Ultrasound Backscattering Is Anisotropic in Bovine Articular Cartilage

Discovering 3D hidden elasticity in isotropic and transversely isotropic materials with physics-informed UNets

Three-dimensional variation in structural components or fiber alignments results in complex mechanical property distribution in tissues and biomaterials. In this paper, we use a physics-informed UNet-based neural network model (El-UNet) to discover the three-dimensional (3D) internal composition and space-dependent material properties of heterogeneous isotropic and transversely isotropic materials without a priori knowledge of the composition. We then show the capabilities of El-UNet by validating against data obtained from finite-element simulations of two soft tissues, namely, brain tissue and articular cartilage, under various loading conditions. We first simulated compressive loading of 3D brain tissue comprising of distinct white matter and gray matter mechanical properties undergoing small strains with isotropic linear elastic behavior, where El-UNet reached mean absolute relative errors under 1.5 % for elastic modulus and Poisson's ratio estimations across the 3D volume. We showed that the 3D solution achieved by El-UNet was superior to relative stiffness mapping by inverse of axial strain and two-dimensional plane stress/plane strain approximations. Additionally, we simulated a transversely isotropic articular cartilage with known fiber orientations undergoing compressive loading, and accurately estimated the spatial distribution of all five material parameters, with mean absolute relative errors under 5 %. Our work demonstrates the application of the computationally efficient physics-informed El-UNet in 3D elasticity imaging and provides methods for translation to experimental 3D characterization of soft tissues and other materials. The proposed El-UNet offers a powerful tool for both in vitro and ex vivo tissue analysis, with potential extensions to in vivo diagnostics. STATEMENT OF SIGNIFICANCE: Elasticity imaging is a technique that reconstructs mechanical properties of tissue using deformation and force measurements. Given the complexity of this reconstruction, most existing methods have mostly focused on 2D problems. Our work is the first implementation of physics-informed UNets to reconstruct three-dimensional material parameter distributions for isotropic and transversely isotropic linear elastic materials by having deformation and force measurements. We comprehensively validate our model using synthetic data generated using finite element models of biological tissues with high bio-fidelity-the brain and articular cartilage. Our method can be implemented in elasticity imaging scenarios for in vitro and ex vivo mechanical characterization of biomaterials and biological tissues, with potential extensions to in vivo diagnostics.

A Review of the Collagen Orientation in the Articular Cartilage

OBJECTIVE

There has been a debate as to the alignment of the collagen fibers. Using a hand lens, Sir William Hunter demonstrated that the collagen fibers ran perpendicular and later aspects were supported by Benninghoff. Despite these 2 historical studies, modern technology has conflicting data on the collagen alignment.

DESIGN

Ten mature New Zealand rabbits were used to obtain 40 condyle specimens. The specimens were passed through ascending grades of alcohol, subjected to critical point drying (CPD), and viewed in the scanning electron microscope. Specimens revealed splits from the dehydration process. When observing the fibers exposed within the opening of the splits, parallel fibers were observed to run in a radial direction, normal to the surface of the articular cartilage, radiating from the deep zone and arcading as they approach the surface layer. After these observations, the same samples were mechanically fractured and damaged by scalpel.

RESULTS

The splits in the articular surface created deep fissures, exposing parallel bundles of collagen fibers, radiating from the deep zone and arcading as they approach the surface layer. On higher magnification, individual fibers were observed to run parallel to one another, traversing radially toward the surface of the articular cartilage and arcading. Mechanical fracturing and scalpel damage induced on the same specimens with the splits showed randomly oriented fibers.

CONCLUSION

Collagen fiber orientation corroborates aspects of Hunter's findings and compliments Benninghoff. Investigators must be aware of the limits of their processing and imaging techniques in order to interpret collagen fiber orientation in cartilage.

Quantitative Evaluation of Enzyme-Induced Porcine Articular Cartilage Degeneration Based on Observation of Entire Cartilage Layer Using Ultrasound

Enzyme-induced articular cartilage degeneration resembling osteoarthritis was evaluated using a newly defined acoustic parameter, the "averaged magnitude ratio" (AMR), which has been suggested as an indicator of articular cartilage degeneration. In vitro experiments were conducted on porcine cartilage samples digested with trypsin for 2 h (n = 10) and 4 h (n = 13) and healthy control samples (n = 13). AMR was determined with 15- and 25-MHz ultrasound, and the integrated reflection coefficient (IRC) and apparent integrated backscattering coefficient (AIB) were also calculated for comparison. The Young's modulus of superficial cartilage was measured using atomic force microscopy. Performance of the AMR differs between 15 and 25 MHz, possibly because of frequency-related attenuation and resolution of ultrasound. At the proper settings, AMR exhibited a competence similar to that of IRC and AIB in detecting cartilage degeneration and could also detect differences in deeper positions. Furthermore, AMR has the advantages of being easy to measure and requiring no reference material.

Regular chondrocyte spacing is a potential cause for coherent ultrasound backscatter in human articular cartilage

The potential of quantitative ultrasound (QUS) to assess the regular cellular spacing in the superficial cartilage zones was investigated experimentally and numerically. Nine osteochondral samples, extracted from two human cadaver knee joints, were measured using a 50-MHz ultrasound scanning device and evaluated using Mankin score. Simulated backscattered power spectra from models with an idealized cell alignment exhibited a pronounced frequency peak. From the peak, cell spacing in the range between 15 and 40 μm between cell layers was detected with an average error of 0.2 μm. The mean QUS-based cell spacing was 28.3 ± 5.3 μm. Strong correlation (R²= 0.59, p ≤ 0.001) between spacing estimates from light microscopy (LM) and QUS was found for samples with Mankin score ≤3. For higher scores, QUS-based spacing was significantly higher (p ≤ 0.05) compared to LM-based spacing. QUS-based spacing estimates together with other QUS parameters may serve as future biomarkers for detecting early signs of osteoarthrosis.

Finite difference time domain model of ultrasound propagation in agarose scaffold containing collagen or chondrocytes

Measurement of ultrasound backscattering is a promising diagnostic technique for arthroscopic evaluation of articular cartilage. However, contribution of collagen and chondrocytes on ultrasound backscattering and speed of sound in cartilage is not fully understood and is experimentally difficult to study. Agarose hydrogels have been used in tissue engineering applications of cartilage. Therefore, the aim of this study was to simulate the propagation of high frequency ultrasound (40 MHz) in agarose scaffolds with varying concentrations of chondrocytes (1 to 32 × 10(6) cells/ml) and collagen (1.56-200 mg/ml) using transversely isotropic two-dimensional finite difference time domain method (FDTD). Backscatter and speed of sound were evaluated from the simulated pulse-echo and through transmission measurements, respectively. Ultrasound backscatter increased with increasing collagen and chondrocyte concentrations. Furthermore, speed of sound increased with increasing collagen concentration. However, this was not observed with increasing chondrocyte concentrations. The present study suggests that the FDTD method may have some applicability in simulations of ultrasound scattering and propagation in constructs containing collagen and chondrocytes. Findings of this study indicate the significant role of collagen and chondrocytes as ultrasound scatterers and can aid in development of modeling approaches for understanding how cartilage architecture affects to the propagation of high frequency ultrasound.