Recapitulating aortic valve disease hemodynamics with a highly tunable bio-inspired soft robotic aortic sleeve

Existing models of aortic stenosis (AS) are limited to inducing left ventricular pressure overload. As they have reduced control over the severity of aortic constriction, the clinical relevance of these models is largely hindered by their inability to mimic AS hemodynamics and recapitulate ow patterns associated with congenital valve defects, responsible for the accelerated onset and progression of AS. Here we report the development of a highly tunable bio-inspired soft robotic tool that enables the recapitulation of AS in a porcine model, in which customization of actuation patterns allows hemodynamic mimicry of AS and congenital aortic valve defects. In vitro and computational tools including lumped-parameter, nite element, and computational uid dynamics platforms were developed to predict the hemodynamics induced by the bio-inspired soft robotic sleeve. The controllability of our in vivo model and its ability to replicate ow patterns of AS and congenital defects were demonstrated in swine through echocardiography, left ventricular catheterization, and magnetic resonance imaging. This work supports the use of soft robotics to simulate human physiology and disease, while paving the way towards the development of patient-specic models of AS and congenital defects that can guide clinical decisions to improve the management and treatment of these patients. recreate the bicommissural, unicommissural, and aortic stenosis proles observed in vitro and predicted in silico. Acute changes in cardiac function and aortic hemodynamics were re-evaluated before sacrice eight days post implantation (D8) through transapical LV catheterization and transepicardial echocardiography. During this study, a ow probe was inserted on the thoracic aorta to record changes in blood ow. Findings from these studies were used to validate the FE and LP platforms, as well as the computational uid dynamics (CFD) model described later in this work.


Introduction
Advances in soft robotics have led to the development of high-delity simulators of pathophysiology for biomedical applications 1 . By utilizing materials with mechanical properties similar to those of biological tissues, soft robots are capable of recapitulating the biomechanical function and complex motion dynamics of various organ systems, including the heart 2 , the gastrointestinal tract 3,4 , the respiratory system 5,6 and others 7,8 . These simulators could serve as platforms for testing and development of medical therapies, as well as studies of human physiology and disease. However, they can only model organ systems in isolation, failing to capture the complex physiologic interplay arising for example from neurohormonal control and feedback or compensation mechanisms. Here, we present an in vivo disease model that utilizes a bio-inspired soft robotic sleeve to recapitulate the hemodynamics of aortic stenosis (AS) and congenital aortic valve defects in swine, and describe the use of computational tools and 4D magnetic resonance imaging (MRI), among other techniques, to ensure faithful hemodynamic mimicry.
The prevalence of AS is rising in the U.S., with more than 1.5 million Americans being diagnosed every year 9 . AS is an obstruction of blood ow through the aortic valve mediated by calci cation and in ammatory processes, often accelerated by congenital aortic valve defects [9][10][11] . If untreated, AS can result in heart failure [11][12][13][14] and sudden death 15 . High-delity in vivo models of AS may advance the development of risk strati cation frameworks to guide the management of AS, and particularly of asymptomatic cases of severe AS for whom interventional guidelines remain heterogeneous 11,16 . Further, these models may help elucidate why, despite the elevated overall success rates of aortic valve replacement, repeat procedures and perioperative mortality rates remain high in certain patient groups 17,18 .
The majority of former in vivo models of AS utilize rigid bands or in atable cuffs around the ascending aorta to induce left ventricular (LV) pressure overload [19][20][21] . These devices can only achieve concentric constriction of the aorta, and fail to recreate the complex 3D ow patterns observed in AS. Moreover, their limited control prevents them from recapitulating the hemodynamics of congenital aortic valve defectsoften accelerating the onset and progression of AS, as well as aortic remodeling, potentially leading to other complications including aortic aneurysms, dissection, and regurgitation 22 . Bicuspid aortic valve (BAV) disease is the most common congenital valve disease. In this work, we speci cally focus on bicommissural bicuspid valves (henceforth simply referred to as bicommissural) 11,23,24 . Another disease phenotype is unicommissural aortic valve (UAV). UAV is more rare and associated with an even poorer prognosis than BAV, albeit depending on the morphology of the defect [25][26][27] .
Here, we report the development of a highly tunable bio-inspired soft robotic aortic sleeve that recapitulates the hemodynamics of AS and of congenital valvular defects -unicommissural or bicommissural ( Fig. 1). With the potential to recreate patient-speci c hemodynamic pro les, this research pioneers the development of high-delity, customizable in vivo models of human disease. This bioinspired soft robotic technology is poised to model a broader spectrum of human diseases, paving the way towards other medical applications including studies of vascular (e.g., carotid, peripheral arterial disease, aortic coarctation) or pulmonary valve stenosis, urinary or gastrointestinal sphincter dysfunction, and airway obstruction. These models could therefore provide insights into a wide range of pathophysiological conditions and support translational research by guiding innovation in medical devices and therapies.

Results
Design and development of a highly tunable bio-inspired soft robotic aortic sleeve A highly tunable bio-inspired soft robotic aortic sleeve was developed to recapitulate the hemodynamics of AS and congenital aortic valve disease. This is composed of three expandable elements or pockets, each connected to one hydraulic line for actuation, where activation of one pocket mimics fusion or stiffening of one corresponding commissure -the area where the valve lea ets abut. An inelastic fabric sheet spanning across the base of the soft actuator restrains the expansion of the pockets to one direction under hydraulic pressure and a slit and strip mechanism allows positioning around the outer wall of the porcine aorta.
The expandable bladder is made of two vacuum formed sheets of Thermoplastic Polyurethane (TPU), whereas a TPU-coated Nylon fabric is used as the constraining layer. A positive and a negative mold of the bladder were made for vacuum forming and sealing of the expandable elements respectively (Fig. 2ab) (see Methods). Figure 2c illustrates the mechanical response to uniaxial loading of the TPU and Nylon layers, and the axial force generated by the sleeve versus actuation volume is depicted in Fig. 2d (see Methods). 3D representations of the sleeve with details of the pockets, the constraining layer, the positioning mechanism, and the actuation lines are shown in Fig. 2e-f. Histology studies on each of the materials constituting the aortic sleeve resulted in minimal brous tissue and no signi cant lymphocytic in ltrates (see Methods and Supplementary Information).
This highly tunable bio-inspired soft robotic sleeve was designed to recapitulate the hemodynamics of AS and of congenital defects, namely of unicommissural and bicommissural aortic valves.
Selective pocket actuation enables customization of aortic luminal geometries for hemodynamic mimicry of aortic valve defects: in vitro and nite element studies A simple mock circulatory loop (MCL) and a nite element (FE) simulation were developed to predict the structural response of the ascending aorta upon activation of the sleeve. A schematic representation of the main elements constituting the MCL, including a mock aortic vessel with a modulus matched with native aortic tissue for placement of the sleeve, is provided in Fig. 3a. Changes in the luminal crosssection of the aorta are visualized using an endoscopic camera inserted in the MCL. Figure 3b illustrates an accurate 3D representation of the sleeve placed around the ascending aorta of the Living Heart Model on Abaqus 2018 (Dassault Systèmes, Simulia) 28,29 for the FE study. Details of the MCL and FE simulation set-up can be found in the Methods.
Selective activation of the pockets of the aortic sleeve results in various constriction pro les, where each actuated pocket mimics the hemodynamics associated with a fused commissure of the aortic valve ( Fig.  3c-e). Speci cally, a bicommissural pro le is obtained from actuation of one pocket (Fig. 3c), a unicommissural geometry is achieved when two pockets are activated (Fig. 3d), while actuation of all the three pockets results in partial fusion of the three commissures, leading to a stenotic pro le (Fig. 3e).
Following the same pocket actuation schemes, structural FE characterization of the ascending aorta show analogous ndings to those obtained in the MCL study. Figure 3c-e illustrates the cross-sectional pro les obtained via FE, further corroborating the ability of the sleeve to recapitulate bicommissural, unicommissural and stenotic aortic geometries.
Lumped-parameter in silico model predicts the hemodynamics of aortic constriction A lumped-parameter (LP) model previously developed by our group 30,31 was adapted to the porcine physiology to simulate the hemodynamics of aortic constriction. The domain (Fig. 4a) is composed of a four-chamber heart, proximal vasculature, and lumped-parameter elements modeling the peripheral and pulmonary circulations. Constrictions of the ascending aorta were simulated as reductions in the luminal cross-sectional area of the Band element (see Methods). Left ventricular (LV) pressure-volume (PV) loops were obtained at baseline and at Intermediate (80%) and Full (90%) constrictions (Fig. 4b), and metrics of cardiac function such as arterial elastance (Ea), peak LV pressure (LVP) and stroke volume (SV) were extracted ( Fig. 4c-e). Further, the maximum transaortic pressure gradient (Fig. 4f) was computed for cross-validation with the MCL in vitro system (Fig. 4g). Figure 4b shows that aortic constriction results in elevated LVP and a drop in the volume of blood ejected during each heart cycle -the stroke volume (SV). This occurs because aortic constriction intrinsically increases the afterload, i.e., the pressure against which the heart has to eject blood during systole, which is re ected in the surge in Ea (2.0 to 22.0 mmHg/mL), as shown in Fig. 4c. Correspondingly, the peak LVP increases from baseline values of 93.2 to 166.6 mmHg, and the SV drops from 40.3 to 7.0 mL. While the peak LVP rises in an approximately linear fashion, the SV decreases more signi cantly at elevated degrees of aortic constriction.
The maximum transaortic gradient increases exponentially with aortic constriction both according to the LP and the MCL in vitro models. Results show that the transaortic pressure gradient begins to rise signi cantly from values of aortic constriction of approximately 70%. At 80% aortic constriction, gradients of 46.9 mmHg and 45.5 ± 2.3 mmHg were obtained on the LP and MCL platforms respectively, these increasing to 94.0 mmHg and 85.6 ± 7.5 mmHg at 90% constriction (Fig. 4g). Clinically, gradients between 40-65 mmHg correspond to moderate cases of AS, whereas gradients greater than 65 mmHg are indicative of severe AS 32,33 . Overall, these ndings suggest that the proposed sleeve is capable of accurately recreating clinically relevant hemodynamics of AS.

Study Design And Overview
The aortic sleeve was implanted in 6 Yorkshire pigs (~ 38-45kg). The timeline of the investigation is shown in Fig. 5. Cardiac function was assessed at the beginning of the study on transthoracic echocardiography (TTE) prior to implantation on day 0 (D0). MRI was performed on D6 to evaluate cardiac function and visualize aortic ow hemodynamics acutely at progressive levels of constriction and following pocket-selective actuation to recreate the bicommissural, unicommissural, and aortic stenosis pro les observed in vitro and predicted in silico. Acute changes in cardiac function and aortic hemodynamics were re-evaluated before sacri ce eight days post implantation (D8) through transapical LV catheterization and transepicardial echocardiography. During this study, a ow probe was inserted on the thoracic aorta to record changes in blood ow. Findings from these studies were used to validate the FE and LP platforms, as well as the computational uid dynamics (CFD) model described later in this work.
The effects of various degrees of aortic constriction were evaluated in the aortic stenosis con guration. Further, pocket-speci c actuation was performed to recreate bicommissural and unicommissural aortic constriction pro les as previously described. Due to the prolonged time required for MRI image acquisition and associated risks, we limited the severity of aortic constriction during MRI studies.
Through this investigation, one swine was euthanized due to severe cardiac effusion ndings on MRI, while two trials were excluded from the analysis due to unsuccessful tensioning of the sleeve during implantation. We report the role of tensioning during implantation of the sleeve and its effect on the degree of constriction in the Supplementary Information. All animal procedures were approved by the Institutional Animal Care and Use Committee (IACUC) of our institute (see Methods).

Highly controllable aortic constriction and in vivo hemodynamics
The hemodynamics induced acutely by actuation of the bio-inspired soft robotic aortic sleeve were measured in swine at day 8 (D8). The sleeve was actuated continuously to two degrees of aortic constriction, namely Intermediate and Full, with up to 3 mL and 4.75 mL of volume deployed respectively. Figure 6a-c shows color map images of blood ow through the aortic valve ori ce during ejection on transepicardial echocardiography at baseline (Fig. 6a), and intermediate ( Fig. 6b) and full ( Fig. 6c) actuation, the latter resulting in mostly complete obstruction of blood ow. Measurements of the corresponding peak aortic ow velocity and estimates of the transaortic pressure gradient (Fig. 6d) yielded peak ow velocities values up to 4.85 ± 0.14 m/s and pressure gradients of 94.13 ± 5.49 mmHg, corresponding to severe clinical cases of AS 32,33 . Analysis of LV systolic function through measurements of left ventricular ejection fraction (LVEF) showed a progressive drop at intermediate (31.5 ± 2.8 %) and full (10.9 ± 4.2 %) constriction, while comparison between baseline at D8 (50.3 ± 2.7 %) and D0 (55.8 ± 4.0 %) revealed no remarkable changes induced by sole implantation of the sleeve prior to actuation (Fig. 6e). Correspondingly, mean blood ow at the thoracic aorta dropped 5-fold from baseline values of 2.60 ± 0.23 L/min to 0.52 ± 0.14 L/min at full constriction ( Fig. 6f).
Results from LV catheterization with a PV catheter ( Fig. 6g-j) show similar trends as those predicted by the LP model, with a sharp increase in Ea (1.86 ± 0.18 to 24.24 ± 3.13 mmHg/mL) (Fig. 6h), an approximately linear rise in peak LVP (90.31 ± 9.45 to 164.89 ± 9.49 mmHg) (Fig. 6i) and a drop in SV (44.02 ± 2.9 to 6.23 ± 1.00 mL), which becomes increasingly signi cant at more severe degrees of aortic constriction (Fig. 6j). Notably, these changes are statistically signi cant for both degrees of aortic constriction and in close agreement with the in silico model. Details of the techniques used for hemodynamic assessment, and a summary of the data and statistical analysis can be found in the Methods and Supplementary Information.

Discussion
High-delity models of human physiology and disease are poised to have important implications in human health and clinical medicine. Soft robotic technology has enhanced the accuracy of benchtop or biohybrid simulators that can recapitulate the biomechanics and function of a variety of organ systems 1 . Although animal models of human disease are not as broadly documented in the scienti c literature, attempts have been made to induce pressure overload secondary to aortic stenosis (AS) -one of the most highly prevalent valvular heart diseases 19,21,34 . However, existing technologies only enable concentric aortic constriction of the aorta, thus failing to recreate the complex aortic ow hemodynamics associated with AS. Further, they suffer from limited controllability, elevated mortality rates, and the inability to recapitulate the hemodynamics of congenital valve defects, which often accelerate symptoms of AS, emphasizing the need for more comprehensive and representative models of this condition.
In this work, we described the development of a high-delity in vivo model of AS by means of a bioinspired soft robotic aortic sleeve. This is composed of expandable elements or pockets that can be individually activated to enable customization of aortic ow patterns. A broad array of computational tools, including lumped-parameter (LP), nite element (FE) and computational uid dynamic (CFD) platforms were developed to predict the structural and hemodynamic effects induced by the aortic sleeve, then validated in vivo. Speci cally, echocardiography, and LV catheterization were leveraged to evaluate cardiac function and aortic hemodynamics, whereas 4D-MRI enabled visualization of aortic ow patterns and comparison with CFD modeling.
This in vivo disease model can simulate abnormalities in peak aortic ow velocity, transaortic pressure gradient, and LV hemodynamics in a controllable way. Intermediate and full activation of the aortic sleeve yielded signi cant differences in aortic ow, and metrics of left ventricular ejection fraction (LVEF), arterial elastance (Ea), peak left ventricular pressure (LVP) and stroke volume (SV). Notably, the changes induced upon constriction were seen to correspond to clinical cases of AS according to the American Society of Echocardiography (ASE) and the European Association of Cardiovascular Imaging (EACVI) 33 . In addition to approximating clinically relevant metrics for AS assessment, this model was shown to recreate bicommissural, unicommissural, and stenosis geometries and hemodynamics similar to those associated with congenital valve defects or calci c AS.
The enhanced control provided by this bio-inspired soft robotic aortic sleeve could enable patient-speci c studies of pressure overload secondary to AS, supporting the development of interventions for AS and of hemodynamics-based algorithms for clinical decision making. Chronically, AS may lead concentric remodeling and symptoms of heart failure with preserved ejection fraction (HFpEF) 14,35 . Further, depressed contractility and heart failure with reduced ejection fraction (HFrEF) may ensue in severe cases of AS when cardiac compensation is inadequate 36 . By enabling recapitulation of patient-speci c hemodynamics, this work could allow hemodynamically accurate studies of the progression of heart failure secondary to AS, closely mimicking the pathophysiology of chronic disease and overcoming the limitations of existing models, such as reduced controllability and elevated mortality rates. In addition, reversing the degree of aortic constriction in a controlled way could help explore the e cacy of aortic valve replacement procedures in ameliorating adverse remodeling, and investigate the onset of plasticity during these processes, following which hemodynamic and pathophysiological derangements cannot be fully overturned 37,38 .
Congenital valve defects lead to a dramatic acceleration in the progression of AS and associated symptomatology 23,25,27 . While ex vivo models of congenital valve disease have been recently developed 39 , in this work, we have recreated the hemodynamics of bicommissural and unicommissural congenital defects as well as calci c AS, using a combination of in silico, in vitro and in vivo techniques. The ability of this bio-inspired soft robotic sleeve to be programmed and recon gured to different constriction pro les over time makes it ideal for long-term studies of aortic constriction and congenital defects.
Feeding in vivo data into the proposed computational platforms could enhance their physiologic relevance. These in silico tools could be optimized to customize the design of the sleeve and actuation patterns to closely approximate patient-speci c ow pro les. This would enable the development of patient-speci c in vivo models of disease, which could provide a holistic view of the relevant pathophysiology and better inform prognosis and treatment strategies.
This research pioneers the development of high-delity in vivo models of human disease by leveraging soft robotics technology and advances in MRI for hemodynamic mimicry and with potential for patientspeci c applications. It could inspire in vivo models of other pathophysiological conditions, within and beyond the cardiovascular eld. For example, the design of the aortic sleeve could be modi ed to enable studies of pulmonary hypertension and right heart failure where ow patterns across the pulmonary valve can be accurately recreated. Other examples may involve studies of esophageal and swallowing disorders, including abnormal peristalsis, spasms, and of the aerodynamics of airway obstructions for a variety of respiratory or other biomedical applications.

Bio-inspired soft robotic aortic sleeve manufacture
Each soft actuator is manufactured by rst vacuum forming two sheets of Thermoplastic Polyurethane (TPU) into a 3D-printed mold. A 1mm diameter opening is created in the geometrical center of each of the three pockets of one of the two sheets, where half of a PVC is then inserted. The two TPU sheets are then heat-sealed at a temperature of 320F for 10 seconds. The same heat-sealing procedure is then repeated to attach the bottom side of the TPU bladder (i.e., where the PVC connectors are inserted) to the coated inelastic fabric which has three openings corresponding to the TPU connectors. Soft tubing is then secured to each of the connectors to enable independent activation of each of the three pockets of the actuator. The fabric is then cut to shape to create a slit along its short side and a strip on its long axis for positioning around the aorta. A detailed description of the manufacturing process and the materials used can be found in the Supplementary Information.

Mechanical characterization
The modulus of elasticity (E-modulus) of the TPU and fabric layers was determined under uniaxial tensile loading using an electromechanical tester (Instron 5566, 2kN load cell, Norwood, USA), according to the ISO 527-1 and ISO 13934-1 standards for plastics and textiles respectively. The E-modulus was calculated as the slope of the stress-strain curve at 0-5% elongation.
The axial force exerted by the actuator at in ation was measured on the same instrument. The lower plate of the electromechanical tester served as an attachment point for the aortic sleeve, whereas the upper one was connected to the load cell and brought in close contact with the upper surface of the actuator. The sleeve was actuated by deploying up to 5mL of saline using a syringe pump (70-3007 PHD ULTRA™ Syringe Pump Infuse/Withdraw, Harvard Apparatus) continuously at a rate of 0.2 mL/sec, and the applied force was measured by the load cell. Each of these mechanical tests was conducted on three samples (n = 3). Average values and SD were calculated.

Mock circulatory loop (MCL)
A simple mock circulatory loop (MCL) was built utilizing a pulsatile pump (55-3305 Pulsatile Blood Pump, Harvard Apparatus), two adjustable compliance chambers and resistive valves in series, and a lowmodulus latex tubing (E ≈ 1.4 MPa, d in = 1/2", d out = 5/8", McMaster-Carr) to approximate the elasticity and geometry of the porcine ascending aorta. Pressure sensors (Wireless Pressure Sensor PS-3203, PASCO) enabled pressure measurements across the mock vessel. An endoscopic camera (1080P HD, 30 fps, NIDAGE) was inserted in the MCL to visualize the cross-section of the aorta. The stroke volume and the rate of the pulsatile pump were manually adjusted to values of 30 mL and 100 bpm. The soft robotic actuator was secured around the mock vessel. Activation was performed by deploying up to 6 mL of saline through a syringe pump as described in the Mechanical characterization Methods section above. The pressure across the aorta was continuously recorded and displayed in real-time on the PASCO Capstone 2.2.0 software (PASCO) throughout actuation. The maximum transaortic pressure gradient was calculated, whilst synchronous images of the luminal cross-section of the aorta were processed on the Image Labeler Application of the MATLAB Image Processing and Computer Vision toolbox (MathWorks®) to estimate the luminal aortic cross-sectional area.

Lumped-parameter (LP) modeling
A lumped-parameter model was constructed on the MATLAB-based object-oriented environment SIMSCAPE FLUIDS™ (MathWorks®), based on our previous work 30,31 . The geometrical dimensions of the heart chambers, heart valves, and proximal vasculature were de ned using CINE MRI, while other lumpedparameter resistive and capacitive elements were adapted from our previous work to approximate the porcine hemodynamics measured through LV catheterization in vivo. A summary of the input parameters and of the simulated hemodynamics at baseline and comparison with in vivo data can be found in the Supplementary Information. Aortic constriction (AC) was simulated by reducing the luminal crosssectional area of the Band element (Fig. 3a) by 10-90% in 10%-step increments. PV loops were obtained for values of aortic constriction equal to 80% (intermediate) and 90% (full).

Finite element (FE) modeling
Finite element analysis (FEA) was conducted to evaluate the biomechanical effects of the soft robotic sleeve on the ascending aorta. The heart model was adapted from the Living Heart Model (LHM) 29 and used on Abaqus 2018 software (Simulia, Dassault Systèmes). The LHM represents a well-de ned human anatomy, including four dynamic ventricles, aorta (ascending and aortic arch), atria and pulmonary artery based on cardiac MRI data 28 . To simulate aortic constriction in a swine model, the aortic arch was scaled down to approximate in vivo measurements (ID ~ 19mm, OD ~ 20mm).
Nonlinear explicit dynamic analysis was performed to simulate the constriction pro les and the deformation of aorta. An accurate 3D representation of the band was constructed in SOLIDWORKS (Dassault Systèmes, 2019) and imported into the FEA model. The sleeve pockets were modeled as 3-node triangular shell elements (S3R) and assigned Neo-Hookean hyperelastic TPU material properties. Uniaxial test data (Fig. 2c) was used as an input source for the hyperelastic model. The aorta was modeled using an anisotropic hyperelastic material model for cardiac tissue 29 . Further details regarding the LHM can be found in previous studies 28,29,40 . Surface-based uid cavities were de ned to represent the uid inside the actuator pockets and the ascending aorta. The hydrostatic uid elements inside the surfaces govern the relationship between mechanical deformation, cavity pressure and volume, hence predict the mechanical response of uid-lled structures.
The FEA simulation consisted of two steps. In the rst step, the pockets were depressurized to achieve a de ated shape, and the aortic pressure was increased to 100 mmHg. In the next and nal step, the pockets were gradually pressurized to achieve full aortic constriction. These studies were performed using Abaqus/Explicit solver and were completed in approximately 3 hours on a desktop PC with a 3.0 GHZ i7-9700 processor with 8 cores and 32 GB RAM. Computational uid dynamic (CFD) modeling In this study, a Large-Eddy Simulation (LES) turbulence model was utilized in XFlow 2020 software (Dassault Systèmes) using a particle-based and fully Lagrangian approach to model aortic ow patterns. Blood was modeled as an incompressible Newtonian uid and turbulence was simulated using the Wall-Adapting Local Eddy viscosity model 41,42 . The deformed structure of the ascending aorta was imported into the XFlow domain for each actuation pro le. The inlet surface of the ascending aorta was extended to facilitate convergence. Further details regarding the de nition of the inlet and outlet boundary conditions can be found in the Supplementary Information.
The wall surface was assumed to be rigid, and the no-slip condition was applied. The total simulation time was set to 1.45 seconds (~ 2 cycles) and the time step ∆t = 1x10 − 5 s was applied for each simulation to ensure numerical stability. Grid independency was achieved at 0.8 mm resolution with approximately 159,000 elements. The re nement method with 0.2 mm resolution was applied near the walls to ensure a su cient amount of lattice elements at the constriction region as a boundary layer. Analysis was completed in ~ 6 hours on a desktop PC with a 3.0 GHZ i7-9700 processor with 8 cores and 32 GB RAM. Histology studies Each of the materials constituting the aortic sleeve presented in this work was implanted subcutaneously in one Sprague Dawley rat to investigate the response of the surrounding tissue 28 days postimplantation. Four subcutaneous pockets were created surgically on the back of the rat to enable placement of the materials. The samples implanted were as follows: the TPU sheet constituting the expandable elements of the sleeve; the TPU-coated fabric used as the inelastic constraining layer of the sleeve; a short segment of the actuation line made of Polyurethane, and a Polycarbonate connector.
Images of the digitized slides can be found in Supplementary Information, as well as further details regarding animal handling and the implantation procedure.

Animal preparation
In vivo studies were conducted on a total of 6 Yorkshire swine (~ 38-45kg) housed in the Massachusetts General Hospital Center for Comparative Medicine Large Animal Facility. The swine were kept under 12-h light/12-h dark cycles with access to a standard diet of food and water ad libitum. Starting 72h prior to the implantation procedure, animals were given oral amiodarone. Before the procedure, animals were anesthetized, intubated with an endotracheal tube and placed on a ventilator with iso urane and oxygen.
Immediately prior to the procedure, animals received an intramuscular injection of buprenorphine, carprofen and a continuous infusion of fentanyl citrate. The swine were administered cefazolin, and a constant infusion of amiodarone and 2% Lidocaine for the duration of the procedure.
Implantation of the aortic band involved a thoracotomy with incisions at the level of the fourth intercostal space. Muscles layers were separated through blunt dissection to access the thoracic cavity and the ascending aorta. The sleeve was wrapped around the ascending aorta, pre-tensioned by pulling the strip through the slit, and then secured using sutures. Pre-tensioning was considered successful when the strip could be pulled entirely through the slit and when no space between the sleeve and the porcine aorta could be noticed upon visual and tactile inspection. Due to anatomical variations, adequate pretensioning could not be achieved in 2 of the 6 pigs, which were therefore discarded from the analysis.
Details of the effects of pre-tensioning on the hemodynamics of aortic constriction can be found in the Supplementary Information.
Following successful implantation, the apical suture and retractor were removed. The lungs were overin ated for 3-4 breaths to evacuate excess uid and prevent pneumothorax. The cavity and skin could then be closed via suturing in a layer-by-layer fashion. The lines from the sleeve remained external to the animal. Postoperative analgesia was provided with a transdermal fentanyl path and oral carprofen. Oral antibiotics were administered 72h post operation.
Prior to the MRI study (D6), the animals were administered anesthesia and intubated. Body temperature was supported using a circulating water heat pad placed between the animal and the MRI table. A pulse oximeter, blood pressure cuff and spirometer were all placed to monitor the animals' vitals throughout scanning procedures. MRI revealed signi cant pericardial effusion of one animal, which was therefore euthanized prior to conducting any aortic constriction procedures. Following successful MRI, animals were recovered and monitored.
Before terminal hemodynamic evaluation (D8), the swine were placed under anesthesia following the same regiment as described above. After echocardiography, LV catheterization, and thoracic aortic ow measurements, animals were euthanized with saturated potassium chloride. Changes in the animal's heart rate and blood pressure due to anesthesia were monitored. More details on the animal procedure and drug dosages can be found in the Supplementary Information.

Echocardiography
LV systolic function and ow pro le across the proximal ascending aorta were evaluated using a commercial ultrasound system (IE33/X5-1 or X7-2 transducer, Philips, Andover, MA) at D0 (transthoracic) and at D8 (transepicardial). M-mode echocardiography on the LV in short axis view and continuous pulse-Doppler echocardiography across the proximal ascending aorta in an apical view were recorded during continuous activation of the aortic sleeve to evaluate changes in the LV function and the ow pro le due to aortic constriction 43 . Acquired echocardiographic data were analyzed with syngo Dynamics (Siemens Healthineers, Erlangen, Germany). From measurements of the LV end-diastolic and -systolic diameters, LV volumes and ejection fraction were estimated with the Teichholz method 44 .
Echocardiographic studies were conducted on n = 2 swine, as these procedures were included in the protocol only at a later stage.

Magnetic resonance imaging
Each animal was scanned one of two 3T clinical MRI systems (Biograph mMR scanner, 45mT/m gradient system and a MAGNETOM Prisma, 80mT/m gradient system, Siemens Healthineers, Erlangen, Germany), both equipped with a standard 32-channel antero-posterior surface coil. Animals were imaged with a whole heart CINE MRI as well as 2D/4D cardiac ow MRI sequences centered on the aortic constriction.
Whole heart CINE MRI acquisitions were performed with a balanced steady-state free precession (bSSFP) sequence along the short axis plane with the following parameters (resolution 1.4x1.4x6.0 mm 3 , matrix size 128/85, 10/15 slices depending on the heart size, pixel bandwidth (BW) 1500 Hz/pixel, echo time (TE) 2.79 ms, repetition time (TR) 30.72 ms and retrospective ECG gating with 25 segments). The aortic ow sequence was done with a 2D or 3D gradient echo (GRE) sequence depending on the scanner utilized.
On the Biograph mMR scanner, 2D ow was acquired with velocity encoding along the through-plane direction and images obtained in the short axis plane centered on the aortic band. The sequence parameters for the 2D ow were the following: velocity encoding (VENC) 500 mm/s, resolution 1.4x1.4x6.0 mm 3 , matrix size 256x152 and 12 to 15 slices, BW 490 Hz/pixel, TE/TR 3.41/23.52 ms and retrospective ECG gating over 23 segments.
On the MAGNETOM Prisma scanner, the 4D ow sequence was acquired with velocity encoding along the through-plane direction, left/right and head/feet directions and images obtained in the short axis plane centered on the aortic band. The sequence parameters were the following: velocity encoding (VENC) 500 mm/s, resolution 1.4x1.4x2.5 mm 3 , matrix size 208x166 and 28 slices to cover the entire aortic arch, BW 490 Hz/pixel, TE/TR 2.07/15.6 ms, retrospective ECG gating over 27 segments and respiratory gating with a pencil beam navigator placed on the liver dome and acceptance window of 8mm.
Details on the reconstruction of the LV geometries, 4D ow analysis and estimates of LVEF on MRI can be found in the Supplementary Information.

Left ventricle catheterization
In vivo LV PV data were collected using the Transonic ADV500 PV System and the 5F straight tip PV loop catheter (Transonic Systems, Inc., Ithaca, NY). The catheter was inserted transapically during the openchest surgery. Through real-time pressure measurements, the catheter was guided through the aortic valve and gradually retrack back to the LV to ensure consistent catheter positioning. The catheter was then rotated to minimize the interference with mitral-valve and/or papillary muscle. Data were collected with 400 Hz sampling rate with a 50 Hz low-pass lter applied to the volume data. Thoracic aorta ow Flow at the thoracic aorta was measured using the TS420 Perivascular Flowmeter Module with the MA-12PAU ow probe (Transonic Systems, Inc., Ithaca, NY). Data were collected under low range setup (0 ~ 1.2 Volt) with a 10 Hz lter. Flow rate was estimated using the pre-calibrated unit conversion factor (25mL/min/V).
Data processing and visualization MATLAB® R2020a (MathWorks®) was used for data processing and visualization. One-way analysis of variance (ANOVA) was performed to determine signi cance across groups. Data are shown as mean ± SD across trials. When present, smaller error bars indicate the SD of three representative consecutive heart cycles within one trial. The number of heart cycles was kept at a minimum to minimize the risks associated with prolonged full constriction, i.e., when blood ow at ejection is almost entirely blocked by the soft robotic sleeve. For consistency, three representative heart cycles were also averaged for

Code availability
Codes used for modelling, and data acquisition, processing, and analysis are available upon request. models. L.R., C.O., Y.F., J.F-C, Y.N. conducted in vivo testing. L.R., S.C., R.E., J.K. provided support for all animal handling procedures. A.M., JL. G. performed animal surgeries. Figure 1 Overview of research impact. A high-delity in vivo model of aortic valve disease based on a bio-inspired soft robotic aortic sleeve. The tunability of the sleeve enables the recreation of the hemodynamics of aortic stenosis (AS) and of congenital valve abnormalities, including those of bicommissural and unicommissural aortic valves, which arise from the fusion of one and two commissures respectively and are responsible for the accelerated onset and progression of AS. Magnetic Resonance Imaging allows visualization of the ow pattern induced by the soft robotic sleeve and hemodynamic mimicry of each valvular defect. By developing a high-delity animal model of aortic valve disease hemodynamics, this research is poised to profoundly impact the interventional paradigm for this condition. Illustration created by BioHues Digital.

Figure 2
Design and manufacturing of the soft robotic aortic sleeve. a, Two thermoplastic polyurethane (TPU) sheets are vacuum formed to a positive 3D-printed mould. b, The two TPU sheets are then heat-sealed together creating three distinct expandable elements or pockets. They are then attached to a strainlimiting fabric thorough a heat-sealing process that utilizes a negative of the 3D-printed mould. c, Stressstrain response of the TPU and fabric layers under uniaxial tension. d, Axial force exerted by the sleeve at continuous actuation. e-f, 3D views of the aortic with details of the individual pockets, constraining fabric, hydraulic lines for actuation lines, and fabric slit and strip for positioning around the porcine ascending aorta. Data show mean ± SD, n = 3 for each data point.    area corresponds to mean ± SD of three consecutive heartbeats. h, Arterial elastance (Ea) measurements via LV catheterization (n = 3). i, Peak left ventricular pressure (LVP) measurements via LV catheterization (n = 3). j, Stroke volume (SV) measurements via LV catheterization (n = 3). In bar plots, large error bars represent 1 SD from the mean value across the animals, while smaller error bars show the SD within each animal averaged from 3 consecutive heart cycles. n.s: non-signi cant; *: P < 0.1, **: P < 0.05, ***: P < 0.01, ****: P < 0.001.