When random measurement noise was applied to the VAD rpm, the measured responses were all significantly different than the defined normal condition (3.5 cP viscosity) responses. Furthermore, the responses did not overlap with the normal condition responses at any of the tested measurement noise levels (Figure 6).
As VADs are used more frequently and for longer durations, such as destination therapy, the risk of VAD malfunction and failure may increase the cause for concern. Currently, methods to detect VAD faults are limited, which places patients using VAD at a greater risk for a catastrophic device failure. The VAD fault detection algorithm described in this article demonstrates proof-of-concept for a simple and noninvasive method for fault detection. The fault detection algorithm showed success with both axial and centrifugal VAD models, suggesting that this algorithm is device independent for continuous flow pumps.
A significant advantage of the proposed VAD fault test is that only measurement of VAD rpm is needed, which does not require additional sensor(s). In clinical use, VAD speed can be accurately measured with nonblood-contacting sensors (e.g., Hall effect sensor) or noninvasively using an acoustic technique.28 Rotational speed is already measured in most continuous flow VAD. Thus, using speed measurements for fault detection would neither compromise device durability nor increase hardware complexity.
Motor fault detection strategies can be categorized as methods based on signal analysis, motor dynamic models, and knowledge, as described by Liu et al. 17 The fault test proposed in this article is based on signal analysis, which has several advantages in the context of VAD. The signal analysis method avoids the complicated modeling of the VAD motor. Although this study used parameter-based models of two VADs (axial and centrifugal) and the cardiovascular system, this was only necessary for the computational simulation of the integrated VAD-cardiovascular system. Parametric or dynamic models of the VAD are not needed to clinically implement the proposed fault test. The proposed fault detection test is VAD-independent, as it uses signals that are ubiquitous for all continuous flow VADs: current as the input signal and rotational speed (rpm) as the output signal. Consequently, the same fault detection algorithm was able to detect >90% of faults in both axial and centrifugal VADs, even with 10% rpm measurement noise (Figures 3 and 4).
The knowledge-based method for fault detection can be accurate, but it is very complicated and time-consuming to generate the data (i.e., experience) necessary to build this type of model. The proposed fault detection algorithm only requires knowledge of step responses to controlled input current during normal VAD operation to detect faults. Therefore, a knowledge base of unpredictable and infrequent VAD fault modes is not necessary. The analysis of device speed in response to a well-controlled input step, as developed in this study, has the potential to be widely and quickly adopted for patients with heart failure, supported by continuous flow VADs.
The proposed VAD fault detection test requires a step change in motor current. Issues of VAD speed response sensitivity and physiologic consequences for the patient were considered when selecting the magnitude and direction of the step change. A motor current step increase could be limited by the baseline level of VAD support per patient or by maximum operating motor speeds. Therefore, a motor current step down was chosen for the fault detection test; however, a step down would lead to a temporary reduction in the level of mechanical support provided to the patient. A motor current step down was chosen that only partially decreased VAD flow (~2.5 L/min) to maintain considerable support for the patient and avoid retrograde flow through the device. The results of the article demonstrated that a motor current step down of this magnitude was sufficient to detect AF and CF VAD faults. A partial and brief (<1 minute) reduction in VAD flow during this test should be well tolerated by patients with end-stage heart failure and will be conducted under clinical supervision, which will pose minimal clinical risk. The proposed fault detection algorithm may enable planned device exchanges when significant faults are detected and minimize the risk of catastrophic VAD failures.
The tested fault conditions in this study were extensive to demonstrate the efficacy of the proposed fault detection method that requires only prior knowledge of VADs during normal operation. The fault conditions of this study were simulated by varying all physical (J, B, K B and J 1, T R, K 1) and experimentally determined parameters (a 0, a 1, b 0, b 1, b 2 and c 1, c 2, c 3, c 4, K 2) of the VAD models. To simulate realistic fault conditions, the magnitudes of variation for the physical parameters were adapted from the study by Liu et al. 17 (Table 1). The maximum positive and negative relative changes (“% variation”) in the motor parameters used in the study by Liu et al. were set as the bounds for % variation of the matched parameters in this model (J, B, K B). The ranges of variation for the nonphysical parameters were conservatively selected based on the bounds of the physical parameters. By this method, the impact of potential faults on the motor parameters was less likely to be exaggerated. Accordingly, many of the simulated fault conditions in this article are expected to be representative of actual VAD faults.
The VAD speed responses chosen to analyze were initial rpm, final rpm, and settling time. Overall, these responses were significantly affected by simulated faults (Table 2). However, there were some notable differences between the AF VAD and CF VAD responses because of parameter changes. The mean initial rpm had the least sensitive response for AF VAD, whereas the settling time was the least sensitive response for CF VAD. The moment of inertia for CF VAD did not significantly alter any of the VAD speed responses. Consequently, faults associated with changes in the inertia of a CF VAD rotor, such as minor deposition of thrombus or rotor wear/erosion, may not be detectable using this algorithm.
In clinical practice, theoretical VAD speed responses will not be known a priori. Hence, the baseline range of VAD speed responses will need to be measured and characterized in each patient. This can be routinely accomplished soon after device implantation and while the device is known to be operating in a normal condition. During subsequent scheduled patient visits to the hospital, the VAD speed responses to the motor current step down test can be measured and compared with the baseline responses. As established in this study, responses that do not overlap with the baseline speed responses would indicate a potential fault. This fault detection method had a detection rate of approximately 95% for AF VAD and 90% for CF VAD. Importantly, the fault detection algorithm is very robust, as demonstrated by the >90% fault detection rates, tested with more than 750 simulated fault modes. It should be noted that these detection rates are for the worst-case scenario of uniformly distributed rpm measurement noise of 10%. In clinical practice, VAD rpm measurement errors are more likely to be in the order of 1 to 2%, which is typical for a Hall effect rpm sensor. Furthermore, uniformly distributed measurement noise is much more difficult to overcome than normally distributed measurement noise.
Blood viscosity significantly affects motor speed responses during the fault detection tests. Therefore, blood viscosity must be measured or estimated accurately to determine VAD faults. The VAD fault detection test will need to be performed in a clinical setting where blood viscosity can be accurately determined using a simple blood draw and measurement of hematocrit. The initial rpm, final rpm, and settling time are linear over the physiologic blood viscosity range (3.5–5.1 cP), as demonstrated by the data (Figure 5). Thus, the baseline VAD speed responses to the motor current step can be adjusted based on the patient’s current blood viscosity.
There are several limitations associated with the computer simulation model. The performance of the computer simulation during the failing heart test condition is representative of clinical observations from a purely hemodynamic viewpoint. Clearly, a computer simulation is not intended to replace the importance and significance of in vivo models and is incapable of replicating all expected clinical responses. However, cardiovascular and VAD computer models do provide a valuable, initial proof-of-concept platform for testing the VAD fault detection algorithm. A potential limitation of the proposed fault detection algorithm is the dependence on a known-patient baseline response, which may vary as a result of acute or chronic changes of patient cardiovascular status (e.g., increased ventricular contractility, changes in afterload). However, chronic myocardial recovery has been reported in less than 5% of patients undergoing VAD implantation. In addition, patients with heart failure have significantly diminished baroreflex and autonomic regulation and are often under medication to avoid hypertension during VAD support, which would minimize significant changes in afterload.29,30 Thus, this proof-of-concept study focused on simulating a wide range of potential VAD fault conditions with a fixed model of the human cardiovascular system. Studies quantitatively determine the impact of patient cardiovascular status on the fault detection algorithm to account for baseline variations is currently ongoing.
Fault detection methods are not meant to substitute for optimal and fault-tolerant VAD designs. The benefits of VAD durability and accurate fault detection are multiplicative, yet the best way to minimize undetected faults is to minimize the occurrence of faults. Despite these limitations, this study demonstrates feasibility of the VAD-independent fault detection algorithm which uses a simple motor current step test and rpm sensor. With further refinement, the proposed fault detection algorithm may become a valuable test for detecting faults and averting catastrophic VAD failures.
The authors thank Dr. Tadashi Kitamura, who graciously provided the experimentally determined centrifugal VAD model parameters used in this study.
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Keywords:Copyright © 2013 by the American Society for Artificial Internal Organs
heart failure; ventricular assist device; VAD failure; axial flow; centrifugal flow