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Barsimantov J, Payne J, de Lucio M, Hakim M, Gomez H, Solorio L, Tepole AB. Poroelastic Characterization and Modeling of Subcutaneous Tissue Under Confined Compression. Ann Biomed Eng 2024; 52:1638-1652. [PMID: 38472602 DOI: 10.1007/s10439-024-03477-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2023] [Accepted: 02/17/2024] [Indexed: 03/14/2024]
Abstract
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.
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Affiliation(s)
- Jacques Barsimantov
- School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA
| | - Jordanna Payne
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, USA
- Indiana University School of Medicine, Indianapolis, IN, USA
| | - Mario de Lucio
- School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA
| | - Mazin Hakim
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, USA
| | - Hector Gomez
- School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA
| | - Luis Solorio
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, USA
| | - Adrian B Tepole
- School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA.
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, USA.
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Nguyen Q, Lejeune E. Segmenting mechanically heterogeneous domains via unsupervised learning. Biomech Model Mechanobiol 2024; 23:349-372. [PMID: 38217746 DOI: 10.1007/s10237-023-01779-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2023] [Accepted: 09/30/2023] [Indexed: 01/15/2024]
Abstract
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.
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Affiliation(s)
- Quan Nguyen
- Department of Mechanical Engineering, Boston University, Boston, MA, 02215, USA
| | - Emma Lejeune
- Department of Mechanical Engineering, Boston University, Boston, MA, 02215, USA.
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Taç V, Linka K, Sahli-Costabal F, Kuhl E, Tepole AB. Benchmarking physics-informed frameworks for data-driven hyperelasticity. COMPUTATIONAL MECHANICS 2024; 73:49-65. [PMID: 38741577 PMCID: PMC11090478 DOI: 10.1007/s00466-023-02355-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2023] [Accepted: 05/13/2023] [Indexed: 05/16/2024]
Abstract
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.
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Affiliation(s)
- Vahidullah Taç
- School of Mechanical Engineering, Purdue University, West Lafayette, USA
| | - Kevin Linka
- Department of Mechanical Engineering, Stanford University, Stanford, USA
| | - Francisco Sahli-Costabal
- Department of Mechanical and Metallurgical Engineering, Institute for Biological and Medical Engineering, Pontificia Universidad Catolica de Chile, Santiago, Chile
| | - Ellen Kuhl
- Department of Mechanical Engineering, Stanford University, Stanford, USA
| | - Adrian Buganza Tepole
- School of Mechanical Engineering, Purdue University, West Lafayette, USA
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, USA
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de Lucio M, Leng Y, Wang H, Ardekani AM, Vlachos PP, Shi G, Gomez H. Computational modeling of the effect of skin pinch and stretch on subcutaneous injection of monoclonal antibodies using autoinjector devices. Biomech Model Mechanobiol 2023; 22:1965-1982. [PMID: 37526775 DOI: 10.1007/s10237-023-01746-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2023] [Accepted: 07/06/2023] [Indexed: 08/02/2023]
Abstract
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.
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Affiliation(s)
- Mario de Lucio
- School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN, 47907, USA
| | - Yu Leng
- School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN, 47907, USA
| | - Hao Wang
- School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN, 47907, USA
| | - Arezoo M Ardekani
- School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN, 47907, USA
| | - Pavlos P Vlachos
- School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN, 47907, USA
| | - Galen Shi
- Eli Lilly and Company, Indianapolis, IN, USA
| | - Hector Gomez
- School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN, 47907, USA.
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Toaquiza Tubon J, Sree VD, Payne J, Solorio L, Tepole AB. Mechanical damage in porcine dermis: Micro-mechanical model and experimental characterization. J Mech Behav Biomed Mater 2023; 147:106143. [PMID: 37778167 DOI: 10.1016/j.jmbbm.2023.106143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2023] [Revised: 05/25/2023] [Accepted: 09/20/2023] [Indexed: 10/03/2023]
Abstract
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.
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Affiliation(s)
| | - Vivek D Sree
- School of Mechanical Engineering Purdue University, West Lafayette, IN, USA
| | - Jordanna Payne
- Weldon School of Biomedical Engineering Purdue University, West Lafayette, IN, USA
| | - Luis Solorio
- Weldon School of Biomedical Engineering Purdue University, West Lafayette, IN, USA
| | - Adrian Buganza Tepole
- School of Mechanical Engineering Purdue University, West Lafayette, IN, USA; Weldon School of Biomedical Engineering Purdue University, West Lafayette, IN, USA.
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Sree VD, Toaquiza-Tubon JD, Payne J, Solorio L, Tepole AB. Damage and Fracture Mechanics of Porcine Subcutaneous Tissue Under Tensile Loading. Ann Biomed Eng 2023; 51:2056-2069. [PMID: 37233856 DOI: 10.1007/s10439-023-03233-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2022] [Accepted: 05/04/2023] [Indexed: 05/27/2023]
Abstract
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.
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Affiliation(s)
- Vivek D Sree
- School of Mechanical Engineering, Purdue University, West Lafayette, USA
| | | | - Jordanna Payne
- School of Mechanical Engineering, Purdue University, West Lafayette, USA
| | - Luis Solorio
- School of Mechanical Engineering, Purdue University, West Lafayette, USA
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Montanari M, Brighenti R, Terzano M, Spagnoli A. Puncturing of soft tissues: experimental and fracture mechanics-based study. SOFT MATTER 2023; 19:3629-3639. [PMID: 37161966 DOI: 10.1039/d3sm00011g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
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.
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Affiliation(s)
- Matteo Montanari
- Department of Engineering and Architecture, University of Parma, Parco Area delle Scienze 181/A, 43124 Parma, Italy.
| | - Roberto Brighenti
- Department of Engineering and Architecture, University of Parma, Parco Area delle Scienze 181/A, 43124 Parma, Italy.
| | - Michele Terzano
- Institute of Biomechanics, Graz University of Technology, Stremayrgasse 16/2, 8010 Graz, Austria
| | - Andrea Spagnoli
- Department of Engineering and Architecture, University of Parma, Parco Area delle Scienze 181/A, 43124 Parma, Italy.
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