An Atraumatic Mock Loop for Realistic Hemocompatibility Assessment of Blood Pumps

Objective: Conventional mock circulatory loops (MCLs) cannot replicate realistic hemodynamic conditions without inducing blood trauma. This constrains in-vitro hemocompatibility examinations of blood pumps to static test loops that do not mimic clinical scenarios. This study aimed at developing an atraumatic MCL based on a hardware-in-the-loop concept (H-MCL) for realistic hemocompatibility assessment. Methods: The H-MCL was designed for 450 <inline-formula><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 50 ml of blood with the polycarbonate reservoirs, the silicone/polyvinyl-chloride tubing, and the blood pump under investigation as the sole blood-contacting components. To account for inherent coupling effects a decoupling pressure control was derived by feedback linearization, whereas the level control was addressed by an optimization task to overcome periodic loss of controllability. The HeartMate 3 was showcased to evaluate the H-MCL's accuracy at typical hemodynamic conditions. To verify the atraumatic properties of the H-MCL, hemolysis (bovine blood, n = 6) was evaluated using the H-MCL in both inactive (static) and active (minor pulsatility) mode, and compared to results achieved in conventional loops. Results: Typical hemodynamic scenarios were replicated with marginal coupling effects and root mean square error (RMSE) below 1.74 <inline-formula><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 1.37 mmHg while the fluid level remained within <inline-formula><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula>4% of its target value. The normalized indices of hemolysis (NIH) for the inactive H-MCL showed no significant differences to conventional loops (<inline-formula><tex-math notation="LaTeX">$\Delta$</tex-math></inline-formula>NIH = −1.6 mg/100 L). Further, no significant difference was evident between the active and inactive mode in the H-MCL (<inline-formula><tex-math notation="LaTeX">$\Delta$</tex-math></inline-formula>NIH = +0.3 mg/100 L). Conclusion and significance: Collectively, these findings indicated the H-MCL's potential for in-vitro hemocompatibility assessment of blood pumps within realistic hemodynamic conditions, eliminating inherent setup-related risks for blood trauma.


I. INTRODUCTION
H EART failure (HF) is a leading cause of death in developed countries with a prevalence that is predicted to rise in the upcoming decades [1].Heart transplantation is the therapy of choice for end-stage HF patients, yet increasingly challenged by the shortage of donor organs [2].For these patients, mechanical circulatory support (MCS) provides a valuable treatment option to improve survival and quality of life.Rotodynamic blood pumps (RBPs), predominantly used as left ventricular assist devices (LVADs), denote the vast majority of MCS devices implanted in the past decade with survival rates above 70% two years post-implantation [3], [4].However, clinical outcomes remain constrained by severe hemocompatibility-related adverse events (HRAEs), such as gastrointestinal bleeding and thromboembolic complications [5].To date, only 30% of all LVAD recipients remain free from life-threatening major adverse events including bleeding or strokes one year post-implantation [3].The high incidence of HRAEs with RBPs denotes an ongoing discussion.One evident limitation of current RBPs is their hydraulic conception based on classical turbomachinery for optimized hydraulic efficiency at one constant operating point, yet with potentially disturbed flow structures in off-design conditions [6].This idealized constant mode of operation does not reflect clinical settings, where LVAD support is characterized by a wide range of hemodynamic conditions, frequently leading to off-design operation: LVADs experience dynamic changes in head pressure resulting from the difference between arterial and pulsatile left ventricular pressures.Accordingly, LVADs operate in off-design conditions for approximately 50% of the cardiac cycle in typical patients [7] or even more in patients with smaller body height.Such off-design operation may be associated with compromised pump hemocompatibility [8], [9], [10] with clinical evidence pointing toward elevated blood trauma potential and increased risk for adverse events [9], [11], [12].
To date, detailed investigations of these blood trauma mechanisms under realistic hemodynamic conditions are limited by the lack of appropriate experimental models.In-vitro analysis of hemocompatibility remains restricted to experiments with constant flow and pressure conditions [13], [14], which are predominantly performed with blood from animals [10].Although numerous mock circulatory loops (MCL) were proposed [15], none of the presented setups seems to fulfill the requirements to replicate realistic hemodynamics without inducing collateral blood trauma by mechanical valves [16] or additional pumps [17].Thus, these setups significantly exceed the hardware-related hemolysis proportion compared to the standardized setup proposed by the American Society for Testing and Materials (ASTM) [13], [14].Consequently, we defined an MCL to be atraumatic if no additional hardware-related hemolysis is created compared to the current standard.Accordingly, key requirements for the design of an atraumatic pulsatile MCL include the incorporation of (i) hemocompatible materials with small surface area, (ii) sensors, actuators, and heating components without blood contact, and (iii) a circuit designed for low blood volumes to allow the use of one standard blood bag (450 ± 50 ml) in compliance with the standards of the ASTM [13], [14].
Most evolved, conventional MCLs are based on a hardwarein-the-loop (HIL) setup as previously proposed by Ochsner et al. [17].In such hybrid MCLs (H-MCLs), a numerical model of the cardiovascular system communicates in real-time with the physical RBP under investigation via a numericalhydraulic interface (composed of two characteristic reservoirs).The numerical-hydraulic interface simulates realistic in-and outlet pressures for the RBP by mimicking the cardiovascular response to the measured pump flow.This forms a multiple-input multiple-output (MIMO) system, which is characterized by inherent coupling effects, e.g. one input affects multiple outputs.Although coupling between the reservoir pressures upstream and downstream of the RBP may be anticipated, state-of-theart H-MCLs rely on single-input single-output (SISO) control strategies.In these setups, coupling effects are damped by hardware choices e.g.large fluid volumes in wide reservoirs and long tubing.Typically, additional pumps are implemented to control the fluid level of the two reservoirs.However, these characteristics are in conflict with the requirements for an atraumatic H-MCL.
The aim of this study was to realize and examine a novel H-MCL with an atraumatic design and an advanced control strategy for the hemocompatibility assessment of RBPs under realistic hemodynamic conditions.Hemolysis experiments were conducted to confirm that the novel setup does not induce  1. Atraumatic H-MCL setup with characteristic components and variables.The setup can be divided into a pneumatic part, consisting of the pneumatic supply network, two pneumatic proportional valves, and two pressure sensors, and a hydraulic part filled with blood, incorporating the RBP (HeartMate 3), two flow sensors, two level sensors, and a proportional pinch valve.The two reservoirs act as an interface between hydraulic and pneumatic parts.
additional hardware-related blood trauma compared to standardized static flow loops proposed for state-of-the-art hemolysis testing.

II. MATERIAL AND METHODS
In order to develop a setup that meets the requirements for an atraumatic H-MCL (Table I) a three-stage approach was followed: First, the hardware of the numerical-hydraulic interface was iteratively optimized.Second, a model of the numericalhydraulic interface was developed.Third, an advanced control strategy was derived and optimized for respective hardware choices.

A. Hardware
Fig. 1 shows the setup of the atraumatic MCL with its sensors and actuators.The hydraulic subsystem consists of two reservoirs (mimicking the left ventricle and the aorta, respectively) that are made of sealed cylindrical polycarbonate (Ø 75 mm × 3 mm × 130 mm), placed upstream and downstream of the RBP under investigation (here: HeartMate 3 (HM3), Abbott Inc, Chicago, USA).The pump's inflow cannula is directly inserted into the left ventricular reservoir, while the outflow is connected via a tube (l = 200 mm) with a clamp-on flow sensor (Sonoflow CO55, Sonotec GmbH, Halle, Germany) to the aortic reservoir.For all connections, hemocompatible 1/2 in (12.7 mm) silicone/polyvinyl chloride tubing is used.In the back-flow path, a proportional pinch valve (HPPV-12, Resolution Air Ltd., Cincinnati, USA) and a second clamp-on flow sensor (Sonoflow CO55, Sonotec GmbH, Halle, Germany) are attached to the tubing (l = 250 mm).The pinch valve allows adaptations of blood flow and therefore a control of the blood level monitored by capacitive level sensors (BCW0004, Balluff GmbH, Neuhausen, Germany), which are attached to the outside of both reservoirs.The flow throughout the pinch valve is strongly dependent on the current pressures in the reservoirs: If the pressures are equal, there is no driving force to generate a flow in the back-flow path -in this case, the pinch valve has no impact on the system.
The two reservoirs act as an interface between the hydraulic and pneumatic subsystems: The fluid pressures in both reservoirs are equal to the air pressure above its surface plus the hydrostatic pressure of the fluid column.Therefore, blood pressure can be controlled via the air mass inflow and outflow.To adjust the air mass flow, pneumatic proportional valves (MPYE-5-1/4-010-B, Festo SE & Co. KG, Esslingen am Neckar, Germany), connected to a pressurized air and vacuum network, are employed.Via relief valves (Niezgodka GmbH 91-2508-4 and 1831, Hamburg, Germany) the air and vacuum supply is limited to a relative pressure of approximately +0.68 bar (+510 mmHg) and −0.5 bar (−380 mmHg), respectively.The pneumatic connections consist of pneumatic quick couplings and suitable pneumatic tubing of Ø 12 mm.The current pressure inside the reservoirs is measured by clinical pressure transducers (TruWave, Edwards Lifesciences Corp., Irvine, CA, USA; measurement error ± 1 mmHg) that are approved for the use with blood.
The primary source of working fluid in the hydraulic loop is blood from one blood bag (450 ± 50 ml).Accordingly, the entire system is kept at body temperature to maintain physiologic conditions.For this purpose, the assembly is located under a transparent, air-tight dome (800 mm × 800 mm × 800 mm) made of polyvinyl chloride, with a large sealable aperture to take samples and operate the system.To keep the air temperature inside the dome at 37 °C, the temperature is monitored by a temperature sensor (Pt100, E-4, 5 × 17-Pt-3L-B-2Ts-M6, −90 to +200 °C) and connected to a temperature controller (A-senco TR-81, Pohltechnik.comGbR, Essingen, Germany) which controls a heat gun (ELEKTRON, Leister Technologies AG, Kaegiswil, Switzerland) that is inflating the dome with warm air.
The sensor and actuator signals are processed by a dSpace MicroLabBox (dSpace GmbH, Paderborn, Germany), that is running a control strategy described in Section II-C to control the pressure and blood level of the left ventricular and aortic reservoir, respectively.Note that the reference of the pressure control is calculated in real-time by a numerical model of the cardiovascular system as described in II-B1, based on the measured flow rate of the RBP.This control strategy is implemented and compiled in MATLAB Simulink (The MathWorks, Natrick, MA, USA) with a fixed step Backward Euler type solver and a step size of 0.0005 s.

B. Numerical Models 1) Model of the Cardiovascular System:
To calculate a realistic hemodynamic response to the flow rate of the RBP (physically measured in the H-MCL), an open loop numerical model for the cardiovascular system of a virtual patient was used [7]: The model of the left ventricle is based on Colacino et al. [18] and includes a time-varying elastance model with a nonlinear end-systolic and end-diastolic pressure-volume relationship.The cardiovascular parameters were chosen to meet patient data from Gupta et al. [19], with a heart rate of 91 bpm, a left atrial pressure of 13 mmHg, an aortic pressure of 84 mmHg and a right atrial pressure of 10 mmHg.Different parameter sets were chosen to mimic realistic physiological conditions of full support (no aortic valve opening) and partial support (aortic valve opening): Cardiac contractility was adapted by changing the peak pressure of the nonlinear end-systolic pressure volume relationship to 40 mmHg in full support and 92.5 mmHg in partial support condition [18].With a targeted total cardiac output of 4.75 ± 0.15 L/min in both conditions, the VAD speed was chosen to achieve a pump flow of about 2.25 ± 0.15 L/min in the partial support and 4.75 ± 0.15 L/min in the full support condition.To further assess the dynamic performance of the system two different heart rates (60 bpm and 120 bpm) were additionally investigated.

2) Model of the Numerical-Hydraulic Interface:
The atraumatic H-MCL was modeled focussing on the interaction between the pneumatic and hydraulic subsystems.One simplified assumption was made: Temperature-dependent terms were neglected, given that the whole system is tempered to 37 °C.Fig. 1 introduces important variables describing the system.
Pneumatic subsystem: The air pressure in reservoir i is described by the ideal gas law.With the time derivative of the ideal gas law, one obtains where d dt m i = ṁi is the air mass flow to the reservoir, and V i = V 0 − A h i is the air volume in dependency of the fluid level h i .Together with the specific gas constant R, the temperature T , the reservoir cross-sectional area A, and the volume of the empty reservoir V 0 , the air pressure is given by The mass flow rate ṁi passing a pneumatic proportional valve was modeled according to ISO 6358 and Beater et al. [20] and can be distinguished according to the normalized valve slide x pv in a negative ṁi− and positive ṁi+ flow rate Further the mass flow rate depends on the pressure ratio downstream and upstream of the valve.With the critical pressure ratio b (taken from the literature [20]) two cases can be distinguished: The flow rate equals the local speed of sound for respectively.With the supply pressure p + , the supply vacuum pressure p − , and the reservoir pressure p i , one obtains where C i (x pv , p i ) is the sonic conductance, ρ 0 is the density of air at reference condition, T 0 is the air temperature at reference condition and T is the upstream air temperature.The sonic conductance C i was measured in dependence of the normalized valve slide x pv and various pressures in the reservoir p i , to represent the inherent flow properties of the valve for a wide range of operating conditions.Hydraulic subsystem: The fluid level in reservoir i is described by a volume balance equation considering the flow upstream Q up and downstream Q down of the reservoir where Q up and Q down refer to the flow rates of the RBP Q p and the pinch valve Q hv , respectively.The flow through the pinch valve Q hv can be modeled with resistive R hv and inductive terms L hv .The resistance was modeled with the Darcy-Weisbach equation that allows the calculation of the pressure loss in the tubing considering both pipe friction and additional losses due to the pinch valve where l and d are the length and the inner diameter of the tube, λ is the friction factor, ρ is the fluid density, and ζ is the variable loss coefficient describing the resistance of the pinch valve.The friction factor λ was calculated depending on the flow regime, with the Hagen-Poiseuille equation (laminar flow) or with the Blasius equation (turbulent flow).The loss coefficient ζ(x hv , Q hv ) was determined from static experiments to map the characteristic resistance of the pinch valve as a function of the valve slide x hv and the current flow Q hv .The pressure difference to accelerate and decelerate the fluid due to its inertia L hv is given by Accordingly, the sum of ( 6) and ( 7) represents the overall pressure loss Δp hv of the pinch valve, which can be used to derive a differential equation for the pinch valve flow Accordingly, the pressure loss Δp hv equals the pressure difference between the reservoirs which comprises the air pressures p i and the hydrostatic pressure of the respective fluid column (= ρgh i ) with the fluid density ρ and the acceleration due to gravity g.These submodels result in four coupled nonlinear differential equations for the numerical-hydraulic interface representing the pressure and flow relationships within both the left ventricular and aortic reservoir

C. Control Strategy
To control the setup, initially, a SISO control structure was derived and implemented as suggested in state-of-the-art H-MCLs [17].This allowed the operation of the novel H-MCL, albeit strong coupling effects were observed with the small volume design that could not be eliminated despite careful tuning of the control parameters.
Therefore, given the nonlinear model of the hydraulicpneumatic interface (9), a decoupling control strategy was chosen to ensure precise trajectory tracking without deviations due to inherent coupling effects, while accounting for the nonlinearities of the system.For this purpose, a control approach was derived based on the method of feedback linearization and dynamic extension.
Atraumatic control behavior was defined by precise trajectory tracking of the hemodynamic pressures in combination with a low motion control of the pinch valve, characterized by marginal deviation of a constant valve position.Therefore, the minimal possible valve motion was assessed in an optimization task, showing that each cardiac cycle can be addressed by a constant valve opening.With these methods, an atraumatic and decoupling feedback control structure was derived.
1) Feedback Linearization: Feedback linearization describes an approach in which a nonlinear state feedback controller is designed to compensate for all nonlinearities of the system, thus creating an overall linear control loop [21].
To do so, a nonlinear multivariate system of the form Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
is considered, with m-dimensional input vector u, output vector y, and n-dimensional state vector x (Fig. 1).Accordingly, our nonlinear multivariate system ( 9) is described by a suitable choice of state, input, and output vectors and the corresponding vector fields f (x), g(x), and h(x), where denotes the head pressure between the reservoirs For feedback linearization to work, the system is reformulated by applying the time derivative to each system output where L f and L g represent Lie derivatives, that are defined as the product of the gradient of a scalar function h(x) and a vector field f (x) and g(x), respectively [21].In the case of L g j h k (x) = 0 for all inputs j = 1, 2, . . ., m, the control inputs u j do not affect the first time derivative of the output y k .In this case, extra time derivatives are computed consecutively until L g j h k (x) = 0 holds for at least one input u j .Then the corresponding output can be formulated as where the time derivative δ k is called the relative degree of the corresponding k th output, i.e. the relative degree corresponds to the number of differentiations of the output y k until one input u j appears explicitly.By applying this procedure to all three outputs an input-output relation for the multivariate system is obtained ⎡ ⎣ y where l(x) and J(x) result in Considering our nonlinear multivariate system the relative degree of each respective output is equal to one, i.e.
The matrix J(x) given in (16b) is the nonlinear coupling matrix that relates the three control inputs to the three chosen outputs.Notably, J(x) has an upper triangular structure which will be beneficial in decoupling the three outputs from one another.Also, it is evident that the effect of u 3 on all three outputs depends on the head pressure H(x).If H(x) is close to or equal to zero, u 3 becomes ineffective and the third output y 3 becomes uncontrollable in that case.This fact requires special consideration.
For feedback linearization, it is decisive whether the system has full vector relative degree, which is if Δ = m k=1 δ k = n holds [21].In our case, the vector relative degree amounts to Δ = 3 < 4, which means we have to deal with the case of non full vector relative degree.
Dynamic extension algorithm: This method aims to extend the relative degree of a system with initial non full vector relative degree Δ < n by introducing a feedback structure that incorporates additional state variables.This algorithm is repeated until the vector relative degree is raised to the system order Δ = n.
In our context, preferably the relative degree of the third output y 3 is increased, to avoid additional dynamics in the pressure control of y 1 and y 2 .This is done by introducing a new state variable ξ 3 and a synthetic input v 3 according to With the additional state variable, the multivariate system has full vector relative degree and can be linearized with the aid of an input and state transformation.Within the input transformation, a synthetic input vector v is chosen according to v k = y and with respect to the new state variable introduced in (18), which results in Together with a state transformation that contains the new state variable Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
a linear state space representation of the multivariate system is obtained which is composed of m = 3 linear and decoupled SISO subsystems.With such linear representation, arbitrary linear methods can be used for controller design.By rearranging the input-output relation from (15) with the new state variable according to (18) and the synthetic input, a decoupling control law for the input u is obtained that includes the inherent nonlinearities of the system which, however, only works if the coupling matrix J(x) is regular.
2) Feedback Control: From ( 22) it can be derived that the structure of the coupling matrix J(x) is decisive in choosing the proper control law: Only when the coupling matrix is regular and therefore invertible, a linearizing and decoupling control law ( 22) can be applied [21].
For our system, the coupling matrix (16b) is only regular as long as J 33 = −H(x)/A = 0, where the numerator expresses the pressure difference between the reservoirs of the H-MCL.In the case of zero pressure difference, there is no driving force to create a flow through the pinch valve, hence u 3 has no effect on the system (lack of controllability).Notably, with realistic hemodynamic pressures of the partial support condition a periodic loss of controllability must be considered as left ventricular and aortic pressures are approximately equal during systole (with an open aortic valve).As a result, loss of controllability must be expected during each cardiac cycle.Therefore, the control of the two pressures y 1 and y 2 , which can draw the full benefit from decoupling feedback linearization, and that of output y 3 , which is affected by periodic loss of controllability are treated separately.
Decoupling pressure control: Considering the special structure of the coupling matrix (16b) the nonlinear decoupling control law (22) can be formulated for the two outputs y 1 and y 2 , which results in where J mn are the individual elements of the coupling matrix from (16b).Note that (23) constitutes a decoupling control where v 1 and v 2 are used to steer the two outputs independently, eliminating the effect of the third control input u 3 on these two outputs.
To control the two outputs a desired linear reference behavior is chosen as where a i,δ are the coefficients of the desired closed-loop characteristic polynomial and w 1,2 are the reference values of the left ventricular and aortic pressures from the cardiovascular system model that should be emulated.This results in a state feedback control law for v 1 and v 2 , respectively: By inserting (25) in (23) a nonlinear control law is obtained, which decouples the pressures in both reservoirs: Periodically uncontrollable output: Due to the mentioned periodic loss of controllability of the third output y 3 , linear reference behavior of the subsystem in analogy to (24) can not be ensured.
As an alternative, a control approach is chosen that determines a control trajectory for u 3 which accounts for both controllable and uncontrollable periods of y 3 within each cardiac cycle.There are two control objectives to be satisfied: First, it has to be ensured that the level fluctuation of y 3 does not exceed ±10% of its target value.Second, atraumatic control behavior of the pinch valve, which is actuated by u 3 , has to be ensured, allowing only marginal movement of the pinch valve slide x hv .
To achieve both control objectives, a trajectory for the state variable ξ 3 is determined through an optimization problem in which a cost function J is minimized over the period of one cardiac cycle (i.e.t s ≤ τ ≤ t e ): In (27) the reference for the aortic reservoir level y 3 is denoted by h dmd = 0.035 m which is kept constant throughout the operation of the system.In the optimization, α is a weighting factor that accounts for the penalty on the motion of the pinch valve slide x hv .Note that α is a direct means to continuously affect atraumatic control action.Expressed in terms of the physical control input u 3 , the dynamics of the reservoir level y 3 are The system dynamics show the link between the reservoir level y 3 , the pump flow rate Q p , and the pinch valve flow rate H(x)u 3 .This indicates that the level is dependent on the pressure difference H(x) between the reservoirs and the valve resistance u 3 = 1/R hv (x hv ), which is determined from ( 22) where J 33 = 0 is assumed, otherwise u 3 is kept at its preceding value.Therefore, the reference pressure characteristics determine if the level can be controlled and a trajectory for ξ 3 in compliance with the boundary conditions is obtained from solving (27): Considering the partial support condition and a large α, which penalizes the valve motion, the optimization problem provides a control trajectory for ξ 3 , that results in marginal valve motion within each cardiac cycle, without violating the boundary conditions of the fluid level.
A result is depicted in Fig. 2, where the valve resistance is approximately constant except for the uncontrollable timespan during systole, highlighted in grey color.This peak describes a numerical phenomenon, which does not affect the system, due to its multiplication with zero pressure difference.With such steady resistance, the uncontrollable timespan demonstrates an increasing aortic level y 3 , due to a rising pump flow rate and a declining pinch valve flow rate.Within the controllable timespan of the cardiac cycle, this level deviation is compensated by opposing flow characteristics, where the increasing flow rate through the pinch valve results in a decreasing aortic level and consequently a fluctuation around its target value.
Therefore, the optimization problem provides an atraumatic solution for the control task, which accounts for the periodic loss of controllability within the subsystem.
The block diagram of the final control design is depicted in Fig. 3.This combines the decoupling control law from feedback linearization and the control trajectory from the optimization task to achieve both a decoupled control for left ventricular and aortic pressures as well as an atraumatic pinch valve control, despite a periodic loss of controllability within each cardiac cycle.

D. Experimental Verification
To evaluate the performance of the novel H-MCL, the reference tracking and disturbance rejection properties of the system were examined within hemodynamic experiments.In addition, the hardware-related traumatic effects of the system on blood were assessed based on hemolysis experiments.
1) Hemodynamic Assessment: The performance of the novel control strategy in terms of hemodynamic reference tracking and decoupling of the pressures with little pinch valve motion was investigated by different hemodynamic reference curves provided by the numerical model of the cardiovascular system (II-B1).Within the hemodynamic assessment, the system was filled with a water-glycerol mixture adapted to the viscosity of blood (3.5 cP).
To assess the performance, an excerpt of 15 s was examined illustrating a step from a partial support condition to a full support condition at t = 5 s.Although this may not be a clinically relevant case, it was chosen to represent a challenging, highly dynamic example with several parameter adaptations at the same time: The HM3 was showcased with a pump speed of 4450 rpm in partial support that increases stepwise to 5450 rpm in full support, with a rapid rise in the average target flow through the pump (2.25 ± 0.15 vs. 4.75 ± 0.15 L/min).In addition, ventricular and arterial pressure pulsatility and consequently pump flow pulsatility are affected concurrently.This challenging example permits an assessment of the control performance in terms of reference tracking characteristics, as well as disturbance rejection.
Additionally, to further evaluate the dynamics of the system, the heart rate was adapted from rest (91 bpm) to a lower (60 bpm) and a higher (120 bpm) heart rate and investigated for partial and full support condition, respectively.Furthermore, results from a previous SISO control structure were provided for comparison.
The quality of the pressure reference tracking was quantified by the absolute reference tracking error e = w − y and root mean square error (RMSE).In addition, the reference behavior of the pressure controllers was simulated with the controller transfer functions from (25), for which a characteristic reference tracking error e * = y ref − y and the corresponding RMSE were provided for comparison.
2) Hemocompatibility Assessment: Bovine blood experiments (n = 6) were conducted to examine whether the novel H-MCL inherently induces blood trauma compared to conventional ASTM test loops.Specifically, the HM3 was integrated into the novel H-MCL, and hemolysis was assessed in a conventional static condition (inactive mode; pump speed: 5450 rpm; mean target flow: 4.75 ± 0.15 L/min) and a corresponding condition with minor pulsatility (active mode; pump speed: 5450 rpm; mean target flow: 4.75 ± 0.15 L/min).The inactive (static) condition of the novel setup mimics a standardized hemolysis setup as described by the ASTM-1841 [14] with the only non-conformance of one additional reservoir.Comparison of this condition with results obtained in a conventional hemolysis test loop [10] served to identify whether the proposed hardware could introduce system-inherent hemolytic effects compared to conventional ASTM loops.Moreover, comparing the inactive (static) condition with the active (minor pulsatility) condition served to verify whether the control strategy induces any form of blood trauma.
The hemolysis experiments were conducted as previously described [9], [10] and based on ASTM standards [13], [14].Briefly, the bovine blood was collected from a local slaughterhouse under immediate anticoagulation (15'000 international units (IU) of heparin per liter).For comparability with previously reported hemolysis results, and to provide freedom to harvest sufficient blood volume by dilution, a hematocrit of 30 ± 2% (in line with ASTM-F1841-97) was chosen.Upon hematocrit adjustment [14] by dilution with phosphate buffered saline (PBS), the blood was filtered (Cardiotomy Reservoir EL404, Medtronic, Minneapolis, USA) to remove potential debris and gently filled into the H-MCL thereafter.
In experiments of 4 to 8 h the two operating conditions (inactive and active) were changed every 2 h.A sampling port served to collect blood samples at defined intervals: starting with a first sample (baseline) 5 minutes after the start of the HM3 (to ensure blood mixing), samples were extracted every 30 minutes.Importantly, sampling was performed by discarding an initial volume of 1 ml (stagnant blood in the sampling port) while drawing another sample of 1 ml for actual analysis.The samples were analyzed by photometric detection of the plasma  free hemoglobin as previously described [9], [10], and corresponding results reported as the normalized index of hemolysis (NIH) [14].The continuous loss of blood volume in the loop due to sample extraction was compensated for by computing the NIH using the actual loop volume, calculated by subtracting the sampling volumes from the initial loop volume.Hemolysis experiments were conducted within 4 hours of blood collection, while the temperature was maintained at 37 °C throughout the experiment.

A. Hemodynamics
Fig. 4 shows the reference tracking results of a conventional SISO control approach as initially implemented for the novel H-MCL design.Corresponding errors are summarized in Table II.The absolute control error results in an RMSE of 3.92 mmHg and 2.89 mmHg for the left ventricle and the aorta, respectively, during the partial support condition.During full support condition, the RMSE is reduced by approximately 1 mmHg resulting in 2.61 mmHg and 1.95 mmHg, respectively.The maximal reference tracking error is observed in partial support for the left ventricular pressure with 15.00 mmHg.Fig. 5 shows the reference tracking results of the novel decoupling MIMO control approach.In addition, the pressure error is shown, which is maximal in left ventricular pressure with a RMSE of 2.9 mmHg and 1.3 mmHg in partial and full support, respectively.By comparing the results with Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.the characteristic reference behavior (in accordance with the transfer function of the controller) the RMSE is reduced to 0.8 mmHg and 0.4 mmHg, respectively.The RMSE of the aortic pressure is 0.6 mmHg in partial support and 0.2 mmHg in full support.Table III summarizes the pressure errors including the RMSE and the maximal deviation from the reference curve.
The panels of Fig. 6 depict the measurement results of the hemodynamic experiment conducted with the decoupling MIMO control strategy, characterized by a step from partial to full support condition at t = 5 s.The upper panel of Fig. 6(a) shows the resulting left ventricular and aortic pressure curve, in combination with the resulting pressure difference (head pressure) between the reservoirs.The pressures change periodically with the heart rate (91 bpm): The left ventricular pressure fluctuates between 91.6 ± 0.1 mmHg and 9.4 ± 0.1 mmHg in partial support, and between 48.7 ± 0.1 mmHg and 10.9 ± 0.1 mmHg in full support condition.Analogously, the aortic pressure alternates between 92.7 ± 0.1 mmHg and 71.3 ± 0.2 mmHg in partial support (mean arterial pressure: 82.19 ± 7.22 mmHg), and between 78.4 ± 0.1 mmHg and 76.1 ± 0.1 mmHg in full support condition (mean arterial pressure: 77.18 ± 0.62 mmHg).Due to the lower peak pressure of the ESPVR during full support, a decrease in pulsatility can be observed.With lower pulsatility, the mean head pressure affecting the RBP increases from 44.5 ± 30.6 mmHg to 53.5 ± 13.9 mmHg.Fig. 6(b) shows the VAD flow rate and the corresponding backflow through the pinch valve, with a stepwise increase from 2.3 ± 2.1 L/min to 4.6 ± 0.6 L/min.HM3 and pinch valve flow rates pulsate inversely, which is induced by the hemodynamic pressure curves.Due to a high pulsatility in the HM3 flow rate within partial support, a periodical backflow of -0.2 ± 0.1 L/min is observed during diastole.In contrast, the flow rate in the pinch valve shows less pulsatility with an all-positive flow rate.Fig. 6(c) depicts the resulting fluid levels for the left ventricular and aortic reservoir, which show inverse characteristics.The left ventricular and aortic levels fluctuate around the target level of 35.0 mm, which corresponds to 50.0% of filling, with a mean value of 35.0 ± 1.4 mm (50.0 ± 2.1%) in partial support, and 34.9 ± 0.6 mm (49.9 ± 0.8%) in full support, respectively.The level deviation does not exceed ±5% despite a stepwise change  in the operating conditions.Fig. 6(d) shows the pinch valve stroke which can be assumed constant with 1179 ± 1 step and 1105 ± 2 steps corresponding to 0.012 mm and 0.024 mm valve movement in partial and full support condition, respectively.Only in case of a stepwise change in the operating condition, a momentary valve action (70 steps, 0.84 mm) is apparent.Different dynamics were assessed by changing the heart rate to 60 bpm and 120 bpm, respectively (Fig. 7).At 60 bpm the left ventricular RMSE results in 2.3 mmHg in partial support, and 1.1 mmHg in full support condition.It increases at 120 bpm to 3.6 mmHg and 2.4 mmHg in partial and full support, respectively.This conforms to an error growth of 0.02 mmHg/bpm.In contrast, the aortic pressure shows no effect due to changing dynamics, further results are stated in Table IV.

B. Hemocompatibility
In the six blood experiments, hemolysis measurements were conducted over a cumulative period of 40 h.Baseline blood properties were characterized by a pH of 7.46 ± 0.08 and a total hemoglobin Hb of 13.67 ± 1.58 g/dL.No significant difference was evident between the NIH obtained in the H-MCL in inactive mode and the previously reported NIH with the HM3 examined in conventional test loops (ΔNIH = -1.6 mg/100 L) [10].Moreover, the NIH showed no significant difference between the active and inactive mode in the H-MCL (ΔNIH = +0.3mg/100 L) (Fig. 8).

IV. DISCUSSION
This study presented a novel, atraumatic H-MCL for use with blood, which generates a realistic hemodynamic environment for the RBP under investigation thus enhancing state-of-the-art blood trauma assessment.
To realize such atraumatic H-MCL, a previously presented H-MCL concept [17] was advanced for use with blood.Novel design features include the low volume conception (450 ± 50 ml) with the sole blood contacting components being the two reservoirs, the silicon/polyvinyl tubing, and the RBP under investigation.All sensors and actuators were realized without direct blood contact: e.g. a novel proportional pinch valve was implemented in the backflow path, allowing the adaptation of the hydraulic resistance by pinching the tubing.Further, a heating concept was developed to maintain a blood temperature of 37 °C.These design choices were made based on the ASTM standards [13], [14], resulting in similar blood contacting components compared to the standard with the exception of an additional reservoir.
However, these hardware adaptations required a more sophisticated MIMO control strategy that decouples the pressures within the system to ensure accurate reference tracking and considers atraumatic level control by marginal pinch valve motion.We showed that the reference pressure signals were precisely tracked by the novel control strategy without any discernible coupling effects.This was only feasible with a novel control approach based on feedback linearization, which decouples the pressures within the system.This led to improved trajectory tracking compared to the results of a conventional SISO control structure where similar performance could not be achieved: The results from an SISO control approach indicate strong inherent coupling effects of the system, despite carefully tuning the control parameters.Although the resulting RMSE is in acceptable range with less than 4 mmHg, such deviations may considerably affect the RBP flow, especially in flat regions of the pump's Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.characteristic HQ-curve, where even small pressure deviations result in large changes in the flow rate [7].Therefore, with the described hardware adaptions of the novel H-MCL, a conventional SISO control approach did not meet the requirements for adequate reference tracking.
The decoupling control approach (MIMO) leads to significantly improved trajectory tracking with a twofold decreased mean RMSE of 1.27 ± 1.21 mmHg compared to 2.84 ± 0.82 mmHg for the SISO control.By considering the reference behavior of the implemented decoupling pressure control, the mean RMSE reduces to 0.53 ± 0.27 mmHg, which corresponds to the magnitude of the measurement error of the pressure sensors used.Given different reference dynamics, the RMSE of the novel H-MCL increases only slightly with heart rate (+0.02 mmHg/bpm).The decoupling pressure control consistently met the requirements of accurate reference tracking for the novel H-MCL design.
The MIMO control strategy was completed by an atraumatic control structure to control the fluid levels within the H-MCL.This addresses a pinch valve, which allows a defined flow control without direct blood contact by changing the flow resistance.The control of the pinch valve was challenged by two limitations: First, in case of a pressure difference of zero across the pinch valve (e.g. in case of partial support during systole), the flow rate is zero and consequently the pinch valve condition does not affect the system, resulting in a loss of controllability.Second, to warrant atraumatic performance, only a marginal motion of the pinch valve during each heart cycle is permitted.
The presented control strategy addresses both limitations successfully: The fluid volumes of the reservoirs were balanced (< 4%) by driving the system along a suitable trajectory for each cardiac cycle without substantial motion of the pinch valve (< 0.024 mm).Consequently, pulsatile blood trauma experiments with the novel H-MCL are comparable to the standardized static blood trauma assessment of RBP where a constant resistance is used.Of note, changes in the reservoir's fluid volume cannot be eliminated completely due to the periodic lack of controllability during systole, which leads to a temporary level increase in the aortic reservoir.The approach to mitigate the loss of controllability required to solve an optimization problem that calculates a suitable control trajectory for each cardiac cycle to ensure marginal pinch valve motion and a level deviation within the chosen boundary conditions.
In the beginning, we defined an atraumatic H-MCL as a setup with no additional increase in hemolysis compared to a state-ofthe-art setup for hemolysis testing (defined by the ASTM).The absence of a significant difference between the NIH obtained in the novel H-MCL in an inactive mode (static condition) and previously reported data obtained in a conventional test loop under similar condition and with equivalent anticoagulation regime [10] confirmed that the setup of the novel H-MCL does not inherently introduce confounding traumatic effects.Moreover, the absence of a significant difference in NIH between the H-MCL in active and inactive modes validated that the active control mode does not inherently induce traumatic effects on the blood.Accordingly, the hemolysis experiments provided a validation of the novel H-MCL's readiness for the use in future, thorough hemolysis assessment of VADs under realistic, pulsatile operating conditions.Based on previous studies that demonstrated increased levels of hemolysis during off-design pump operation, marked differences in hemolysis are to be expected during those clinically relevant operating conditions compared to corresponding static considerations as the pump will periodically be exposed to varying pressures and thus flow rates.To identify the influence of pulsatility on hemolysis, those future experiments are planned in combination with a clinically known comparator in a static state-of-the-art hemolysis testbench.Transitioning from conventional hemolysis assessment at simplified nominal operating conditions (e.g., 5 L/min against 100 mmHg) toward the examination of hemolysis under clinically relevant hemodynamic conditions, this H-MCL will help the targeted assessment of VAD designs at distinct dynamic loads that are specific to the device under investigation (e.g.pediatric VAD support).
In addition to the showcased application, a number of other scenarios for studies with the novel H-MCL are conceivable.The new setup has a modular design and therefore allows plug-and-play connection of other RBPs and prototypes.This does not require any adjustments of the control structure or modeling of the device under investigation as the resulting flow rate within the H-MCL is measured and processed directly.In addition, the numerical model of the cardiovascular system can be flexibly adapted and assigned to the interface of the H-MCL.Thus, other clinical scenarios can be investigated, e.g.in-vitro implantation of an RBP at the left atrium or the right ventricle and consequently the hemodynamic and traumatic effects of such treatment method.This extends the application of state-of-the-art H-MCLs and allows the investigation of dynamic blood trauma effects caused by e.g. the impeller displacement in LVADs with magnetic bearings during pulsatile operation or intermittent backflow scenarios during diastole in LVADs operated at lower speeds or high arterial pressures.

V. CONCLUSION
A novel atraumatic H-MCL was successfully implemented, characterized by an atraumatic low-volume design and an advanced control strategy.The hemodynamic experiments showed that the implemented control strategy decouples the pressures of the system, which is reflected in precise reference tracking.Further, hemolysis experiments conducted with active and inactive control strategy indicated the atraumatic behavior of the setup.Hence, the novel atraumatic H-MCL enables in-vitro hemocompatibility assessment of physical RBPs within realistic hemodynamic conditions.

ACKNOWLEDGMENT
The financial support by the Christian Doppler Research Association is gratefully acknowledged.Additionally, thanks are extended to Dr. Xiangyu He and Mr. Krishnaraj Narayanaswamy MSc for their invaluable contributions during the blood experiments.

Fig. 2 .
Fig. 2. Optimization results for one cardiac cycle (partial support condition).The four panels depict the time course of (a) the hemodynamic pressures of the left ventricle and aorta and the head pressure (b) the fluid level in the aortic reservoir, (c) the optimized control trajectory of the additional state variable, and (d) the resulting valve resistance and pinch valve slide.The grey area marks the uncontrollable timespan during systole.

Fig. 3 .
Fig. 3. Block diagram of the control strategy: Optimization task in combination with a nonlinear decoupling transformation (Feedback Linearization).The optimization problem considers data from the last cardiac cycle to overcome periods of no controllability, while the nonlinear decoupling control law ensures precise trajectory tracking.

Fig. 4 .
Fig. 4. Reference tracking of measured left ventricular and aortic pressures for partial and full support with a SISO control approach.The lower panels show the respective absolute control error e. (Reference: dashed black; Left ventricle: blue; Aorta: orange).

Fig. 5 .
Fig. 5. Reference tracking with new control strategy of measured left ventricular and aortic pressures for partial and full support.The panels show the respective absolute control error e and a characteristic control error e * , which considers the reference behavior of the controllers.(Reference: dashed black; Left ventricle: blue; Aorta: orange).

Fig. 6 .
Fig. 6.Measured results of a step from partial support to full support condition at t = 5 s with a novel atraumatic and decoupling control strategy.The four panels depict the time course of (a) the hemodynamic pressures of the left ventricle, aorta, and the resulting head pressure, (b) the resulting flow rate through the HM3 and pinch valve, (c) the fluid level in the left ventricular and aortic reservoir, and (d) the pinch valve stroke.

Fig. 7 .
Fig. 7. Reference tracking with new control strategy of measured left ventricular and aortic pressures for partial (left panels) and full (right panels) support with different heart rates (dynamics): upper panels 60 bpm and lower panels 120 bpm.(Reference: dashed black; Left ventricle: blue; Aorta: orange).

Fig. 8 .
Fig. 8. (a) Boxplots illustrating the Normalized Index of Hemolysis (NIH) obtained (i) in a conventional ASTM hemolysis test loop, (ii) in the novel H-MCL in inactive mode, and (iii) in the novel H-MCL in active mode.(b) Increase in free Hemoglobin (fHb) over the 2 h per condition (samples every 30 minutes), illustrated in the form of the mean and standard deviation over the total of six bovine blood experiments for each of the two conditions (left: inactive; right: active).

TABLE I REQUIREMENTS
FOR AN ATRAUMATIC H-MCL Fig.

TABLE II RMSE
AND MAXIMAL CONTROL ERROR OF SISO CONTROL APPROACH FOR THE LEFT VENTRICLE AND THE AORTA AT PARTIAL AND FULLSUPPORT, RESPECTIVELY

TABLE III RMSE
AND MAXIMAL CONTROL ERROR WITH NOVEL CONTROL STRATEGY RESULTING FROM ABSOLUTE AND CHARACTERISTIC REFERENCE SIGNAL FOR THE LEFT VENTRICLE AND THE AORTA AT PARTIAL AND FULL SUPPORT, RESPECTIVELY

TABLE IV RMSE
AND MAXIMAL CONTROL ERROR WITH NEW CONTROL STRATEGY RESULTING FROM ABSOLUTE REFERENCE SIGNAL AT 60 BPM AND 120 BPM HEART RATE FOR THE LEFT VENTRICLE AND THE AORTA AT PARTIAL AND FULL SUPPORT,