Enhanced polyurethane shape memory intravascular stent optimization design method based on multi-scale coupling

Abstract

The invention discloses an optimized design method of an enhanced polyurethane shape memory intravascular stent based on multi-scale coupling. The method comprises the following steps: firstly, constructing a microcosmic molecular dynamics model, and quantitatively screening out an optimal graphene reinforced filler content and an interface chemical modification scheme by simulating a thermomechanical cycle and interface drawing process; then establishing a cross-scale mapping process between the micromechanics data and the macroscopic constitutive model, and converting microresponse into hyperelasticity and viscoelasticity parameters required by finite element analysis; finally, the whole process of pressing, holding, fixing and releasing of the vascular stent is simulated under the macroscopic scale, and the radial supporting force and the shape recovery performance of the optimized stent are directly predicted. According to the method, a data link between material microscopic design and device macroscopic application is opened through a multi-scale simulation strategy, a traditional experiment trial and error method is effectively replaced, and the research and development efficiency and design accuracy of the intravascular stent are remarkably improved.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of computer-aided material design (CAMD) and biomechanical simulation, specifically involving a multi-scale simulation method for enhancing and modifying polycaprolactone-polyurethane (PCL-PU)-based shape memory polymers, predicting interface properties, and simulating the macroscopic mechanical behavior of vascular stents. Background Technology

[0002] Shape memory materials are attracting increasing attention due to their unique properties in biomedical research. [1–3] In particular, shape memory polymers (SMPs) are able to “memorize” complex shapes and recover to their permanent form under specific conditions, making them ideal candidates for developing tissue engineering scaffolds. [4] These polymers can self-expand through temporary, minute deformations and return to their predetermined shape after implantation, thus enabling complex mechanical deformations without surgical intervention.

[0003] Among various SMPs, polycaprolactone-polyurethane (PCL-PU), polymerized from polycaprolactone diol (soft segment) and hexamethylene diisocyanate (hard segment), has been widely studied for its application in vascular stents due to its tunable soft and hard segment structure and excellent biocompatibility. However, traditional PCL-PU materials often exhibit poor shape retention (Ri) due to limitations in the soft-hard segment ratio and insufficient molecular chain recovery driving force. r ) and shape recovery rate (R f The inherent limitations of PVC-PU (polycarbonate-polyurethane) composites, particularly their weak radial support when used as vascular stents, make it difficult to maintain structural stability in complex vascular mechanical environments over long periods. To improve these properties, physically blended inorganic nanofillers (such as graphene and carbon nanotubes) have become a primary means of enhancing the performance of PCL-PU matrices. Graphene, with its extremely high Young's modulus and specific surface area, can theoretically significantly improve the stiffness and thermal conductivity of the polymer matrix. However, the macroscopic properties of nanocomposites do not increase linearly with filler content; their reinforcing effect is highly dependent on the amount of filler added (threshold effect) and the interfacial interaction between the filler and the polymer matrix. If the graphene content is too high or the interfacial bonding is weak, it can easily lead to nanoparticle aggregation or interfacial slippage, resulting in a decrease in the material's mechanical properties and the failure of its shape memory function.

[0004] Current research and development largely relies on extensive physical experiments for trial and error, which is not only time-consuming and costly, but also makes it difficult to directly predict the specific enhancing effects of different contents and interface modifications (such as -OH, -COOH) in the early design stages. Furthermore, existing simulation techniques often separate microscopic molecular simulation from macroscopic finite element simulation, lacking an effective mechanism to directly convert microscopic interface parameters into macroscopic model inputs. This makes it difficult to directly use microscopic data to predict the actual performance of vascular stents in the human body. Therefore, it is essential to establish a screening and prediction method that can connect the microscopic and macroscopic levels. Summary of the Invention

[0005] To address the lack of effective correlation between microscopic material design and macroscopic device performance prediction in existing polyurethane vascular stent development, which makes it difficult to directly use microscopic simulation data to guide macroscopic stent structure design, this invention provides an optimized design method for enhanced polyurethane shape memory vascular stents based on multi-scale coupling. This method establishes a complete simulation process from atomic-scale parameter selection to macroscopic finite element performance prediction. By mapping the material constitutive parameters obtained from microscopic calculations to the macroscopic model, it achieves cross-scale simulation of the mechanical behavior of vascular stents under multi-field coupling environments.

[0006] The present invention proposes an optimized design method for enhanced polyurethane shape memory vascular stents based on multi-scale coupling, which mainly includes the following steps:

[0007] Step 1: Construction of the micro-benchmark model and screening of the content of reinforcing fillers.

[0008] Step 2: Optimization of chemical modification schemes based on interfacial mechanics.

[0009] Step 3: Simulation of micromechanical response and extraction of constitutive data.

[0010] Step 4: Cross-scale parameter mapping and constitutive model fitting.

[0011] Step 5: Macroscopic stent modeling and performance prediction.

[0012] Step S1: Based on molecular dynamics (MD) methods, a full-atom model of a polyurethane (PCL-PU) matrix with alternating hard and soft segments is constructed. Based on this, composite material models containing different mass fractions of monolayer graphene are established using graphene as a reinforcing filler. Thermomechanical cycling simulations are performed on each model, with the shape fixation rate (R0) used as the metric. f ) and shape recovery rate (R r Using as the evaluation index, the content of the reinforcing phase with the best overall performance was selected.

[0013] Step S2: Based on the optimal content model selected in Step S1, a graphene-polymer interface model is constructed, and the graphene surface is chemically modified with epoxy, hydroxyl, and carboxyl groups respectively. The interface pull-out simulation is performed using MD to calculate the interface strength under different modification states, thereby determining the interface chemical modification scheme with the best reinforcement effect.

[0014] Step S3: For the final composite material model determined in steps S1 and S2, perform uniaxial tensile simulation and stress relaxation MD simulation under multiple temperature fields. Extract stress-strain response data and time-dependent modulus relaxation data at the microscale of the material as the original data source connecting the micro and macro scales.

[0015] Step S4 involves using the nonlinear least squares method to map the microscopic data obtained in step S3 to constitutive model parameters required for macroscopic finite element analysis. Specifically, this includes: 1. Fitting the microscopic stress-strain data to hyperelastic constitutive model parameters (such as Mooney-Rivlin parameters) to describe the material's large deformation behavior; 2. Fitting the microscopic relaxation data to viscoelastic constitutive model parameters (such as shear modulus and relaxation time in the Prony series) to describe the material's time-dependent behavior.

[0016] Step S5: Establish a three-dimensional geometric model of the vascular stent in the finite element analysis software, and assign the optimized constitutive parameters obtained in step S4 to the model. Simulate the thermodynamic behavior of the stent throughout the entire process of "high-temperature gripping - low-temperature fixation - body temperature release" to predict the radial support force, rebound speed, and shape memory effect of the optimized stent in a real vascular environment.

[0017] The beneficial effects of this invention are:

[0018] This invention proposes a systematic simulation method for artificial vascular stents based on microscopic and macroscopic cross-scale coupling. This method first uses molecular dynamics simulations to perform microscopic screening of reinforcing phase content and interface modification, and establishes a parameter transfer process from the atomic scale to the continuous medium scale, thereby directly predicting the service performance of the vascular stent in the macroscopic finite element model. This multi-scale simulation strategy effectively bridges the gap between microscopic material design and macroscopic device application, avoiding the limitations of traditional methods that rely solely on experimental trial and error, and improving R&D efficiency and prediction accuracy. Attached Figure Description

[0019] Figure 1 This is a flowchart of the present invention, "An Optimization Design Method for Enhanced Polyurethane Shape Memory Vascular Stents Based on Multi-Scale Coupling".

[0020] Figure 2The structures are microscopic molecular models, where (a) is the molecular structure of polycaprolactone diol; (b) is the molecular structure of hexamethylene diisocyanate; and (c) is the model cell structure of polyurethane.

[0021] Figure 3 To construct the molecular structure of nano-monolayer graphene and the unit cell structure of the composite material model, (a) is the molecular structure of nano-monolayer graphene; (b) is the unit cell structure of the composite material model.

[0022] Figure 4 This is a schematic diagram of the thermomechanical cycle used in the calculation model for the shape memory effect.

[0023] Figure 5 The following are the initial tangential and normal models of graphene and the model after equilibrium: (a) initial tangential model, (b) tangential equilibrium model, (c) tangential pulling method, (d) initial normal model, (e) normal equilibrium model, and (f) normal pulling method.

[0024] Figure 6 The following are flowcharts of the pulling process for the tangential and normal models: (a) tangential pulling, (b) normal pulling.

[0025] Figure 7 The figures show the uniaxial tension curve and stress relaxation curve, (a) uniaxial tension curve, (b) stress relaxation curve.

[0026] Figure 8 This is a simulation diagram of a vascular stent.

[0027] Figure 9 The accompanying figure is an abstract of the present invention, "An Optimization Design Method for Enhanced Polyurethane Shape Memory Vascular Stents Based on Multi-Scale Coupling". Detailed Implementation

[0028] The technical solution of the present invention will be further described in detail below with reference to specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0029] See Figure 1 This is a flowchart of a molecular simulation method for enhancing the shape memory properties of polyurethane provided in this embodiment. The method mainly includes the following steps:

[0030] Step 1: Constructing a microscopic baseline model and screening the content of the reinforcing phase.

[0031] 101. Construct polyurethane molecular models using polycaprolactone diol and hexamethylene diisocyanate as reacting monomers, respectively, to generate polyurethane molecular chains. The constructed polyurethane molecular chains have a degree of polymerization of 10. Twenty polyurethane molecular chains were then subjected to LAMMPS. [5,6] The components are assembled in the software to form a unit cell.

[0032] 102. To eliminate the edge unsaturation effect of graphene sheets, H atoms were added to the edges of monolayer graphene sheets for passivation. Graphene sheets were randomly inserted into the aforementioned polyurethane matrix at proportions of 1.26 wt%, 3.69 wt%, and 5.99 wt%, respectively, to construct three physically blended composite material models. Figure 3 (a) is the molecular structure of a single layer of graphene. Figure 3 (b) The unit cell structure of the composite material after adding 3.69% graphene, with green representing single-layer graphene.

[0033] 103. Energy minimization (conjugate gradient method) and molecular dynamics equilibrium (NPT ensemble, 298K, 1 atm, 50 ns, step size 1 fs) were performed on the constructed pure PU and three composite models. The density data after equilibrium are shown in Table 1. The simulation results fall within the experimental range of Haryńska et al. (1.02-1.11 g / cm³), which verifies the reliability of the model.

[0034] Table 1. Cell model density of polyurethane and its composites

[0035]

[0036] 104. The glass transition temperature (TVT) determines the shape fixation and recovery temperature of shape memory polymers. The gradient descent method was used to calculate the TVT. This involved keeping the system at 1 atmosphere and cooling it from 500K to 100K in 25K intervals, maintaining relaxation for 500 ps at each temperature, and then averaging the last 100 ps of relaxation data at each temperature. Two tangents were then drawn in the low-temperature and high-temperature regions; the intersection of these two tangents represents the Tg of the model. The calculation results are shown in Table 2.

[0037] Table 2. Tg values ​​of the pure PU model and the graphene-modified model.

[0038]

[0039] Simulations showed that the glass transition temperature of pure PU is 311.1 K, according to Y Wang et al. [7] The measured glass transition temperature of PCL-PU in human experiments was 308±3K, further demonstrating the accuracy of the example model.

[0040] 105. Using molecular dynamics to study thermomechanical cycles. A thermomechanical cycle refers to a complete cyclic process in which a material undergoes heating – deformation – cooling – unloading – reheating under controlled temperature and external forces. A schematic diagram of a thermomechanical cycle can be found here. Figure 4 .

[0041] In this embodiment, the tensile temperature Th = 1.5 Tg, the cooling temperature Tl = 200K, and the maximum strain is set to 0.5. The glass transition temperature is a key indicator for shape memory polymers to undergo shape memory cycling. (Liu et al.) [8] The text mentions that the shape memory stretching temperature reaches 1.27Tg-1.9Tg, resulting in the best shape recovery performance. The formulas for calculating the strain rate are shown in (1-1), the shape retention rate in (1-2), and the shape recovery rate in (1-3).

[0042] (1-1)

[0043] In the formula The length of the unit cell in the x-direction after equilibrium at temperature Th. This represents the length of the unit cell in the x-direction after stretching and the completion of the shape recovery procedure.

[0044] (1-2)

[0045] In the formula The constant strain after cooling and unloading. The initial strain rate is 0.5.

[0046] (1-3)

[0047] In the formula This represents the residual strain after reheating. Specific results from the thermomechanical cycle simulation are shown in Table 3.

[0048] Table 3 Shape fixation rate and recovery rate of polyurethane and its composites

[0049]

[0050] As shown in Table 3, the simulation results indicate that Rf increases slightly with increasing graphene content, but Rr reaches its maximum value (80.48%) at a content of 1.26%, which is a significant improvement compared to pure PU. Therefore, 1.26% is selected as the optimal reinforcing phase content for subsequent interface modification studies.

[0051] Step 2: Optimization of chemical modification schemes based on interfacial mechanics.

[0052] 201. Construct tangential and normal interface models of pure graphene, and simultaneously perform interface modification. Graphene sheets with a graphene content of 1.26% were selected for interface oxidation modification. The interface modification groups were epoxy groups, hydroxyl groups, and carboxyl groups, with an oxidation rate of 5%. The calculation method for the graphene oxidation rate is shown in Equation (2-1).

[0053] (2-1)

[0054] In the formula, This indicates the number of oxygen-containing groups modified on the graphene surface. This represents the total number of C atoms in graphene.

[0055] 202. Energy minimization and molecular dynamics equilibrium were performed on the initial tangential and normal models of pure graphene. Figure 5 The initial tangential and normal models of graphene, and the model after equilibrium, ( Figure 5 (a) Tangential initial model, ( Figure 5 (b) Tangential equilibrium model, Figure 5 (c) Tangential drawing method, Figure 5 (d) Initial model of normal direction, Figure 5 (e) Normal equilibrium model, Figure 5 (f) Normal pulling method.

[0056] 203. The tangential and normal models were stretched by fixing the lower end of the stretching direction, with a uniform stretching speed of 0.001 Å / fs. Because graphene's stiffness and hardness are much greater than those of polyurethane, it was treated as a rigid body in the simulation. Figure 6 (a)) Normal pulling process, ( Figure 6 (b) Tangential drawing process.

[0057] 204. Calculate the maximum pull-out force of the model, and simultaneously calculate the interface strength using formula 2-2. The final calculation results are shown in Table 4 and converted to MPa.

[0058] (2-2)

[0059] In formula (2-2), Indicates interface strength. This represents the maximum pulling force during the entire pulling process. This indicates the area of ​​the graphene sheet.

[0060] Table 4. Interfacial strengths of graphene and modified graphene in the tangential and normal directions.

[0061]

[0062] The interface strength calculated by the normal model is consistent with that in the literature by ZHOU M et al. [9,10] The calculated results are similar, and the interface strength calculated by the tangential model is consistent with that in the literature by JIN Y et al. [11,12] The similar calculation results demonstrate the rationality of the case model. The interfacial strengths in both the normal and tangential directions show that carboxyl modification has the best reinforcing effect on pure graphene. Based on the above two steps, the optimal material formulation is determined to be "1.26% content + carboxyl modification".

[0063] Step 3: Micromechanical response simulation and constitutive data extraction.

[0064] 301. Based on the Tg of the model obtained in step S1, perform uniaxial tensile and compressive strains of 50% at the glass transition temperature of 30K, and output stress-strain curves to characterize the hyperelastic behavior of the material.

[0065] 302. At different Tg temperatures corresponding to different models, a 5% instantaneous strain was applied to the model and kept constant. 311K was selected as the reference temperature. Based on the time-temperature equivalence principle and the WLF equation, a master relaxation curve covering 0 to 100 s was constructed at 311K. The stress decay data over time were recorded to characterize the viscoelastic behavior of the material. The uniaxial tensile curve and stress relaxation curve of pure PU are shown below. Figure 7 .

[0066] Step 4: Cross-scale parameter mapping and constitutive model fitting.

[0067] 401. Use MATLAB to perform nonlinear regression on the transformed data extracted in step S3 to obtain macroscopic constitutive parameters. This includes fitting hyperelastic and viscoelastic parameters.

[0068] 402. Hyperelastic Parameter Fitting (Mooney-Rivlin Model): The Mooney-Rivlin potential function is used to fit the stress-strain curve at 341 K to obtain the MR material parameters. The fitting formula is shown in Equation 4-1.

[0069] (4-1)

[0070] In the formula, For strain energy density, and For MR materials, It is an invariant of equal volume.

[0071] 403. Viscoelastic parameter fitting (Prony series): For the 100s master relaxation curve at 311K after WLF transformation, the generalized Maxwell model (Prony Series) is used for fitting. The fitting formula is shown in 4-2.

[0072] (4-2)

[0073] In the formula, and For viscoelastic material parameters, To balance the modulus ratio, This is the relaxation time.

[0074] By fitting hyperelastic parameters and viscoelastic parameters, the large deformation stiffness of the material in the rubber state is characterized, and the stress relaxation behavior of the material at body temperature for up to 100 s is accurately described.

[0075] Step 5: Macroscopic support modeling and service performance prediction.

[0076] 501. In the ABAQUS finite element analysis software, establish a three-dimensional geometric model of the vascular stent and perform mesh generation. In the material properties module, input the hyperelastic parameters (Mooney-Rivlin model constants) and viscoelastic parameters (Prony series) obtained from the fitting in step S4. The vascular stent model drawn using ABAQUS is shown below. Figure 8 .

[0077] The simulation cycle is set up with three analytical steps: High-temperature compression: The stent is compressed from 4mm to 2mm at 341K (rubber state) (simulating loading). Cooling fixation: While maintaining compression, the stent is cooled to 298K (room temperature) to freeze its shape using the glassy state. Body temperature release: The constraint is removed, and the stent is heated to 311K (body temperature) to simulate a 100s self-expansion process.

[0078] Table 5. Self-expansion time and radial support force of the pure PU model and the graphene-modified model.

[0079]

[0080] Simulation results show that the stent selected using this optimization method exhibits excellent recovery speed at 311K, and the steady-state radial support force is significantly improved compared to pure PU. From the perspectives of radial support force and recovery time, a 1.26% enhancement is the most effective. This macroscopic prediction result confirms the effectiveness and engineering practical value of the proposed "microscopic screening-cross-scale mapping-macroscopic simulation" method.

[0081] References

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Claims

1. A method for optimizing the design of enhanced polyurethane shape memory vascular stents based on multi-scale coupling, characterized in that, Includes the following steps: Step 1: Constructing a microscopic benchmark model and screening the content of reinforcing fillers; constructing a full-atom model of the polyurethane matrix and constructing composite material models containing different mass fractions of reinforcing phases; performing molecular dynamics and thermomechanical cycle simulations on each model, and using shape fixation rate and shape recovery rate as evaluation indicators to screen out the reinforcing phase content with the best comprehensive performance; Step 2: Optimization of chemical modification schemes based on interfacial mechanics; Based on the optimal content model selected in step 1, an interface model between the reinforcing phase and the polymer matrix was constructed, and the surface of the reinforcing phase was modified with different chemical functional groups. Molecular dynamics was used to simulate the interface pull-out, calculate the interface bonding strength, and determine the interface chemical modification scheme with the best reinforcing effect. Step 3: Micromechanical response simulation and constitutive data extraction; For the composite material model optimized in Steps 1 and 2, perform uniaxial tensile simulation and stress relaxation simulation under multiple temperature fields in a molecular dynamics environment to extract stress-strain response data and relaxation modulus data at the microscale. Step 4: Cross-scale parameter mapping and constitutive model fitting; Establish the mapping relationship from microscopic discrete data to macroscopic continuous medium mechanical parameters: Fit microscopic stress-strain data to hyperelastic constitutive model parameters, and fit microscopic relaxation data to viscoelastic constitutive model parameters; Step 5: Macroscopic stent modeling and service performance prediction; establish a three-dimensional finite element model of the vascular stent and assign the hyperelastic and viscoelastic constitutive parameters obtained in Step 4; simulate the thermodynamic behavior of the stent in the entire process of "high temperature gripping - low temperature fixation - body temperature release" and predict the radial support force and shape recovery performance of the optimized stent.

2. The method for optimizing the design of an enhanced polyurethane shape memory vascular stent based on multi-scale coupling according to claim 1, characterized in that, In step 1, the polyurethane matrix is ​​polymerized from soft segment polycaprolactone diol and hard segment hexamethylene diisocyanate; the reinforcing filler is a single-layer graphene sheet.

3. The method for optimizing the design of an enhanced polyurethane shape memory vascular stent based on multi-scale coupling according to claim 1, characterized in that, In step 1, the specific process of the thermomechanical cycle simulation is as follows: uniaxial tension is performed at a temperature higher than the glass transition temperature Tg, the strain is maintained and the temperature is cooled down to a temperature lower than Tg for fixation, the external force is unloaded and the temperature is raised to a temperature higher than Tg for recovery; the shape fixation rate Rf and the shape recovery rate Rr are compared and calculated for selection.

4. The method for optimizing the design of an enhanced polyurethane shape memory vascular stent based on multi-scale coupling according to claim 1, characterized in that, In step 2, the chemical functional group modification includes epoxy, hydroxyl and carboxyl group modification; the interface pull-out simulation includes tangential pull-out and normal pull-out; by calculating the maximum pull-out force and interface shear strength, carboxyl group is preferred as the best interface modification group.

5. The method for optimizing the design of an enhanced polyurethane shape memory vascular stent based on multi-scale coupling according to claim 1, characterized in that, In step 3, the stress relaxation simulation further includes: using the time-temperature equivalence principle and the WLF equation, converting the short-time molecular dynamics relaxation data at high temperature into a long-time master relaxation curve at a reference temperature, preferably the human body temperature of 311K.

6. The method for optimizing the design of an enhanced polyurethane shape memory vascular stent based on multi-scale coupling according to claim 1, characterized in that, In step 4, the parameters of the hyperelastic constitutive model are Mooney-Rivlin model constants, used to describe the large deformation behavior of the material; the parameters of the viscoelastic constitutive model are coefficients in the Prony series, used to describe the time-dependent behavior of the material.

7. The method for optimizing the design of an enhanced polyurethane shape memory vascular stent based on multi-scale coupling according to claim 1, characterized in that, In step 5, the entire process of "high temperature compression-low temperature fixation-body temperature release" specifically includes: the first stage, setting the field variable temperature to the rubber state temperature and applying radial constraints to compress the stent to the catheter size; the second stage, maintaining the radial constraints and lowering the temperature to room temperature to freeze the temporary shape; the third stage, removing the radial constraints and raising the temperature to the human body temperature to simulate the self-expansion and stress relaxation process of the stent.

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