Conditional generative learning for medical image imputation.

Image imputation refers to the task of generating a type of medical image given images of another type. This task becomes challenging when the difference between the available images, and the image to be imputed is large. In this manuscript, one such application is considered. It is derived from the dynamic contrast enhanced computed tomography (CECT) imaging of the kidneys: given an incomplete sequence of three CECT images, we are required to impute the missing image. This task is posed as one of probabilistic inference and a generative algorithm to generate samples of the imputed image, conditioned on the available images, is developed, trained, and tested. The output of this algorithm is the "best guess" of the imputed image, and a pixel-wise image of variance in the imputation. It is demonstrated that this best guess is more accurate than those generated by other, deterministic deep-learning based algorithms, including ones which utilize additional information and more complex loss terms. It is also shown that the pixel-wise variance image, which quantifies the confidence in the reconstruction, can be used to determine whether the result of the imputation meets a specified accuracy threshold and is therefore appropriate for a downstream task.

A Force-Matched Approach to Large-Strain Nonlinearity in Elasticity Imaging for Breast Lesion Characterization.

OBJECTIVE: Ultrasound elasticity imaging is a class of ultrasound techniques with applications that include the detection of malignancy in breast lesions. Although elasticity imaging traditionally assumes linear elasticity, the large strain elastic response of soft tissue is known to be nonlinear. This study evaluates the nonlinear response of breast lesions for the characterization of malignancy using force measurement and force-controlled compression during ultrasound imaging. METHODS: 54 patients were recruited for this study. A custom force-instrumented compression device was used to apply a controlled force during ultrasound imaging. Motion tracking derived strain was averaged over lesion or background ROIs and matched with compression force. The resulting force-matched strain was used for subsequent analysis and curve fitting. RESULTS: Greater median differences between malignant and benign lesions were observed at higher compressional forces (p-value < 0.05 for compressional forces of 2-6N). Of three candidate functions, a power law function produced the best fit to the force-matched strain. A statistically significant difference in the scaling parameter of the power function between malignant and benign lesions was observed (p-value = 0.025). CONCLUSIONS: We observed a greater separation in average lesion strain between malignant and benign lesions at large compression forces and demonstrated the characterization of this nonlinear effect using a power law model. Using this model, we were able to differentiate between malignant and benign breast lesions. SIGNIFICANCE: With further development, the proposed method to utilize the nonlinear elastic response of breast tissue has the potential for improving non-invasive lesion characterization for potential malignancy.

Probabilistic Brain Extraction in MR Images via Conditional Generative Adversarial Networks.

Brain extraction, or the task of segmenting the brain in MR images, forms an essential step for many neuroimaging applications. These include quantifying brain tissue volumes, monitoring neurological diseases, and estimating brain atrophy. Several algorithms have been proposed for brain extraction, including image-to-image deep learning methods that have demonstrated significant gains in accuracy. However, none of them account for the inherent uncertainty in brain extraction. Motivated by this, we propose a novel, probabilistic deep learning algorithm for brain extraction that recasts this task as a Bayesian inference problem and utilizes a conditional generative adversarial network (cGAN) to solve it. The input to the cGAN's generator is an MR image of the head, and the output is a collection of likely brain images drawn from a probability density conditioned on the input. These images are used to generate a pixel-wise mean image, serving as the estimate for the extracted brain, and a standard deviation image, which quantifies the uncertainty in the prediction. We test our algorithm on head MR images from five datasets: NFBS, CC359, LPBA, IBSR, and their combination. Our datasets are heterogeneous regarding multiple factors, including subjects (with and without symptoms), magnetic field strengths, and manufacturers. Our experiments demonstrate that the proposed approach is more accurate and robust than a widely used brain extraction tool and at least as accurate as the other deep learning methods. They also highlight the utility of quantifying uncertainty in downstream applications. Additional information and codes for our method are available at: https://github.com/bmri/bmri.

Graph Laplacian-based spectral multi-fidelity modeling.

Low-fidelity data is typically inexpensive to generate but inaccurate, whereas high-fidelity data is accurate but expensive. To address this, multi-fidelity methods use a small set of high-fidelity data to enhance the accuracy of a large set of low-fidelity data. In the approach described in this paper, this is accomplished by constructing a graph Laplacian from the low-fidelity data and computing its low-lying spectrum. This is used to cluster the data and identify points closest to the cluster centroids, where high-fidelity data is acquired. Thereafter, a transformation that maps every low-fidelity data point to a multi-fidelity counterpart is determined by minimizing the discrepancy between the multi- and high-fidelity data while preserving the underlying structure of the low-fidelity data distribution. The method is tested with problems in solid and fluid mechanics. By utilizing only a small fraction of high-fidelity data, the accuracy of a large set of low-fidelity data is significantly improved.

Deep learning image segmentation approaches for malignant bone lesions: a systematic review and meta-analysis.

Introduction: Image segmentation is an important process for quantifying characteristics of malignant bone lesions, but this task is challenging and laborious for radiologists. Deep learning has shown promise in automating image segmentation in radiology, including for malignant bone lesions. The purpose of this review is to investigate deep learning-based image segmentation methods for malignant bone lesions on Computed Tomography (CT), Magnetic Resonance Imaging (MRI), and Positron-Emission Tomography/CT (PET/CT). Method: The literature search of deep learning-based image segmentation of malignant bony lesions on CT and MRI was conducted in PubMed, Embase, Web of Science, and Scopus electronic databases following the guidelines of Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA). A total of 41 original articles published between February 2017 and March 2023 were included in the review. Results: The majority of papers studied MRI, followed by CT, PET/CT, and PET/MRI. There was relatively even distribution of papers studying primary vs. secondary malignancies, as well as utilizing 3-dimensional vs. 2-dimensional data. Many papers utilize custom built models as a modification or variation of U-Net. The most common metric for evaluation was the dice similarity coefficient (DSC). Most models achieved a DSC above 0.6, with medians for all imaging modalities between 0.85-0.9. Discussion: Deep learning methods show promising ability to segment malignant osseous lesions on CT, MRI, and PET/CT. Some strategies which are commonly applied to help improve performance include data augmentation, utilization of large public datasets, preprocessing including denoising and cropping, and U-Net architecture modification. Future directions include overcoming dataset and annotation homogeneity and generalizing for clinical applicability.

Stretchable ultrasonic arrays for the three-dimensional mapping of the modulus of deep tissue.

Serial assessment of the biomechanical properties of tissues can be used to aid the early detection and management of pathophysiological conditions, to track the evolution of lesions and to evaluate the progress of rehabilitation. However, current methods are invasive, can be used only for short-term measurements, or have insufficient penetration depth or spatial resolution. Here we describe a stretchable ultrasonic array for performing serial non-invasive elastographic measurements of tissues up to 4 cm beneath the skin at a spatial resolution of 0.5 mm. The array conforms to human skin and acoustically couples with it, allowing for accurate elastographic imaging, which we validated via magnetic resonance elastography. We used the device to map three-dimensional distributions of the Young's modulus of tissues ex vivo, to detect microstructural damage in the muscles of volunteers before the onset of soreness and to monitor the dynamic recovery process of muscle injuries during physiotherapies. The technology may facilitate the diagnosis and treatment of diseases affecting tissue biomechanics.

A Mechanistic Model of Aqueous Humor Flow to Study Effects of Angle Closure on Intraocular Pressure.

Purpose: To study the relationship between the circumferential extent of angle closure and elevation in intraocular pressure (IOP) using a novel mechanistic model of aqueous humor (AH) flow. Methods: AH flow through conventional and unconventional outflow pathways was modeled using the unified Stokes and Darcy equations, which were solved using the finite element method. The severity and circumferential extent of angle closure were modeled by lowering the permeability of the outflow pathways. The IOP predicted by the model was compared with biometric and IOP data from the Chinese American Eye Study, wherein the circumferential extent of angle closure was determined using anterior segment OCT measurements of angle opening distance. Results: The mechanistic model predicted an initial linear rise in IOP with increasing extent of angle closure which became nonlinear when the extent of closure exceeded around one-half of the circumference. The nonlinear rise in IOP was associated with a nonlinear increase in AH outflow velocity in the open regions of the angle. These predictions were consistent with the nonlinear relationship between angle closure and IOP observed in the clinical data. Conclusions: IOP increases rapidly when the circumferential extent of angle closure exceeds 180°. Residual AH outflow may explain why not all angle closure eyes develop elevated IOP when angle closure is extensive. Translational Relevance: This study provides insight into the extent of angle closure that is clinically relevant and confers increased risk of elevated IOP. The proposed model can be utilized to study other mechanisms of impaired aqueous outflow.

Hyperelastic continuum models for isotropic athermal fibrous networks.

Many biological materials contain fibrous protein networks as their main structural components. Understanding the mechanical properties of such networks is important for creating biomimicking materials for cell and tissue engineering, and for developing novel tools for detecting and diagnosing disease. In this work, we develop continuum models for isotropic, athermal fibrous networks by combining a single-fibre model that describes the axial response of individual fibres, with network models that assemble individual fibre properties into overall network behaviour. In particular, we consider four different network models, including the affine, three-chain, eight-chain, and micro-sphere models, which employ different assumptions about network structure and kinematics. We systematically investigate the ability of these models to describe the mechanical response of athermal collagen and fibrin networks by comparing model predictions with experimental data. We test how each model captures network behaviour under three different loading conditions: uniaxial tension, simple shear, and combined tension and shear. We find that the affine and three-chain models can accurately describe both the axial and shear behaviour, whereas the eight-chain and micro-sphere models fail to capture the shear response, leading to unphysical zero shear moduli at infinitesimal strains. Our study is the first to systematically investigate the applicability of popular network models for describing the macroscopic behaviour of athermal fibrous networks, offering insights for selecting efficient models that can be used for large-scale, finite-element simulations of athermal networks.

High-Frequency Ultrasound Elastography to Assess the Nonlinear Elastic Properties of the Cornea and Ciliary Body.

Mechanical properties of the anterior anatomical structures of the eye, such as the cornea and ciliary body, play a key role in the ocular function and homeostasis. However, measuring the biomechanical properties of the anterior ocular structures, especially deeper structures, such as the ciliary body, remains a challenge due to the lack of high-resolution imaging tools. Herein, we implement a mechanical shaker-based high-frequency ultrasound elastography technique that can track the induced elastic wave propagation to assess the linear and nonlinear elastic properties of anterior ocular structures. The findings of this study advance our understanding of the role of anterior ocular structures in the pathogenesis of different ocular disorders, such as glaucoma.

A Radiomic-based Machine Learning Algorithm to Reliably Differentiate Benign Renal Masses from Renal Cell Carcinoma.

BACKGROUND: A substantial proportion of patients undergo treatment for renal masses where active surveillance or observation may be more appropriate. OBJECTIVE: To determine whether radiomic-based machine learning platforms can distinguish benign from malignant renal masses. DESIGN, SETTING, AND PARTICIPANTS: A prospectively maintained single-institutional renal mass registry was queried to identify patients with a computed tomography-proven clinically localized renal mass who underwent partial or radical nephrectomy. INTERVENTION: Radiomic analysis of preoperative scans was performed. Clinical and radiomic variables of importance were identified through decision tree analysis, which were incorporated into Random Forest and REAL Adaboost predictive models. OUTCOME MEASUREMENTS AND STATISTICAL ANALYSIS: The primary outcome was the degree of congruity between the virtual diagnosis and final pathology. Subanalyses were performed for small renal masses and patients who had percutaneous renal mass biopsies as part of their workup. Receiver operating characteristic curves were used to evaluate each model's discriminatory function. RESULTS AND LIMITATIONS: A total of 684 patients met the selection criteria. Of them, 76% had renal cell carcinoma; 57% had small renal masses, of which 73% were malignant. Predictive modeling differentiated benign pathology from malignant with an area under the curve (AUC) of 0.84 (95% confidence interval [CI] 0.79-0.9). In small renal masses, radiomic analysis yielded a discriminatory AUC of 0.77 (95% CI 0.69-0.85). When negative and nondiagnostic biopsies were supplemented with radiomic analysis, accuracy increased from 83.3% to 93.4%. CONCLUSIONS: Radiomic-based predictive modeling may distinguish benign from malignant renal masses. Clinical factors did not substantially improve the diagnostic accuracy of predictive models. Enhanced diagnostic predictability may improve patient selection before surgery and increase the utilization of active surveillance protocols. PATIENT SUMMARY: Not all kidney tumors are cancerous, and some can be watched. We evaluated a new method that uses radiographic features invisible to the naked eye to distinguish benign masses from true cancers and found that it can do so with acceptable accuracy.

Predicting clinical outcomes in COVID-19 using radiomics on chest radiographs.

OBJECTIVES: For optimal utilization of healthcare resources, there is a critical need for early identification of COVID-19 patients at risk of poor prognosis as defined by the need for intensive unit care and mechanical ventilation. We tested the feasibility of chest X-ray (CXR)-based radiomics metrics to develop machine-learning algorithms for predicting patients with poor outcomes. METHODS: In this Institutional Review Board (IRB) approved, Health Insurance Portability and Accountability Act (HIPAA) compliant, retrospective study, we evaluated CXRs performed around the time of admission from 167 COVID-19 patients. Of the 167 patients, 68 (40.72%) required intensive care during their stay, 45 (26.95%) required intubation, and 25 (14.97%) died. Lung opacities were manually segmented using ITK-SNAP (open-source software). CaPTk (open-source software) was used to perform 2D radiomics analysis. RESULTS: Of all the algorithms considered, the AdaBoost classifier performed the best with AUC = 0.72 to predict the need for intubation, AUC = 0.71 to predict death, and AUC = 0.61 to predict the need for admission to the intensive care unit (ICU). AdaBoost had similar performance with ElasticNet in predicting the need for admission to ICU. Analysis of the key radiomic metrics that drive model prediction and performance showed the importance of first-order texture metrics compared to other radiomics panel metrics. Using a Venn-diagram analysis, two first-order texture metrics and one second-order texture metric that consistently played an important role in driving model performance in all three outcome predictions were identified. CONCLUSIONS: Considering the quantitative nature and reliability of radiomic metrics, they can be used prospectively as prognostic markers to individualize treatment plans for COVID-19 patients and also assist with healthcare resource management. ADVANCES IN KNOWLEDGE: We report on the performance of CXR-based imaging metrics extracted from RT-PCR positive COVID-19 patients at admission to develop machine-learning algorithms for predicting the need for ICU, the need for intubation, and mortality, respectively.

Benchmarking Various Radiomic Toolkit Features While Applying the Image Biomarker Standardization Initiative toward Clinical Translation of Radiomic Analysis.

The image biomarkers standardization initiative (IBSI) was formed to address the standardization of extraction of quantifiable imaging metrics. Despite its effort, there remains a lack of consensus or established guidelines regarding radiomic feature terminology, the underlying mathematics and their implementation across various software programs. This creates a scenario where features extracted using different toolboxes cannot be used to build or validate the same model leading to a non-generalization of radiomic results. In this study, IBSI-established phantom and benchmark values were used to compare the variation of the radiomic features while using 6 publicly available software programs and 1 in-house radiomics pipeline. All IBSI-standardized features (11 classes, 173 in total) were extracted. The relative differences between the extracted feature values from the different software programs and the IBSI benchmark values were calculated to measure the inter-software agreement. To better understand the variations, features are further grouped into 3 categories according to their properties: 1) morphology, 2) statistic/histogram and 3)texture features. While a good agreement was observed for a majority of radiomics features across the various tested programs, relatively poor agreement was observed for morphology features. Significant differences were also found in programs that use different gray-level discretization approaches. Since these software programs do not include all IBSI features, the level of quantitative assessment for each category was analyzed using Venn and UpSet diagrams and quantified using two ad hoc metrics. Morphology features earned lowest scores for both metrics, indicating that morphological features are not consistently evaluated among software programs. We conclude that radiomic features calculated using different software programs may not be interchangeable. Further studies are needed to standardize the workflow of radiomic feature extraction.

A comprehensive spatial-temporal infection model.

Motivated by analogies between the spread of infections and of chemical processes, we develop a model that accounts for infection and transport where infected populations correspond to chemical species. Areal densities emerge as the key variables, thus capturing the effect of spatial density. We derive expressions for the kinetics of the infection rates, and for the important parameter R 0 , that include areal density and its spatial distribution. We present results for a batch reactor, the chemical process equivalent of the SIR model, where we examine how the dependence of R 0 on process extent, the initial density of infected individuals, and fluctuations in population densities effect the progression of the disease. We then consider spatially distributed systems. Diffusion generates traveling waves that propagate at a constant speed, proportional to the square root of the diffusivity and R 0 . Preliminary analysis shows a similar behavior for the effect of stochastic advection.

Machine learning based predictors for COVID-19 disease severity.

Predictors of the need for intensive care and mechanical ventilation can help healthcare systems in planning for surge capacity for COVID-19. We used socio-demographic data, clinical data, and blood panel profile data at the time of initial presentation to develop machine learning algorithms for predicting the need for intensive care and mechanical ventilation. Among the algorithms considered, the Random Forest classifier performed the best with [Formula: see text] for predicting ICU need and [Formula: see text] for predicting the need for mechanical ventilation. We also determined the most influential features in making this prediction, and concluded that all three categories of data are important. We determined the relative importance of blood panel profile data and noted that the AUC dropped by 0.12 units when this data was not included, thus indicating that it provided valuable information in predicting disease severity. Finally, we generated RF predictors with a reduced set of five features that retained the performance of the predictors trained on all features. These predictors, which rely only on quantitative data, are less prone to errors and subjectivity.

Repeatability of Linear and Nonlinear Elastic Modulus Maps From Repeat Scans in the Breast.

Compression elastography allows the precise measurement of large deformations of soft tissue in vivo. From an image sequence showing tissue undergoing large deformation, an inverse problem for both the linear and nonlinear elastic moduli distributions can be solved. As part of a larger clinical study to evaluate nonlinear elastic modulus maps (NEMs) in breast cancer, we evaluate the repeatability of linear and nonlinear modulus maps from repeat measurements. Within the cohort of subjects scanned to date, 20 had repeat scans. These repeated scans were processed to evaluate NEM repeatability. In vivo data were acquired by a custom-built, digitally controlled, uniaxial compression device with force feedback from the pressure-plate. RF-data were acquired using plane-wave imaging, at a frame-rate of 200 Hz, with a ramp-and-hold compressive force of 8N, applied at 8N/sec. A 2D block-matching algorithm was used to obtain sample-level displacement fields which were then tracked at subsample resolution using 2D cross correlation. Linear and nonlinear elasticity parameters in a modified Veronda-Westmann model of tissue elasticity were estimated using an iterative optimization method. For the repeated scans, B-mode images, strain images, and linear and nonlinear elastic modulus maps are measured and compared. Results indicate that when images are acquired in the same region of tissue and sufficiently high strain is used to recover nonlinearity parameters, then the reconstructed modulus maps are consistent.

Shape and texture-based radiomics signature on CT effectively discriminates benign from malignant renal masses.

OBJECTIVES: Using a radiomics framework to quantitatively analyze tumor shape and texture features in three dimensions, we tested its ability to objectively and robustly distinguish between benign and malignant renal masses. We assessed the relative contributions of shape and texture metrics separately and together in the prediction model. MATERIALS AND METHODS: Computed tomography (CT) images of 735 patients with 539 malignant and 196 benign masses were segmented in this retrospective study. Thirty-three shape and 760 texture metrics were calculated per tumor. Tumor classification models using shape, texture, and both metrics were built using random forest and AdaBoost with tenfold cross-validation. Sensitivity analyses on five sub-cohorts with respect to the acquisition phase were conducted. Additional sensitivity analyses after multiple imputation were also conducted. Model performance was assessed using AUC. RESULTS: Random forest classifier showed shape metrics featuring within the top 10% performing metrics regardless of phase, attaining the highest variable importance in the corticomedullary phase. Convex hull perimeter ratio is a consistently high-performing shape feature. Shape metrics alone achieved an AUC ranging 0.64-0.68 across multiple classifiers, compared with 0.67-0.75 and 0.68-0.75 achieved by texture-only and combined models, respectively. CONCLUSION: Shape metrics alone attain high prediction performance and high variable importance in the combined model, while being independent of the acquisition phase (unlike texture). Shape analysis therefore should not be overlooked in its potential to distinguish benign from malignant tumors, and future radiomics platforms powered by machine learning should harness both shape and texture metrics. KEY POINTS: • Current radiomics research is heavily weighted towards texture analysis, but quantitative shape metrics should not be ignored in their potential to distinguish benign from malignant renal tumors. • Shape metrics alone can attain high prediction performance and demonstrate high variable importance in the combined shape and texture radiomics model. • Any future radiomics platform powered by machine learning should harness both shape and texture metrics, especially since tumor shape (unlike texture) is independent of the acquisition phase and more robust from the imaging variations.

Deep learning based classification of solid lipid-poor contrast enhancing renal masses using contrast enhanced CT.

OBJECTIVE: Establish a workflow that utilizes convolutional neural nets (CNN) to classify solid, lipid-poor, contrast enhancing renal masses using multiphase contrast enhanced CT (CECT) images and to assess the performance of the resulting network. METHODS: In this institutional review board approved study of 143 patients with predominantly solid, lipid-poor, contrast enhancing renal lesions (46 benign and 97 malignant), patients with a pre-operative multiphase CECT of the abdomen and pelvis obtained between June 2009 and June 2015 were retrospectively queried. Benign renal masses included oncocytoma and lipid-poor angiomyolipoma and the malignant group included clear cell, papillary, and chromophobe carcinomas.Region of interests of whole tumor volumes were manually segmented, and CT phase images with the largest cross-section of the segmented tumor in the axial plane were used for assessment. Post-surgical pathological evaluation was used to establish diagnosis.The segmented images of renal masses were used as input to a CNN. The data were augmented and split into training (83.9%) and validation sets (16.1%) to determine the hyperparameters of the CNN. Thereafter. the performance of the resulting CNN was quantified using eightfold cross-validation. RESULTS: The CNN-based classifier demonstrated an overall accuracy of 78% (95% confidence interval: 76-80%), sensitivity of 70% (95% confidence interval: 66-74%), specificity of 81% (79-83%) and an area under the curve of 0.82. CONCLUSION: A CNN-based classifier to diagnose solid enhancing malignant renal masses based on multiphase CECT images was developed. ADVANCES IN KNOWLEDGE: It was established that a CNN-based classifier could be trained to accurately distinguish malignant renal lesions.

Recovery of Tractions Exerted by Single Cells in Three-Dimensional Nonlinear Matrices.

Cell-generated tractions play an important role in various physiological and pathological processes such as stem-cell differentiation, cell migration, wound healing, and cancer metastasis. Traction force microscopy (TFM) is a technique for quantifying cellular tractions during cell-matrix interactions. Most applications of this technique have heretofore assumed that the matrix surrounding the cells is linear elastic and undergoes infinitesimal strains, but recent experiments have shown that the traction-induced strains can be large (e.g., more than 50%). In this paper, we propose a novel three-dimensional (3D) TFM approach that consistently accounts for both the geometric nonlinearity introduced by large strains in the matrix, and the material nonlinearity due to strain-stiffening of the matrix. In particular, we pose the TFM problem as a nonlinear inverse hyperelasticity problem in the stressed configuration of the matrix, with the objective of determining the cellular tractions that are consistent with the measured displacement field in the matrix. We formulate the inverse problem as a constrained minimization problem and develop an efficient adjoint-based minimization procedure to solve it. We first validate our approach using simulated data, and quantify its sensitivity to noise. We then employ the new approach to recover tractions exerted by NIH 3T3 cells fully encapsulated in hydrogel matrices of varying stiffness. We find that neglecting nonlinear effects can induce significant errors in traction reconstructions. We also find that cellular tractions roughly increase with gel stiffness, while the strain energy appears to saturate.

Characterization of Spatially Graded Biomechanical Scaffolds.

Advances in fabrication have allowed tissue engineers to better mimic complex structures and tissue interfaces by designing nanofibrous scaffolds with spatially graded material properties. However, the nonuniform properties that grant the desired biomechanical function also make these constructs difficult to characterize. In light of this, we developed a novel procedure to create graded nanofibrous scaffolds and determine the spatial distribution of their material properties. Multilayered nanofiber constructs were synthesized, controlling spatial gradation of the stiffness to mimic the soft tissue gradients found in tendon or ligament tissue. Constructs were characterized using uniaxial tension testing with digital image correlation (DIC) to measure the displacements throughout the sample, in a noncontacting fashion, as it deformed. Noise was removed from the displacement data using principal component analysis (PCA), and the final denoised field served as the input to an inverse elasticity problem whose solution determines the spatial distribution of the Young's modulus throughout the material, up to a multiplicative factor. Our approach was able to construct, characterize, and determine the spatially varying moduli, in four electrospun scaffolds, highlighting its great promise for analyzing tissues and engineered constructs with spatial gradations in modulus, such as those at the interfaces between two disparate tissues (e.g., myotendinous junction, tendon- and ligament-to-bone entheses).