Automatic identification and validation of planar collagen organization in the aorta wall with application to abdominal aortic aneurysm

Fourier transform-based method for quantifying the three-dimensional orientation distribution of fibrous units

Several materials and tissues are characterized by a microstructure composed of fibrous units embedded in a ground matrix. In this paper, a novel three-dimensional (3D) Fourier transform-based method for quantifying the distribution of fiber orientations is presented. The method allows for an accurate identification of individual fiber families, their in-plane and out-of-plane dispersion, and showed fast computation times. We validated the method using artificially generated 3D images, in terms of fiber dispersion by considering the error between the standard deviation of the reconstructed and the prescribed distributions of the artificial fibers. In addition, we considered the measured mean orientation angles of the fibers and validated the robustness using a measure of fiber density. Finally, the method is employed to reconstruct a full 3D view of the distribution of collagen fiber orientations based on in vitro second harmonic generation microscopy of collagen fibers in human and mouse skin. The dispersion parameters of the reconstructed fiber network can be used to inform mechanical models of soft fiber-reinforced materials and biological tissues that account for non-symmetrical fiber dispersion.

MATLAB-Based Algorithm and Software for Analysis of Wavy Collagen Fibers

Knowledge of soft tissue fiber structure is necessary for accurate characterization and modeling of their mechanical response. Fiber configuration and structure informs both our understanding of healthy tissue physiology and of pathological processes resulting from diseased states. This study develops an automatic algorithm to simultaneously estimate fiber global orientation, abundance, and waviness in an investigated image. To our best knowledge, this is the first validated algorithm which can reliably separate fiber waviness from its global orientation for considerably wavy fibers. This is much needed feature for biological tissue characterization. The algorithm is based on incremental movement of local regions of interest (ROI) and analyzes two-dimensional images. Pixels belonging to the fiber are identified in the ROI, and ROI movement is determined according to local orientation of fiber within the ROI. The algorithm is validated with artificial images and ten images of porcine trachea containing wavy fibers. In each image, 80-120 fibers were tracked manually to serve as verification. The coefficient of determination R2 between curve lengths and histograms documenting the fiber waviness and global orientation were used as metrics for analysis. Verification-confirmed results were independent of image rotation and degree of fiber waviness, with curve length accuracy demonstrated to be below 1% of fiber curved length. Validation-confirmed median and interquartile range of R2, respectively, were 0.90 and 0.05 for curved length, 0.92 and 0.07 for waviness, and 0.96 and 0.04 for global orientation histograms. Software constructed from the proposed algorithm was able to track one fiber in about 1.1 s using a typical office computer. The proposed algorithm can reliably and accurately estimate fiber waviness, curve length, and global orientation simultaneously, moving beyond the limitations of prior methods.

Region- and layer-specific investigations of the human menisci using SHG imaging and biaxial testing

In this paper, we examine the region- and layer-specific collagen fiber morphology via second harmonic generation (SHG) in combination with planar biaxial tension testing to suggest a structure-based constitutive model for the human meniscal tissue. Five lateral and four medial menisci were utilized, with samples excised across the thickness from the anterior, mid-body, and posterior regions of each meniscus. An optical clearing protocol enhanced the scan depth. SHG imaging revealed that the top samples consisted of randomly oriented fibers with a mean fiber orientation of 43.3 ^o . The bottom samples were dominated by circumferentially organized fibers, with a mean orientation of 9.5 ^o . Biaxial testing revealed a clear anisotropic response, with the circumferential direction being stiffer than the radial direction. The bottom samples from the anterior region of the medial menisci exhibited higher circumferential elastic modulus with a mean value of 21 MPa. The data from the two testing protocols were combined to characterize the tissue with an anisotropic hyperelastic material model based on the generalized structure tensor approach. The model showed good agreement in representing the material anisotropy with a mean r ² = 0.92.

Microstructure and mechanics of the bovine trachea: Layer specific investigations through SHG imaging and biaxial testing

The trachea is a complex tissue made up of hyaline cartilage, fibrous tissue, and muscle fibers. Currently, the knowledge of microscopic structural organization of these components and their role in determining the tissue's mechanical response is very limited. The purpose of this study is to provide data on the microstructure of the tracheal components and its influence on tissue's mechanical response. Five bovine tracheae were used in this study. Adventitia, cartilage, mucosa/submucosa, and trachealis muscle layers were methodically cut out from the whole tissue. Second-harmonic generation(SHG) via multi-photon microscopy (MPM) enabled imaging of collagen fibers and muscle fibers. Simultaneously, a planar biaxial test rig was used to record the mechanical behavior of each layer. In total 60 samples were tested and analyzed. Fiber architecture in the adventitia and mucosa/submucosa layer showed high degree of anisotropy with the mean fiber angle varying from sample to sample. The trachealis muscle displayed neat layers of fibers organized in the longitudinal direction. The cartilage also displayed a structure of thick mesh-work of collagen type II organized predominantly towards the circumferential direction. Further, mechanical testing demonstrated the anisotropic nature of the tissue components. The cartilage was identified as the stiffest component for strain level < 20% and hence the primary load bearing component. The other three layers displayed a non-linear mechanical response which could be explained by the structure and organization of their fibers. This study is useful in enhancing the utilization of structurally motivated material models for predicting tracheal overall mechanical response.

Full-Range Optical Imaging of Planar Collagen Fiber Orientation Using Polarized Light Microscopy

A novel method for semiautomated assessment of directions of collagen fibers in soft tissues using histological image analysis is presented. It is based on multiple rotated images obtained via polarized light microscopy without any additional components, i.e., with just two polarizers being either perpendicular or nonperpendicular (rotated). This arrangement breaks the limitation of 90° periodicity of polarized light intensity and evaluates the in-plane fiber orientation over the whole 180° range accurately and quickly. After having verified the method, we used histological specimens of porcine Achilles tendon and aorta to validate the proposed algorithm and to lower the number of rotated images needed for evaluation. Our algorithm is capable to analyze 5·105 pixels in one micrograph in a few seconds and is thus a powerful and cheap tool promising a broad application in detection of collagen fiber distribution in soft tissues.

General method for classification of fiber families in fiber-reinforced materials: application to in-vivo human skin images

Fiber structures play a major role for the function of fiber-reinforced materials such as biological tissue. An objective classification of the fiber orientations into fiber families is crucial to understand its mechanical properties. We introduce the Fiber Image Network Evaluation Algorithm (FINE algorithm) to classify and quantify the number of fiber families in scientific images. Each fiber family is characterized by an amplitude, a mean orientation, and a dispersion. A new alignment index giving the averaged fraction of aligned fibers is defined. The FINE algorithm is validated by realistic grayscale Monte-Carlo fiber images. We apply the algorithm to an in-vivo depth scan of second harmonic generation images of dermal collagen in human skin. The derived alignment index exhibits a crossover at a critical depth where two fiber families with a perpendicular orientation around the main tension line arise. This strongly suggests the presence of a transition from the papillary to the reticular dermis. Hence, the FINE algorithm provides a valuable tool for a reliable classification and a meaningful interpretation of in-vivo collagen fiber networks and general fiber reinforced materials.

Noise reduction and quantification of fiber orientations in greyscale images

Quantification of the angular orientation distribution of fibrous tissue structures in scientific images benefits from the Fourier image analysis to obtain quantitative information. Measurement uncertainties represent a major challenge and need to be considered by propagating them in order to determine an adaptive anisotropic Fourier filter. Our adaptive filter method (AF) is based on the maximum relative uncertainty δcut of the power spectrum as well as a weighted radial sum with weighting factor α. We use a Monte-Carlo simulation to obtain realistic greyscale images that include defined variations in fiber thickness, length, and angular dispersion as well as variations in noise. From this simulation the best agreement between predefined and derived angular orientation distribution is found for evaluation parameters δcut = 2.1% and α = 1.5. The resulting cumulative orientation distribution was modeled by a sigmoid function to obtain the mean angle and the fiber dispersion. A comparison to a state-of-the-art band-pass method revealed that the AF method is more suitable for the application on greyscale fiber images, since the error of the fiber dispersion significantly decreased from (33.9 ± 26.5)% to (13.2 ± 12.7)%. Both methods were found to accurately quantify the mean fiber orientation with an error of (1.9 ± 1.5)° and (2.3 ± 2.1)° in case of the AF and the band-pass method, respectively. We demonstrate that the AF method is able to accurately quantify the fiber orientation distribution in in vivo second-harmonic generation images of dermal collagen with a mean fiber orientation error of (6.0 ± 4.0)° and a dispersion error of (9.3 ± 12.1)%.

A computational model for understanding the micro-mechanics of collagen fiber network in the tunica adventitia

Abdominal aortic aneurysm is a prevalent cardiovascular disease with high mortality rates. The mechanical response of the arterial wall relies on the organizational and structural behavior of its microstructural components, and thus, a detailed understanding of the microscopic mechanical response of the arterial wall layers at loads ranging up to rupture is necessary to improve diagnostic techniques and possibly treatments. Following the common notion that adventitia is the ultimate barrier at loads close to rupture, in the present study, a finite element model of adventitial collagen network was developed to study the mechanical state at the fiber level under uniaxial loading. Image stacks of the rabbit carotid adventitial tissue at rest and under uniaxial tension obtained using multi-photon microscopy were used in this study, as well as the force-displacement curves obtained from previously published experiments. Morphological parameters like fiber orientation distribution, waviness, and volume fraction were extracted for one sample from the confocal image stacks. An inverse random sampling approach combined with a random walk algorithm was employed to reconstruct the collagen network for numerical simulation. The model was then verified using experimental stress-stretch curves. The model shows the remarkable capacity of collagen fibers to uncrimp and reorient in the loading direction. These results further show that at high stretches, collagen network behaves in a highly non-affine manner, which was quantified for each sample. A comprehensive parameter study to understand the relationship between structural parameters and their influence on mechanical behavior is presented. Through this study, the model was used to conclude important structure-function relationships that control the mechanical response. Our results also show that at loads close to rupture, the probability of failure occurring at the fiber level is up to 2%. Uncertainties in usually employed rupture risk indicators and the stochastic nature of the event of rupture combined with limited knowledge on the microscopic determinants motivate the development of such an analysis. Moreover, this study will advance the study of coupling microscopic mechanisms to rupture of the artery as a whole.

Multi-scale Modeling of the Cardiovascular System: Disease Development, Progression, and Clinical Intervention

Cardiovascular diseases (CVDs) are the leading cause of death in the western world. With the current development of clinical diagnostics to more accurately measure the extent and specifics of CVDs, a laudable goal is a better understanding of the structure-function relation in the cardiovascular system. Much of this fundamental understanding comes from the development and study of models that integrate biology, medicine, imaging, and biomechanics. Information from these models provides guidance for developing diagnostics, and implementation of these diagnostics to the clinical setting, in turn, provides data for refining the models. In this review, we introduce multi-scale and multi-physical models for understanding disease development, progression, and designing clinical interventions. We begin with multi-scale models of cardiac electrophysiology and mechanics for diagnosis, clinical decision support, personalized and precision medicine in cardiology with examples in arrhythmia and heart failure. We then introduce computational models of vasculature mechanics and associated mechanical forces for understanding vascular disease progression, designing clinical interventions, and elucidating mechanisms that underlie diverse vascular conditions. We conclude with a discussion of barriers that must be overcome to provide enhanced insights, predictions, and decisions in pre-clinical and clinical applications.

A validated software application to measure fiber organization in soft tissue

The mechanical behavior of soft connective tissue is governed by a dense network of fibrillar proteins in the extracellular matrix. Characterization of this fibrous network requires the accurate extraction of descriptive structural parameters from imaging data, including fiber dispersion and mean fiber orientation. Common methods to quantify fiber parameters include fast Fourier transforms (FFT) and structure tensors; however, information is limited on the accuracy of these methods. In this study, we compared these two methods using test images of fiber networks with varying topology. The FFT method with a band-pass filter was the most accurate, with an error of [Formula: see text] in measuring mean fiber orientation and an error of [Formula: see text] in measuring fiber dispersion in the test images. The accuracy of the structure tensor method was approximately five times worse than the FFT band-pass method when measuring fiber dispersion. A free software application, FiberFit, was then developed that utilizes an FFT band-pass filter to fit fiber orientations to a semicircular von Mises distribution. FiberFit was used to measure collagen fibril organization in confocal images of bovine ligament at magnifications of [Formula: see text] and [Formula: see text]. Grayscale conversion prior to FFT analysis gave the most accurate results, with errors of [Formula: see text] for mean fiber orientation and [Formula: see text] for fiber dispersion when measuring confocal images at [Formula: see text]. By developing and validating a software application that facilitates the automated analysis of fiber organization, this study can help advance a mechanistic understanding of collagen networks and help clarify the mechanobiology of soft tissue remodeling and repair.

Microstructural quantification of collagen fiber orientations and its integration in constitutive modeling of the porcine carotid artery

BACKGROUND

Mechanical characteristics of vascular tissue may play a role in different arterial pathologies, which, amongst others, requires robust constitutive descriptions to capture the vessel wall's anisotropic and non-linear properties.Specifically, the complex 3D network of collagen and its interaction with other structural elements has a dominating effect of arterial properties at higher stress levels.The aim of this study is to collect quantitative collagen organization as well as mechanical properties to facilitate structural constitutive models for the porcine carotid artery.This helps the understanding of the mechanics of swine carotid arteries, being a standard in clinical hypothesis testing, in endovascular preclinical trials for example.

METHOD

Porcine common carotid arteries (n=10) were harvested and used to (i) characterize the collagen fiber organization with polarized light microscopy, and (ii) the biaxial mechanical properties by inflation testing.The collagen organization was quantified by the Bingham orientation density function (ODF), which in turn was integrated in a structural constitutive model of the vessel wall.A one-layered and thick-walled model was used to estimate mechanical constitutive parameters by least-square fitting the recorded in vitro inflation test results.Finally, uniaxial data published elsewhere were used to validate the mean collagen organization described by the Bingham ODF.

RESULTS

Thick collagen fibers, i.e.the most mechanically relevant structure, in the common carotid artery are dispersed around the circumferential direction.In addition, almost all samples showed two distinct families of collagen fibers at different elevation, but not azimuthal, angles.Collagen fiber organization could be accurately represented by the Bingham ODF (κ1,2,3=[13.5,0.0,25.2] and κ1,2,3=[14.7,0.0,26.6]; average error of about 5%), and their integration into a structural constitutive model captured the inflation characteristics of individual carotid artery samples.Specifically, only four mechanical parameters were required to reasonably (average error from 14% to 38%) cover the experimental data over a wide range of axial and circumferential stretches.However, it was critical to account for fibrilar links between thick collagen fibers.Finally, the mean Bingham ODF provide also good approximation to uniaxial experimental data.

CONCLUSIONS

The applied structural constitutive model, based on individually measured collagen orientation densities, was able to capture the biaxial properties of the common carotid artery. Since the model required coupling amongst thick collagen fibers, the collagen fiber orientations measured from polarized light microscopy, alone, seem to be insufficient structural information. Alternatively, a larger dispersion of collagen fiber orientations, that is likely to arise from analyzing larger wall sections, could have had a similar effect, i.e. could have avoided coupling amongst thick collagen fibers.

STATEMENT OF SIGNIFICANCE

The applied structural constitutive model, based on individually measured collagen orientation densities, was able to capture the biaxial and uniaxial properties of the common carotid artery. Since the model required coupling amongst thick collagen fibers, an effective orientation density that accounts for cross-links between the main collagen fibers has been porposed. The model provides a good approximation to the experimental data.

Computerized histomorphometric study of the splenic collagen polymorphism: A control-tissue for polarization microscopy

Previous articles have pointed out the presence of type III collagen within the extracellular structure of the parenchymatous organs. This study aimed to quantitatively characterize the collagen polymorphism at the capsule and parenchymal trabeculae of the largest lymphoid organ of the body i.e., the spleen, in mouse, rat, and rabbit models. Following a Picrosirius Red-Polarization procedure and computer assisted image analysis of paraffin sections, the results showed (1) a predominant and significantly higher amount of type III collagen in the trabeculae area compared to the capsule area in the three species, (2) no statistical difference among the three species concerning the parenchymal collagen polymorphism or the type I/type III collagen ratio, (3) a heterogeneous type I/type III collagen ratio varying from 0.86 (mouse) to 6.62 (rabbit) in the fibromuscular capsule region. A qualitative analysis corroborated these histomorphometric results. In conclusion, the spleen may be used as (1) a control tissue to qualitatively visualize type I and III collagen under polarization microscopy and to validate the quality of PSR staining (2) an aid to accurately calibrate the angle of polarization before quantitative measurements of type I and type III collagen. Among the studied species, the rabbit spleen appeared to be the most appropriate control tissue as it showed the highest amount of type I collagen in the capsule and a similarly high amount of type III collagen in the parenchymal trabeculae.

Automatic Evaluation of Collagen Fiber Directions from Polarized Light Microscopy Images

Mechanical properties of the arterial wall depend largely on orientation and density of collagen fiber bundles. Several methods have been developed for observation of collagen orientation and density; the most frequently applied collagen-specific manual approach is based on polarized light (PL). However, it is very time consuming and the results are operator dependent. We have proposed a new automated method for evaluation of collagen fiber direction from two-dimensional polarized light microscopy images (2D PLM). The algorithm has been verified against artificial images and validated against manual measurements. Finally the collagen content has been estimated. The proposed algorithm was capable of estimating orientation of some 35 k points in 15 min when applied to aortic tissue and over 500 k points in 35 min for Achilles tendon. The average angular disagreement between each operator and the algorithm was -9.3±8.6° and -3.8±8.6° in the case of aortic tissue and -1.6±6.4° and 2.6±7.8° for Achilles tendon. Estimated mean collagen content was 30.3±5.8% and 94.3±2.7% for aortic media and Achilles tendon, respectively. The proposed automated approach is operator independent and several orders faster than manual measurements and therefore has the potential to replace manual measurements of collagen orientation via PLM.

Structure-based constitutive model can accurately predict planar biaxial properties of aortic wall tissue

Structure-based constitutive models might help in exploring mechanisms by which arterial wall histology is linked to wall mechanics. This study aims to validate a recently proposed structure-based constitutive model. Specifically, the model's ability to predict mechanical biaxial response of porcine aortic tissue with predefined collagen structure was tested. Histological slices from porcine thoracic aorta wall (n=9) were automatically processed to quantify the collagen fiber organization, and mechanical testing identified the non-linear properties of the wall samples (n=18) over a wide range of biaxial stretches. Histological and mechanical experimental data were used to identify the model parameters of a recently proposed multi-scale constitutive description for arterial layers. The model predictive capability was tested with respect to interpolation and extrapolation. Collagen in the media was predominantly aligned in circumferential direction (planar von Mises distribution with concentration parameter bM=1.03 ± 0.23), and its coherence decreased gradually from the luminal to the abluminal tissue layers (inner media, b=1.54 ± 0.40; outer media, b=0.72 ± 0.20). In contrast, the collagen in the adventitia was aligned almost isotropically (bA=0.27 ± 0.11), and no features, such as families of coherent fibers, were identified. The applied constitutive model captured the aorta biaxial properties accurately (coefficient of determination R(2)=0.95 ± 0.03) over the entire range of biaxial deformations and with physically meaningful model parameters. Good predictive properties, well outside the parameter identification space, were observed (R(2)=0.92 ± 0.04). Multi-scale constitutive models equipped with realistic micro-histological data can predict macroscopic non-linear aorta wall properties. Collagen largely defines already low strain properties of media, which explains the origin of wall anisotropy seen at this strain level. The structure and mechanical properties of adventitia are well designed to protect the media from axial and circumferential overloads.

Limiting extensibility constitutive model with distributed fibre orientations and ageing of abdominal aorta

The abdominal aorta is susceptible to age-related pathological changes (arteriosclerosis, atherosclerosis, aneurysm, and tortuosity). Computational biomechanics and mechanobiology provide models capable of predicting mutual interactions between a changing mechanical environment and patho-physiological processes in ageing. However, a key factor is a constitutive equation which should reflect the internal tissue architecture. Our study investigates three microstructurally-motivated invariant-based hyperelastic anisotropic models suitable for description of the passive mechanical behaviour of the human abdominal aorta at a multiaxial state of stress known from recent literature. The three adopted models have also been supplemented with a newly proposed constitutive model (limiting extensibility with fibre dispersion). All models additively decouple the mechanical response of the isotropic (elastin and smooth muscle cells represented by the neo-Hookean term) and the anisotropic (collagen) parts. Two models use exponential functions to capture large strain stiffening ascribed to the engagement of collagen fibres into the load-bearing process. The other two models are based on the concept of limiting extensibility. Perfect alignment of reinforcing fibres with two preferred directions as well as fibre dispersion are considered. Constitutive models are calibrated to the inflation-extension response adopted from the literature based on the computational model of the residually-stressed thick-walled tube. A correlation analysis of determined material parameters was performed to reveal dependence on the age. The results of the nonlinear regression suggest that limiting fibre extensibility is the concept which is suitable to be used for the constitutive description of the aorta at multiaxial stress states and is highly sensitive to ageing-induced changes in mechanical response.