Artificial ventricle using actuators

Abstract

The present invention is related to an Artificial Ventricle comprising one or more actuator immersed in a passive matrix, said matrix having the geometry of the ventricle resembling a truncated ellipsoid, said matrix being made of an elastomeric material, said one or more actuator is characterised in that it follows a closed curve on a set of nested toroidal surfaces inside the elastomeric matrix, forming a collection of (p,q)-torus knots.

Description

[0001]TITLE: “ARTIFICIAL VENTRICLE USING ACTUATORS” * * * * * * * * * * * * * Background Heart transplantation is an effective treatment for end-stage heart failure. However, due to the severe shortage of donors, artificial ventricles (AVs) and total artificial hearts (TAHs) are used as a bridge to transplantation. Current AVs have rigid walls that are in direct contact with the circulating blood, resulting in reduced blood flow and potential damage to the blood. Sluggish blood flow in these devices leads to elevated levels of coagulation factors, promoting platelet adhesion and aggregation, and ultimately causing blood clot formation (A. Lichota, et al. Factors Affecting the Formation and Treatment of Thrombosis by Natural and Synthetic Compounds, Int. J. Mol. Sci., 2020; 21: 7975). Consequently, patients with AVs require continuous anticoagulant medication, which further complicates their treatment. By closely mimicking the motion of the heart, the side-effects and the need for anticoagulant medication whilst using AVs and TAHs can potentially be minimized. It is therefore a strongly felt need to closely mimic the native heart with an AV, including the complex motions of the left ventricle, providing physiological intraventricular hemodynamic blood loading and flow patterns. For this purpose, it is important to analyse the morphology and motion of the native heart in detail. The heart consists of four main chambers: the left and right ventricles and the two atria. The left ventricle, responsible for pumping blood throughout the body, is more muscular with thicker walls compared to the right ventricle, which pumps blood to the respiratory system for oxygenation. The geometry of the native left ventricle resembles the geometry of a truncated ellipsoid, with the outer layer of myofibers forming a left-handed helix and the inner layer forming a right-handed helix. The angle of these fibers varies smoothly throughout the ventricular walls, being nearly horizontal in the middle and helically angled at the inner endocardial and out epicardial wall (D. D. Streeter, et al., Fiber Orientation in the Canine Left Ventricle during Diastole and Systole, Circ. Res., 1969; 24: 339–347). Additionally, these fibers aggregate in a sheet-like structure, approximately four cells thick, stacked upon each other throughout the ventricle. A commonly used rule-based method assigns the fiber orientation based on the assumption that the fibers lie on nested ellipsoidal surfaces parallel to the inner and outer walls of the left ventricle. However, evidence suggests that the myofibers follow closed curves or geodesics on a set of nested toroidal surfaces rather than open paths from the apex to the base of the ventricle parallel to the walls (C. E. Thomas, The muscular architecture of the ventricles of hog and dog hearts, Am. J. Anat., 1957; 101: 17–57; C. S. Peskin, Fiber architecture of the left ventricular wall: An asymptotic analysis, Commun. Pure Appl. Math., 1989; 42; 79–113; A. Mourad, Characterization and Computation of Closed Geodesics on Toroidal Surfaces, J. Geometry Symmetry in Physics, 2012. doi: 10.7546 / jgsp-16-2009- 23-37; P.-S. Jouk et al., Analysis of the fiber architecture of the heart by quantitative polarized light microscopy. Accuracy, limitations, and contribution to the study of the fiber architecture of the ventricles during foetal and neonatal life, Eur. J. Cardiothorac. Surg., 2007; 31: 915–921). WO2023 / 235832 discloses a 3D bioprinting system based on digital light processing (DLP) which allows organs with structural complexity (such as lung, heart etc.) to be produced. Within this embodiment, it is important to use a soft “bioink” which would allow biological material, such as cells, vessels, or the like to grow and develop. They managed to grow vessels in the shape of torus- knots. The geometry of the vessels they produced is a single torus-knot on a circular torus. WO2021 / 260614 discloses deformable artificial ventricle comprised of active layers with fluidic actuators arranged helically. Several cylindrical fluidic actuators start from the apex and end at the base to form a helix. Multiple actuators placed around the foldable ventricular chamber with inlets (connected to each other to form a single inlet at the apex) and sealed outlets (at the base) compress the ventricular chamber upon contraction. The geometry of their structure is very simple. US2016 / 346449 discloses a direct cardiac compression device by helically and circumferentially arranging multiple cylindrical actuators within an elastomeric matrix to form an active sleeve surrounding the heart. This device won’t be in direct contact with blood since it compresses the external layer of the heart. Like the previous invention, the actuators have an inlet and sealed outlet. This device generates longitudinal shortening and twisting motion due to the presence of helically arranged actuators. The circumferentially arranged actuators can generate the wall thickening in the elastomeric matrix. US2023 / 321817 discloses a soft hydraulic filament artificial muscle (HFAM) that extends and contracts in response to differentiation in hydraulic pressure. In some forms they disclose a design of assistive compressive medical device using these artificial muscles. Their compression robotic heart assist device is made of a single HFAM and acrylic yarns by the weaving techniques. The woven HFAM makes a flat sheet that wraps around the heart. Like the previous invention it is placed on the external surface of the heart. It is able to induce twist and radial expansion on the outer surface of the heart. Description In the present invention, the authors have defined a nested toroidal laminar actuator architecture for the AV, which towards the design of a soft robotic AV can efficiently and durably mimic the contractile motion of the native left ventricle. For the first time, a soft robotic AV with a “nested torus knot” actuator configuration immersed in a soft matrix is here proposed. Description of the drawings Figure 1: A) Schematic of a soft elastomeric passive matrix in the shape of the ventricle surrounding the actuator. (B) exemplificative design of the spatial arrangement of a single cylindrical actuator (ex. McKibben muscle) shown in black as nested (6,5)-torus knots, designed by the method according to the present invention. (C) enlarged view of a portion of a cylindrical actuator. (D) enlarged view of a portion of a cylindrical actuator in operation and subjected to the pressure of fluid. (10): passive matrix, (11): fluid inlet to pressurize the actuator(s), (12): A portion of the cylindrical (fiber-like) actuator, (13): passive sheet hosting the actuator(s), (14): blood inlet, (15): blood outlet. Figure 2: Single sheet-like actuator geometry. Passive matrix (A). Sheet- like actuator inside a passive matrix (B). Enlarged view, geometry of a portion of a sheet-like actuator (C). Sheet-like pneumatic actuator (D).(22) a portion of a sheet-like actuator with three fluid chambers, (23) fluid chambers, (24) sealed edges of the fluid chambers shown in black, (25) channels connecting the adjacent fluid chambers. Figure 3: Schematic of the first step of the method according to the present invention. A: shows a circular torus with major radius of ^^0and minor radius of ^^0. Parameters used to define the nested (p,q) torus knots shown as r being the distance to the centre of the inner circle of the torus, ^^ shows the rotation of the curves around the main axis of revolution while rotating around the inner circle of the torus. B: shows the result of a collection of nested (p,q) torus knots where p=2 and q=1 as a twisted surface within the torus domain. Vectors ^^ (trajectory of the vector field R ⃗(r,θ) along the torus knots) and ^^ (trajectory of the vector field R ⃗(r,θ) transverse to the torus knots) are illustrated on the twisted surface (vector field R ⃗(r,θ)). Figure 4: Schematic of the parameters used in the morphing step of the method according to an embodiment of the present invention. A: shows different boundaries with different patterns on the left ventricle. B: shows different boundaries with different patterns on the circular torus. C: shows the cross section of the ventricle and the torus with the arrows showing the displacement field ^^0used to morph the torus into the left ventricle. The displacement field is obtained by subtracting the coordinates of the points on the boundaries of the circular torus from the points on the corresponding boundaries of the ventricle. (1) Ventricle, (2) circular torus, (3) base, (4) epicardial surface, (5) endocardial surface, (6) apical surface. Figure 5: Schematic of the morphing step according to an embodiment of the present invention. A) shows the twisted surface (vector field R ⃗(r,θ)) within the circular torus before morphing. B) shows the twisted surface (vector field R ⃗(r,θ)) within the ventricular domain after morphing. Figure 6: Lower mean stress accumulated in the fiber direction, but higher contraction achieved in the nested tori model (A) with respect to the nested ellipsoidal, sheet orientations parallel to the walls (comparative, B) and the nested ellipsoidal, sheet orientations perpendicular to the walls (comparative, C). “IVC” stands for the isovolumic contraction phase, “E” stands for the ejection, “IVR” for isovolumic relaxation and “F” stands for filling phases throughout a realistic cardiac cycle. “endo” stands for endocardial surface, “mid” stands for mid-ventricular surface and “epi” stands for the epicardial surface. Figure 7: The kinetic energy of the artificial ventricle using the same excitation input and resulted in a higher energy generation in NT model. “IVC” stands for the isovolumic contraction phase, “E” stands for the ejection, “IVR” for isovolumic relaxation and “F” stands for filling phases throughout a realistic cardiac cycle. Figure 8: Rotation of the inner and outer layer of the artificial ventricle in three different models: NT, nested tori (A). NE||, nested ellipsoidal, sheet orientations parallel to the walls (comparative, B). NE^, nested ellipsoidal, sheet orientations perpendicular to the walls (comparative, C). “IVC” stands for the isovolumic contraction phase, “E” stands for the ejection, “IVR” for isovolumic relaxation and “F” stands for filling phases throughout a realistic cardiac cycle. Figure 9: A single passive sheet (light gray) made of a collection of (p,q)- torus knots hosting a single fiber-like actuator (black) obtained given different p and q values. Definitions • Homomorphic morphing / morphing techniques: according to the present invention this term means obtaining the deformation map between the circular torus and an ellipsoid with a tiny opening at the apex and larger opening at the base. This mapping function then applies in particular to the “homomorphic morphing” of a sheet made of nested (p,q)-torus knots defined inside the torus domain into the (p,q)-torus knots within the geometry of the ellipsoid. • Vectors ^^ and ^^: the derivative in the θ direction represents vector ^^ and the directional derivative in the direction ^^ (minor radius of the torus) is vector ^^ as shown in FIG.3B. The sheet is defined by using the vectors ^^ and ^^. • Structure of an actuator: it can be cylindrical (named also fiber- like, mainly mono-directional) or it can be flat (or sheet-like) with a mainly bi-dimensional structure). The actuator is designed to exert contractile force along the direction of the vector ^^. • Passive matrix (10): the passive matrix has the geometry of the ventricle resembling the geometry of a truncated ellipsoid, and is made of a material selected from the group comprising: an elastomeric material, a gel, air or a combination of the above, or an elastomeric material may only envelope the one or more actuator. Detailed Description The present invention is related to an Artificial Ventricle comprising one or more actuator immersed in a passive matrix (10), said passive matrix having the geometry of a ventricle which resembles the geometry of a truncated ellipsoid, and is made of a material selected from the group comprising: an elastomeric material, a gel, air or a combination of the above. When the passive matrix is made of gel or air, it is comprised within an elastic shell. Alternatively, the one or more actuator is enveloped in an elastomeric material. The one or more actuator is characterised in that it is formed by a collection of (p,q)-torus knots. In an embodiment, said one or more actuator is a pneumatic actuator. In a different embodiment, the actuator can be electrically-driven, chemically-driven or thermally-driven. In an embodiment, said one or more actuator is cylindrical or (fiber-like), and follows distinguished nested (p,q)-torus knots, according to FIG. 1B. In an embodiment, said fiber-like actuator is hold in place using a passive sheet which is designed using the vectors ^^ and ^^ and therefore become a 3D twisted sheet made of the collection (p,q)-torus knots on the nested toroidal surfaces in the ventricle (shown in white), according to FIG.1B. In an embodiment, said one or more actuator is sheet-like and is designed using the vectors ^^ and ^^ and therefore become a 3D twisted sheet made of the collection of (p,q)-torus knots on the nested toroidal surfaces in the ventricle, according to FIG.2B. In an embodiment, said (p,q) torus knots have q ≥ 3, and p > q while p ┴ q (with p and q relatively prime numbers). In an embodiment, said one or more sheet-like actuator comprises rectangular or diamond-like or hexagonal or similar shape fluid chambers, according to FIG.2C and D, where an exemplificative embodiment comprising rectangular fluid chambers is schematically depicted. In this embodiment, each fluid chamber is a double layered sheet made of elastic material, such as rubber or silicone. The black regions show the borders of the fluid chamber where the top and bottom layers are attached to each other. Each fluid chamber is connected to the neighbours by an opening at their center as shown in FIG.2C and D. The fluid chambers, are inflated and take on a pillow- like shape which pulls the two ends of each fluid chamber closer to each other, resulting in contraction. In both top and bottom layers of the fluid chambers, the elastic rubber like material is reinforced with mesh-like structure having higher stiffness in the direction of contraction and lower stiffness in the transverse direction. The inflation or normal expansion of the fluid chambers causes stretching of the mesh-like structure, resulting in preferential expansion alongst the mesh-like structure’s lateral direction with respect to the longitudinal direction. This allows the fluid chamber to expand laterally, and contract longitudinally as shown in FIG.2D. The advantage of the sheet-like actuator design according to the present invention is its ability to generate more homogeneous and continuous force along the desired direction, leading to greater deformation of the soft passive matrix, more efficient contraction, better biomimicry and ultimately, improved overall performance. A comparative example 1 is provided to show the improved efficiency of contraction compared to a nested ellipsoidal (NE) model (FIG.8). In an embodiment, the geometry of the actuators according to the present invention is designed according to a morphing method. To assimilate the ventricle to a geometric solid, the geometry resembling the native left ventricle is a truncated ellipsoid. Specifically, a set of curves and sheets are defined inside a circular torus that later are mapped, using morphing techniques, into the truncated ellipsoid to define the architecture of the actuators in the soft AV. In an embodiment, said method includes a first step in which a circular torus is defined, wherein the volume of said torus is equal to the volume of the ventricle. Said torus has a major radius ^^0 (see FIG.3A) equal to the radius of the mean equatorial wall of the ventricle, as calculated from the ellipsoid, and a minor radius ^^0 such that the volume of the torus is equal to the volume of the ventricle. A vector space is then defined within the circular torus domain. With reference to FIG.3B, the dark gray colored surface represents the vectorspace (^⃗^(^^, θ)) inside the torus. To reach this representation, a set of closedcurves on nested toroidal surfaces, known as nested (p,q)-torus knots, is vectorized and defined as below, resulting in a 3D surface inside the torus domain ^^ = [0,2^^^^]^⃗^(^^, θ) is a collection of nested (p,q)-torus knots resulting in a 3D surfacewithin the torus domain as in FIG.3B. A (p,q)-torus knot winds qtimes around a circle in the interior of the torus, for every p time winding around its axis of rotational symmetry as shown in FIG.3A. At any point on the said 3D surface thus defined, the derivative in the θ direction leads to the vector ^^ and the directional derivative in the direction ^^ which is the minor radius of the torus leads to the vector ^^ shown in FIG.3B. ^^ = ^^^^^⃗^(^^, ^^)Second step is a morphing step and the man skilled in the art knows how to morph a torus obtained from the first step into the shape of the ventricle which is a truncated ellipsoid, wherein the resulting deformation is applied to the vectors ^^and ^^ calculated in the first step to obtain the fiber and sheet direction throughout the ventricle domain. In an embodiment, said morphing step starts by defining (FIG.4A) the outer surface of the ventricle geometry, resembling a truncated ellipsoid (1), as a set of points and identify, on said geometry, four regions: a) basal points (3), the upper surface of the truncated ellipsoid), b) epicardial points (4), the outer wall of the ellipsoid), c) endocardial points (5), the inner wall of the ellipsoid), and d) apical points (6), the small opening on the line connecting the bottom of the endocardium to the epicardium aligned with the axis of revolution of the ellipsoid). Followed by defining (FIG.4B) the outer surface of said the circular torus and divide the same into four subsets of the same size and position as defined on the artificial ventricle geometry, basal (3), epicardial (4), endocardial (5) and apical (6). In an embodiment, said method further comprises: - Obtaining (FIG. 4C) a discrete displacement field by subtracting the coordinates of the corresponding points on the ventricle and the torus surfaces, wherein: ^^^^^^^^ = ^^^^^^^^^^^^,^^^^⋃^^^^^^^^^^^^,^^^^⋃^^^^^^^^^^,^^^^⋃^^^^^^^^^^^^,^^^^ ^^0 = ^^^^^^^^ − ^^^^^^^^^^wherein:^^^^^^^^is the set of regions on the LV as shown in the FIG.4A, ^^^^^^^^^^is the set of regions on the torus as shown in the FIG.4B, (5), the region on the contour or boundary of the LV domain corresponding to endocardium, the small opening on the line connecting the bottom of the endocardium to the apex of the epicardium, = (4), the region on the contour or boundary of the LV domain corresponding to epicardium, = (3) the region on the contour or boundary of the LV domain corresponding to base. The same parameters, with subscript tor relates to the regions on the torus in FIG.4B. The next step involves morphing the torus onto the shape of the LV and is depicted in FIG.5. In an embodiment, this is done using FEM (Finite Element Method) by solving the non-linear mechanical equilibrium withoutaccelerations or body forces for the torus^^^^^^ (^^) = 0 , with ^^ being the Cauchy stress tensor. On the boundaries of thetorus the Dirichlet type boundary condition=^^0 was applied with ^^0 being the displacement field computed in theprevious step. The resulting deformation is applied to the vectors ^^and ^^ calculated in the previous step to obtain the fiber and sheet directions throughout the ventricle domain. The present design allows a more efficient structure and the use of a single actuator per AV which represents the preferred embodiment. According to it, it is possible to use a single inlet connection and this reduces the risk of failure at this critical point. The connection between the pneumatic inlet and the soft actuator is a weak point of the structure and by reducing the number of these connections the durability of the device is significantly improved. The architecture designed according to the present invention further leads to a better biomimicry. In example 1 (FIG.7 and FIG.8), this architecture has been compared to state of the art architectures, resulting, according to our studies in a larger motion (twist, thickening and shortening) of the blood contacting walls therefore reducing the risk of blood flow stagnation that could lead to blood coagulation. Moreover, with respect to energy efficiency, this architecture leads to a higher pumping work output under similar input conditions compared to state-of-the- art architectures (see Example 1, FIG.7). It also promotes a more uniform deformation in the walls of the ventricle (see Example 1, FIG.6), reducing stress along the actuators and within the passive matrix, which can eventually enhance the overall durability of the device. The examples that follow are given to support and illustrate the present invention without, however, limiting it. Example 1: comparative computational analysis of artificial ventricle contraction. A comparative computational study was performed using 3 different actuator architectures: the nested tori (NT) actuator architecture (according to the invention) and two nested ellipsoidal (NE) actuator architectures (comparative). The three models simulate the contraction of an artificial ventricle device. The actuators are embedded as a continuum of locally organized actuators oriented alongst varying fiber-sheet direction planes. We simulate active contraction with fixed physical model parameters, i.e. the combined active and passive constitutive model and parameters, the pressure loading conditions, and the hemodynamic outflow conditions were kept constant across all three models. Only the actuator fiber-sheet direction architecture was varied. The NT actuator architecture according to the invention was obtained by interpolating and morphing a continuous field of nested tori ^^ and ^^ vectors onto the artificial ventricle domain. In contrast, the NE actuator architectures were obtained using a Laplace-Dirichlet rule-based method which provides to define nested ellipsoidal fiber and sheet angles within the artificial ventricular wall based on the transmural depth (Bayer, J.D., Blake, R.C., Plank, G. et al. A Novel Rule-Based Algorithm for Assigning Myocardial Fiber Orientation to Computational Heart Models. Ann Biomed Eng 40, 2243–2254 (2012)). Concomitantly, our computational models single out the effect that differing actuator architecture organizations has on the performance of artificial ventricles under realistic hemodynamic loading conditions. The results are illustrated in FIG.6, 7, 8. In these figures, “IVC” stands for the isovolumic contraction phase, “E” stands for the ejection, “IVR” for isovolumic relaxation and “F” stands for filling phases throughout a realistic cardiac cycle. The results prove that the NT actuator architecture (FIG.6A) is favourable to allow the fibers to contract more while being subjected to a lower stress – which showcases improved efficiency through the here described actuator architecture design. Compared to the NE designs, the NT design according to the invention leads to larger stroke volumes, and increased artificial ventricle longitudinal shortening, radial wall-thickening and circumferential rotation. Importantly, the NT design according to the invention also leads to a more homogeneous stress distribution, which showcases its potential for improved durability. Example 2: Design of the actuators for the soft robotic ventricle. Discrete curves and sheets in the AV domain have been generated, using the method here described. The generated curves, or sheets, are then used to design soft actuators, which are then placed in a soft elastomeric matrix resembling the extracellular matrix in ventricular tissue. The actuators represent the contractile myofibers. Shape and size of the so obtained actuators of the AV are customised according to the parameters “p” and “q”. The actuator shapes can be designed according to the torus knots on the nested toroidal surfaces inside the AV domain to be cylindrical or fiber-like. They can also be designed based on the 3D surface resulted from the collection of the torus knots in the AV domain to be sheet-like in their shapes. For example, cylindrical actuators such as McKibben artificial muscles contract within the range of myofibers and can be produced with diameters as small as 1 mm. FIG.1 illustrates this embodiment, wherein in FIG.1A a passive matrix (10) is shown, with one actuator inlet (11) and a blood inlet (14) and a blood outlet (15). FIG. 1B illustrates a single cylindrical actuator (12) designed according to the method. Said actuator is inside a passive matrix (10) and is hold in place using a passive sheet (13) which is made of the nested (p,q)- torus knots within the passive matrix. FIG.1C shows a portion of the actuator, extended, before entering the fluid and, in FIG. 1D, the same actuator resembling the McKibben muscle in contraction when pressurized by the fluid. In a different embodiment, depicted in FIG.2, the actuator is designed in a sheet form. In this embodiment, it is a single sheet-like actuator that contracts along its length while being inflated. FIG.2A shows a passive matrix (10) with one actuator inlet (11) and a blood inlet (14) and a blood outlet (15). The placement of a sheet-like actuator (22) in the passive matrix is shown in FIG. 2B, wherein the width of the actuator varies throughout its length, and its thickness can vary, depending on the ventricle's size and shape exactly similar to the passive sheet, hosting the fiber-like actuator FIG.1B (13). In an embodiment, shown in FIG. 2C, a portion of a sheet-like pneumatic actuator is depicted. Said actuator contracts along its length when inflated. In this embodiment, said sheet-like actuator is composed of at least two fluid chambers (23), each fluid chamber being double layered sheets made of elastic material. The black regions show the border (24) of each fluid chamber, where the two layers are sealed to each other. Each fluid chamber is connected to the neighbours by an opening (25). When the fluid chambers are pressurized by a fluid, represented in FIG.2D, the fluid passing through the channels (25) from one fluid chamber (23) to another, the fluid chambers are inflated and resemble pillow-like shapes which pulls on the structure along its length and thus initiates contraction. Example 3: Actuators architecture defined by values “p”, “q” The architecture of the actuators is defined by the values “p” and “q”. As an example, FIG.9 shows four different results of the sheets (shown in light gray) containing a fiber-like actuator (shown in black) . FIG.9A shows a sheet with p = 4 and q = 3, FIG.9B shows a sheet with p = 6 and q = 5, FIG.9C shows a sheet with p = 11 and q = 9, and FIG.9D shows a sheet with p = 19 and q = 11 resulting in a denser arrangement of the actuators. In the case of sheet-like actuator the same configuration could be applied.

Claims

CLAIMS 1. An Artificial Ventricle (AV) comprising one or more actuator immersed in a passive matrix (10), said matrix having the geometry of the ventricle resembling a truncated ellipsoid wherein said one or more actuator is characterised by a closed curve on a set of nested toroidal surface structure forming a collection of (p,q)-torus knots inside said passive matrix.

2. The AV according to claim 1, wherein said one or more actuator is designed by a homomorphic morphing of a 3D surface made of nested (p,q)-torus knots inside a torus into a 3D surface within a truncated ellipsoid, wherein said nested (p,q) torus knots inside a torus are defined by:^^ = [0,2^^^^]where ^⃗^(^^, θ) describes the nested (p,q) torus knots resulting in a 3Dsurface inside the torus domain, and where at any point of said surface the derivative in the ^^ direction leads to the vector ^^ and the directional derivative in r direction which is the minor radius of the torus, results in the vector ^^ .

3. The AV according to any one of claims 1-2, wherein, when the structure of the one or more actuator is fiber-like, the design follows the direction of vector ^^; alternatively, when the structure of the one or more actuatoris sheet-like, the design follows both vectors ^^ and ^^.

4. The AV according to any one of claims 1-3, wherein said (p,q) torus knots have q≥3, and p >q, and p┴q, with p and q relatively prime numbers.

5. The AV according to any one of claims 1-4 wherein said one or more actuator is sheet-like and becomes a 3D twisted sheet following the collection of (p,q)-torus knots on the nested toroidal surfaces in the passive matrix (10).

6. The AV according to any one of claims 1-4 wherein said one or more actuator is fiber-like and follows a distinguished nested (p,q)-torus knots inside the ventricle.

7. The AV according to claim 6 wherein said fiber-like actuator is hold in place by a passive sheet which is designed using the vectors ^^ and ^^ becoming a 3D twisted sheet made of the collection (p,q)-torus knots on the nested toroidal surfaces in the passive matrix (10).

8. The AV according to any one of claims 1-5, wherein said one or more actuator is pneumatic and comprises a twisted sheet made of at least two fluid chambers (23), wherein each one of said fluid chamber comprises a double layered sheet of an elastic material, each fluid chambers’ cavity being linked to the other through a channel (25), wherein said one or more actuator is activated by a fluid entering into the fluid chambers through an inlet (11).

9. The AV according to claim 8, wherein said double layered sheet is made of an elastic material and is reinforced with a mesh-like structure, wherein said mesh-like structure has a higher stiffness in the direction of contraction and a lower stiffness in the transverse direction.

10. The AV according to any one of claims 1-9 wherein said passive matrix is made of an elastomeric material, a gel, air or a combination thereof, or an elastomeric material envelopes the one or more actuator.

11. A method for the design of a 3D twisted surface made of nested (p,q) torus knots within a truncated ellipsoid, wherein said nested (p,q) torus knots inside a torus are defined by:-where ^⃗^(^^, θ) describes the nested (p,q) torus knots resulting ina 3D surface inside the torus domain, - where at any point of said surface the derivative in the ^^ direction leads to the vector ^^ and the directional derivative in r direction which is the minor radius of the torus, results in the vector ^^, and a homomorphic morphing between the said torus and the truncated ellipsoid is performed to obtain the ^^ and ^^ vectors inside the truncated ellipsoid, said vectors ^^ and ^^ being used to obtain the 3D twisted surface within said truncated ellipsoid.

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