Anisotropic damage model for collagenous tissues and its application to model fracture and needle insertion mechanics

Crosslinking degree variations enable programming and controlling soft fracture via sideways cracking

Large deformations of soft materials are customarily associated with strong constitutive and geometrical nonlinearities that originate new modes of fracture. Some isotropic materials can develop strong fracture anisotropy, which manifests as modifications of the crack path. Sideways cracking occurs when the crack deviates to propagate in the loading direction, rather than perpendicular to it. This fracture mode results from higher resistance to propagation perpendicular to the principal stretch direction. It has been argued that such fracture anisotropy is related to deformation-induced anisotropy resulting from the microstructural stretching of polymer chains and, in strain-crystallizing elastomers, strain-induced crystallization mechanisms. However, the precise variation of the fracture behavior with the degree of crosslinking remains to be understood. Leveraging experiments and computational simulations, here we show that the tendency of a crack to propagate sideways in the two component Elastosil P7670 increases with the degree of crosslinking. We explore the mixing ratio for the synthesis of the elastomer that establishes the transition from forward to sideways fracturing. To assist the investigations, we construct a novel phase-field model for fracture where the critical energy release rate is directly related to the crosslinking degree. Our results demonstrate that fracture anisotropy can be modulated during the synthesis of the polymer. Then, we propose a roadmap with composite soft structures with low and highly crosslinked phases that allow for control over fracture, arresting and/or directing the fracture. The smart combination of the phases enables soft structures with enhanced fracture tolerance and reduced stiffness. By extending our computational framework as a virtual testbed, we capture the fracture performance of the composite samples and enable predictions based on more intricate composite unit cells. Overall, our work offers promising avenues for enhancing the fracture toughness of soft polymers.

3D Printed Microneedles for the Transdermal Delivery of NAD+ Precursor: Toward Personalization of Skin Delivery

3D printing of microneedles (μNDs) for transdermal therapy has the potential to enable patient personalization based on the target disease, site of application, and dosage requirements. To convert this concept to reality, it is necessary that the 3D printing technology can deliver high resolution, an affordable cost, and large print volumes. With the introduction of benchtop 4K and 8K 3D printers, it is now possible to manufacture medical devices like μNDs at sufficient resolution and low cost. In this research, we systematically optimized the 3D printing design parameters such as resin viscosity, print angle, layer height, and curing time to generate customizable μNDs. We have also developed an innovative 3D coating microtank device to optimize the coating method. We have applied this to the development of novel μNDs to deliver an established NAD+ precursor molecule, nicotinamide mononucleotide (NMN). A methacrylate-based polymer photoresin (eSun resin) was diluted with methanol to adjust the resin viscosity. The 3D print layer height of 25 μm yielded a smooth surface, thus reducing edge-ridge mismatches. Printing μNDs at 90° to the print platform yielded 84.28 ± 2.158% (n = 5) of the input height thus increasing the tip sharpness (48.52 ± 10.43 μm, n = 5). The formulation containing fluorescein (model molecule), sucrose (viscosity modifier), and Tween-20 (surface tension modifier) was coated on the μNDs using the custom designed microtank setup, and the amount deposited was determined fluorescently. The dye-coated μND arrays inserted into human skin (in vitro) showed a fluorescence signal at a depth of 150 μm (n = 3) into the skin. After optimization of the 3D printing parameters and coating protocol using fluorescein, NMN was coated onto the μNDs, and its diffusion was assessed in full-thickness human skin in vitro using a Franz diffusion setup. Approximately 189 ± 34.5 μg (5× dipped coated μNDs) of NMN permeated through the skin and 41.2 ± 7.53 μg was left in the skin after 24 h. Multiphoton microscopy imaging of NMN-coated μND treated mouse ear skin ex vivo demonstrated significantly (p < 0.05) increased free-unbound NADPH and reduced fluorescence lifetime of NADPH, both of which are indicative of cellular metabolic rates. Our study demonstrates that low-cost benchtop 3D printers can be used to print high-fidelity μNDs with the ability to rapidly coat and release NMN which consequently caused changes in intracellular NAD+ levels.

A comprehensive review on modeling aspects of infusion-based drug delivery in the brain

Brain disorders represent an ever-increasing health challenge worldwide. While conventional drug therapies are less effective due to the presence of the blood-brain barrier, infusion-based methods of drug delivery to the brain represent a promising option. Since these methods are mechanically controlled and involve multiple physical phases ranging from the neural and molecular scales to the brain scale, highly efficient and precise delivery procedures can significantly benefit from a comprehensive understanding of drug-brain and device-brain interactions. Behind these interactions are principles of biophysics and biomechanics that can be described and captured using mathematical models. Although biomechanics and biophysics have received considerable attention, a comprehensive mechanistic model for modeling infusion-based drug delivery in the brain has yet to be developed. Therefore, this article reviews the state-of-the-art mechanistic studies that can support the development of next-generation models for infusion-based brain drug delivery from the perspective of fluid mechanics, solid mechanics, and mathematical modeling. The supporting techniques and database are also summarized to provide further insights. Finally, the challenges are highlighted and perspectives on future research directions are provided. STATEMENT OF SIGNIFICANCE: Despite the immense potential of infusion-based drug delivery methods for bypassing the blood-brain barrier and efficiently delivering drugs to the brain, achieving optimal drug distribution remains a significant challenge. This is primarily due to our limited understanding of the complex interactions between drugs and the brain that are governed by principles of biophysics and biomechanics, and can be described using mathematical models. This article provides a comprehensive review of state-of-the-art mechanistic studies that can help to unravel the mechanism of drug transport in the brain across the scales, which underpins the development of next-generation models for infusion-based brain drug delivery. More broadly, this review will serve as a starting point for developing more effective treatments for brain diseases and mechanistic models that can be used to study other soft tissue and biomaterials.

Data-driven continuum damage mechanics with built-in physics

Soft materials such as rubbers and soft tissues often undergo large deformations and experience damage degradation that impairs their function. This energy dissipation mechanism can be described in a thermodynamically consistent framework known as continuum damage mechanics. Recently, data-driven methods have been developed to capture complex material behaviors with unmatched accuracy due to the high flexibility of deep learning architectures. Initial efforts focused on hyperelastic materials, and recent advances now offer the ability to satisfy physics constraints such as polyconvexity of the strain energy density function by default. However, modeling inelastic behavior with deep learning architectures and built-in physics has remained challenging. Here we show that neural ordinary differential equations (NODEs), which we used previously to model arbitrary hyperelastic materials with automatic polyconvexity, can be extended to model energy dissipation in a thermodynamically consistent way by introducing an inelastic potential: a monotonic yield function. We demonstrate the inherent flexibility of our network architecture in terms of different damage models proposed in the literature. Our results suggest that our NODEs re-discover the true damage function from synthetic stress-deformation history data. In addition, they can accurately characterize experimental skin and subcutaneous tissue data.

Poroelastic Characterization and Modeling of Subcutaneous Tissue Under Confined Compression

Subcutaneous tissue mechanics are important for drug delivery. Yet, even though this material is poroelastic, its mechanical characterization has focused on its hyperelastic response. Moreover, advancement in subcutaneous drug delivery requires effective tissue mimics such as hydrogels for which similar gaps of poroelastic data exist. Porcine subcutaneous samples and gelatin hydrogels were tested under confined compression at physiological conditions and strain rates of 0.01%/s in 5% strain steps with 2600 s of stress relaxation between loading steps. Force-time data were used in an inverse finite element approach to obtain material parameters. Tissues and gels were modeled as porous neo-Hookean materials with properties specified via shear modulus, effective solid volume fraction, initial hydraulic permeability, permeability exponent, and normalized viscous relaxation moduli. The constitutive model was implemented into an isogeometric analysis (IGA) framework to study subcutaneous injection. Subcutaneous tissue exhibited an initial spike in stress due to compression of the solid and fluid pressure buildup, with rapid relaxation explained by fluid drainage, and longer time-scale relaxation explained by viscous dissipation. The inferred parameters aligned with the ranges reported in the literature. Hydraulic permeability, the most important parameter for drug delivery, was in the rangek 0 ∈ [ 0.142 , 0.203 ] mm4 /(N s). With these parameters, IGA simulations showed peak stresses due to a 1-mL injection to reach 48.8 kPa at the site of injection, decaying after drug volume disperses into the tissue. The poro-hyper-viscoelastic neo-Hookean model captures the confined compression response of subcutaneous tissue and gelatin hydrogels. IGA implementation enables predictive simulations of drug delivery.

Segmenting mechanically heterogeneous domains via unsupervised learning

From biological organs to soft robotics, highly deformable materials are essential components of natural and engineered systems. These highly deformable materials can have heterogeneous material properties, and can experience heterogeneous deformations with or without underlying material heterogeneity. Many recent works have established that computational modeling approaches are well suited for understanding and predicting the consequences of material heterogeneity and for interpreting observed heterogeneous strain fields. In particular, there has been significant work toward developing inverse analysis approaches that can convert observed kinematic quantities (e.g., displacement, strain) to material properties and mechanical state. Despite the success of these approaches, they are not necessarily generalizable and often rely on tight control and knowledge of boundary conditions. Here, we will build on the recent advances (and ubiquity) of machine learning approaches to explore alternative approaches to detect patterns in heterogeneous material properties and mechanical behavior. Specifically, we will explore unsupervised learning approaches to clustering and ensemble clustering to identify heterogeneous regions. Overall, we find that these approaches are effective, yet limited in their abilities. Through this initial exploration (where all data and code are published alongside this manuscript), we set the stage for future studies that more specifically adapt these methods to mechanical data.

Benchmarking physics-informed frameworks for data-driven hyperelasticity

Data-driven methods have changed the way we understand and model materials. However, while providing unmatched flexibility, these methods have limitations such as reduced capacity to extrapolate, overfitting, and violation of physics constraints. Recently, frameworks that automatically satisfy these requirements have been proposed. Here we review, extend, and compare three promising data-driven methods: Constitutive Artificial Neural Networks (CANN), Input Convex Neural Networks (ICNN), and Neural Ordinary Differential Equations (NODE). Our formulation expands the strain energy potentials in terms of sums of convex non-decreasing functions of invariants and linear combinations of these. The expansion of the energy is shared across all three methods and guarantees the automatic satisfaction of objectivity, material symmetries, and polyconvexity, essential within the context of hyperelasticity. To benchmark the methods, we train them against rubber and skin stress-strain data. All three approaches capture the data almost perfectly, without overfitting, and have some capacity to extrapolate. This is in contrast to unconstrained neural networks which fail to make physically meaningful predictions outside the training range. Interestingly, the methods find different energy functions even though the prediction on the stress data is nearly identical. The most notable differences are observed in the second derivatives, which could impact performance of numerical solvers. On the rich data used in these benchmarks, the models show the anticipated trade-off between number of parameters and accuracy. Overall, CANN, ICNN and NODE retain the flexibility and accuracy of other data-driven methods without compromising on the physics. These methods are ideal options to model arbitrary hyperelastic material behavior.

Computational modeling of the effect of skin pinch and stretch on subcutaneous injection of monoclonal antibodies using autoinjector devices

Subcutaneous injection of monoclonal antibodies (mAbs) has experienced unprecedented growth in the pharmaceutical industry due to its benefits in patient compliance and cost-effectiveness. However, the impact of different injection techniques and autoinjector devices on the drug's transport and uptake is poorly understood. Here, we develop a biphasic large-deformation chemomechanical model that accounts for the components of the extracellular matrix that govern solid deformation and fluid flow within the subcutaneous tissue: interstitial fluid, collagen fibers and negatively charged proteoglycan aggregates. We use this model to build a high-fidelity representation of a virtual patient performing a subcutaneous injection of mAbs. We analyze the impact of the pinch and stretch methods on the injection dynamics and the use of different handheld autoinjector devices. The results suggest that autoinjector base plates with a larger device-skin contact area cause significantly lower tissue mechanical stress, fluid pressure and fluid velocity during the injection process. Our simulations indicate that the stretch technique presents a higher risk of intramuscular injection for autoinjectors with a relatively long needle insertion depth.

Mechanical damage in porcine dermis: Micro-mechanical model and experimental characterization

Skin is subjected to extreme mechanical loading during needle insertion and drug delivery to the subcutaneous space. There is a rich literature on the characterization of porcine skin biomechanics as the preeminent animal model for human skin, but the emphasis has been on the elastic response and specific anatomical locations such as the dorsal and the ventral regions. During drug delivery, however, energy dissipation in the form of damage, softening, and fracture, is expected. Similarly, reports on experimental characterization are complemented by modeling efforts, but with similar gaps in microstructure-driven modeling of dissipative mechanisms. Here we contribute to the bridging of these gaps by testing porcine skin from belly and breast regions, in two different orientation with respect to anatomical axes, and to progressively higher stretches in order to show damage accumulation and stiffness degradation. We complement the mechanical test with imaging of the collagen structure and a micro-mechanics modeling framework. We found that skin from the belly is stiffer with respect to the breast region when comparing the calf stiffness of the J-shaped stress-stretch response observed in most collagenous tissues. No significant direction dependent properties were found in either anatomical location. Both locations showed energy dissipation due to damage, evident though a softening of the stress-stretch response. The microstructure model was able to capture the elastic and damage progression with a small set of parameters, some of which were determined directly from imaging. We anticipate that data and model fits can help in predictive simulations for device design in situations where skin is subject to supra-physiological deformation such as in subcutaneous drug delivery.

Damage and Fracture Mechanics of Porcine Subcutaneous Tissue Under Tensile Loading

Subcutaneous injection, which is a preferred delivery method for many drugs, causes deformation, damage, and fracture of the subcutaneous tissue. Yet, experimental data and constitutive modeling of these dissipation mechanisms in subcutaneous tissue remain limited. Here we show that subcutaneous tissue from the belly and breast anatomical regions in the swine show nonlinear stress-strain response with the characteristic J-shaped behavior of collagenous tissue. Additionally, subcutaneous tissue experiences damage, defined as a decrease in the strain energy capacity, as a function of the previously experienced maximum deformation. The elastic and damage response of the tissue are accurately described by a microstructure-driven constitutive model that relies on the convolution of a neo-Hookean material of individual fibers with a fiber orientation distribution and a fiber recruitment distribution. The model fit revealed that subcutaneous tissue can be treated as initially isotropic, and that changes in the fiber recruitment distribution with loading are enough to explain the dissipation of energy due to damage. When tested until failure, subcutaneous tissue that has undergone damage fails at the same peak stress as virgin samples, but at a much larger stretch, overall increasing the tissue toughness. Together with a finite element implementation, these data and constitutive model may enable improved drug delivery strategies and other applications for which subcutaneous tissue biomechanics are relevant.

Puncturing of soft tissues: experimental and fracture mechanics-based study

The integrity of soft materials against puncturing is of great relevance for their performance because of the high sensitivity to local rupture caused by rigid sharp objects. In this work, the mechanics of puncturing is studied with respect to a sharp-tipped rigid needle with a circular cross section, penetrating a soft target solid. The failure mode associated with puncturing is identified as a mode-I crack propagation, which is analytically described by a two-dimensional model of the target solid, taking place in a plane normal to the penetration axis. It is shown that the force required for the onset of needle penetration is dependent on two energy contributions, that are, the strain energy stored in the target solid and the energy consumed in crack propagation. More specifically, the force is found to be dependent on the fracture toughness of the material, its stiffness and the sharpness of the penetrating tool. The reference case within the framework of small strain elasticity is first investigated, leading to closed-form toughness parameters related to classical linear elastic fracture mechanics. Then, nonlinear finite element analyses for an Ogden hyperelastic material are presented. Supporting the proposed theoretical framework, a series of puncturing experiments on two commercial silicones is presented. The combined experimental-theoretical findings suggest a simple, yet reliable tool to easily handle and assess safety against puncturing of soft materials.