Biomechanical Imaging Research Articles

The noise distribution in a shear wave speed image computed using arrival times at fixed spatial positions

In a number of applications, for example biomechanical imaging of tissue and geophysics, the goal is to recover wave speed from arrival times, the times when a wave front, initiated at a source, arrives at certain points in space. The mathematical model that relates the arrival times to the wave speed is assumed to be the Eikonal equation. Typically the measured arrival time data is noisy so that in turn the recovered wave speed is noisy. Here we assume the noise in the measured arrival times is Gaussian and show that then the recovered wave speed has noise that has an inverse Rician distribution. This latter distribution has infinite variance. Nevertheless, we show using the Kantorovich metric that for small variances in the Gaussian noise (corresponding to a small value of the shape parameter in the Rician random variable), the inverse Rician distribution can be approximated by a Gaussian distribution whose mean is the true wave speed.

Finite Propagation Speed of Waves in Anisotropic Viscoelastic Media

Finite propagation speed properties in mathematical elastic and viscoelastic models are fundamental in many applications where the data exhibits propagating fronts. We note particularly that this property is observed in biomechanical imaging of tissue, in particular in the supersonic imaging experiment, and also in geophysics and ocean acoustics. With these applications in mind, noting that there are many other applications as well, we present finite propagation speed results for very general integro-differential, anisotropic, viscoelastic linear models, which are not necessarily of convolution type. We start with work density, we define work density decomposition, and we achieve our results utilizing energy arguments. One of the advantages of our presented method, instead of using plane wave arguments, is that there is no need to make the homogeneous medium assumption to obtain the finite propagation speed results.

Biomechanical Imaging Markers as Predictors of Abdominal Aortic Aneurysm Growth or Rupture: A Systematic Review

Biomechanical Imaging Markers as Predictors of Abdominal Aortic Aneurysm Growth or Rupture: A Systematic Review

Abstract 515: Comparison of Aging and Disturbed Flow Effects on Arterial Wall Biomechanics

Introduction: Arterial stiffness is an age related disease that doubles ones cardiovascular mortality and functions as an intermediary step in the formation of atherosclerosis. We have recently demonstrated that low and oscillatory wall shear stress, termed disturbed flow (d-flow), leads to arterial stiffness in otherwise normal arteries. Since d-flow has been linked to atherosclerotic plaque formation, our objective is to compare the carotid artery mechanics of 12 week arteries exposed to 4 weeks of d-flow to that of untreated 80 week old s129 mice. We hypothesize that low and oscillatory shear governs the remodeling of the arteries in a way that mimics the effect of arterial stiffening associated with aging. Materials and Methods: We used a partial carotid ligation model in 12-week-old s129 male (n=3) and female (n=3) mice. 4 weeks post surgery we euthanized the animals and performed biaxial extension-inflation biomechanical testing, confocal imaging, histological studies and opening angle studies on the left (partially ligated) carotid artery (LCA) and right (non-ligated) carotid artery (RCA) in order to characterize their biomechanical behavior. The same testing was performed on s129 80-week-old male animals (n=4). Pressure-diameter (P-d) data were collected from cyclic pressurization ramps from 0 to 160 mmHg at constant axial extension levels ranging from 1.3 to 1.9. Compliance was calculated at the in-vivo axial stretch level of 1.7 for both age groups. Intima media thickness was analyzed from H&E stained histological slides. Results were compared with the unpaired, two-tailed t-test and significance was taken at p<0.05. Results and Conclusions: Partial ligation for 4 weeks drastically decreased the compliance of the 12-week-old left carotid in a way that exactly follows the stiffening of the arteries in the 80-week-old mice. The compliance of the non-manipulated right carotid arteries reflected the age related difference in the stiffness of young vs old arteries with statistical difference in the 30 - 90 mmHg range. We have established that low shear stress and oscillatory flow promote the increase in arterial stiffening in the partially ligated young mice in a way that mimics the age-related decrease in arterial compliance in old mice.

A Bayesian approach for characterization of soft tissue viscoelasticity in acoustic radiation force imaging.

Biomechanical imaging techniques based on acoustic radiation force (ARF) have been developed to characterize the viscoelasticity of soft tissue by measuring the motion excited by ARF non-invasively. The unknown stress distribution in the region of excitation limits an accurate inverse characterization of soft tissue viscoelasticity, and single degree-of-freedom simplified models have been applied to solve the inverse problem approximately. In this study, the ARF-induced creep imaging is employed to estimate the time constant of a Voigt viscoelastic tissue model, and an inverse finite element (FE) characterization procedure based on a Bayesian formulation is presented. The Bayesian approach aims to estimate a reasonable quantification of the probability distributions of soft tissue mechanical properties in the presence of measurement noise and model parameter uncertainty. Gaussian process metamodeling is applied to provide a fast statistical approximation based on a small number of computationally expensive FE model runs. Numerical simulation results demonstrate that the Bayesian approach provides an efficient and practical estimation of the probability distributions of time constant in the ARF-induced creep imaging. In a comparison study with the single degree of freedom models, the Bayesian approach with FE models improves the estimation results even in the presence of large uncertainty levels of the model parameters.

Physical therapists' role in prevention and management of patellar tendinopathy injuries in youth, collegiate, and middle-aged indoor volleyball athletes.

Patellar tendinopathy is highly prevalent in all ages and skill levels of volleyball athletes. To illustrate this, we discuss the clinical, biomechanical, and ultrasound imaging presentation and the intervention strategies of three volleyball athletes at different stages of their athletic career: youth, middle-aged, and collegiate. We present our examination strategies and interpret the data collected, including visual movement analysis and dynamics, relating these findings to the probable causes of their pain and dysfunction. Using the framework of the EdUReP concept, incorporating Education, Unloading, Reloading, and Prevention, we propose intervention strategies that target each athlete's specific issues in terms of education, rehabilitation, training, and return to sport. This framework can be generalized to manage patellar tendinopathy in other sports requiring jumping, from youth to middle age, and from recreational to elite competitive levels.

Stiffness versus prestress relationship at subcellular length scale

Local intracellular variations of cell mechanical properties, which are essential for vital cellular functions, have not been well characterized and are poorly understood. Here, we used results from our previous biomechanical imaging study to obtain relationships between intracellular shear modulus and prestress. We found that the subcellular shear modulus vs. prestress relationships exhibited positive linear correlations, consistent with previously observed behaviors at the whole cell and tissue levels. This, in turn, suggests that the prestress may be a unifying factor that determines material properties of living matter at different length scales.

Biomechanics of Forearm Rotation: Force and Efficiency of Pronator Teres

Biomechanical models are useful to assess the effect of muscular forces on bone structure. Using skeletal remains, we analyze pronator teres rotational efficiency and its force components throughout the entire flexion-extension and pronation-supination ranges by means of a new biomechanical model and 3D imaging techniques, and we explore the relationship between these parameters and skeletal structure. The results show that maximal efficiency is the highest in full elbow flexion and is close to forearm neutral position for each elbow angle. The vertical component of pronator teres force is the highest among all components and is greater in pronation and elbow extension. The radial component becomes negative in pronation and reaches lower values as the elbow flexes. Both components could enhance radial curvature, especially in pronation. The model also enables to calculate efficiency and force components simulating changes in osteometric parameters. An increase of radial curvature improves efficiency and displaces the position where the radial component becomes negative towards the end of pronation. A more proximal location of pronator teres radial enthesis and a larger humeral medial epicondyle increase efficiency and displace the position where this component becomes negative towards forearm neutral position, which enhances radial curvature. Efficiency is also affected by medial epicondylar orientation and carrying angle. Moreover, reaching an object and bringing it close to the face in a close-to-neutral position improve efficiency and entail an equilibrium between the forces affecting the elbow joint stability. When the upper-limb skeleton is used in positions of low efficiency, implying unbalanced force components, it undergoes plastic changes, which improve these parameters. These findings are useful for studies on ergonomics and orthopaedics, and the model could also be applied to fossil primates in order to infer their locomotor form. Moreover, activity patterns in human ancient populations could be deduced from parameters reported here.

Biomechanical, Cell Biological and Magnetic Resonance Imaging (MRI)-Morphological Results Comparing Single- and Double-Row Repair

This study confirms that in an acute repair model, double-row repair may enhance the speed of mechanical and histological recovery of the tendon-bone complex when compared with single-row repair in the early postoperative period. A significant controversy exists regarding the optimal fixation technique in rotator cuff repair. The aim of this study was to compare the time-dependent cell biological and biomechanical properties of a single-row technique using arthroscopic Mason-Allen stitches versus a double-row technique using arthroscopic Mason-Allen stitches (lateral) and mattress stitches (medial) in an in-vivo sheep model. Thirty-six female mature merino sheep were randomly assigned to either a single-row group using arthroscopic Mason-Allen stitches, or a double-row group using a combination of arthroscopic Mason-Allen and mattress stitches. Each group was analysed at one of six survival points. The integrity of the cuff repair using MRI, biomechanical properties using a mechanical testing machine, and the expression of collagen type I, II, and III using histological, ultrastructural and molecularbiological methods were evaluated. The mean load to failure was significantly higher in the double-row group compared with the single-row group at 6 and 12 weeks. At 26 weeks, the differences were not statistically significant; however, the double-row group achieved a mean load to failure similar to that of a healthy infraspinatus tendon. In contrast, the single-row group reached only 70% of the load of a healthy infraspinatus tendon. No significant differences were observed based on the MRI investigation. Molecular results show that collagen type III expression remained positive until six weeks postoperatively in the double-row group, whereas it was detectable for 12 weeks in the single-row group. Additionally, collagen Type II expression was increased in the cartilage zone after 12 weeks in the doubdouble-row compared to the single-row group. This study confirms that in an acute repair model, double-row repair may enhance the speed of mechanical and histological recovery of the tendon-bone complex when compared with single-row repair in the early postoperative period. This phenomenon could be explained due to faster tissue revitalization in using this technique. Conversely, the MRI results show no significant differences using both techniques.

Magnetic resonance imaging of the pelvic floor: From clinical to biomechanical imaging

This article reviews the current role of magnetic resonance imaging in the study of the pelvic floor anatomy and pelvic floor dysfunction. The application of static and dynamic magnetic resonance imaging in the clinical context and for biomechanical simulation modeling is assessed, and the main findings are summarized. Additionally, magnetic resonance-based diffusion tensor imaging is presented as a potential tool to evaluate muscle fiber morphology. In this article, focus is set on pelvic floor muscle damage related to urinary incontinence and pelvic organ prolapse, sometimes as a consequence of vaginal delivery. Modeling applications that evaluate anatomical and physiological properties of pelvic floor are presented to further illustrate their particular characteristics. Finally, finite element method is described as a method for modeling and analyzing pelvic floor structures' biomechanical performance, based on material and behavioral properties of the tissues, and considering pressure loads that mimic real-life conditions such as active contraction or Valsalva maneuver.

Biomechanical imaging of cell stiffness and prestress with subcellular resolution

Knowledge of cell mechanical properties, such as elastic modulus, is essential to understanding the mechanisms by which cells carry out many integrated functions in health and disease. Cellular stiffness is regulated by the composition, structural organization, and indigenous mechanical stress (or prestress) borne by the cytoskeleton. Current methods for measuring stiffness and cytoskeletal prestress of living cells necessitate either limited spatial resolution but with high speed, or spatial maps of the entire cell at the expense of long imaging times. We have developed a novel technique, called biomechanical imaging, for generating maps of both cellular stiffness and prestress that requires less than 30 s of interrogation time, but which provides subcellular spatial resolution. The technique is based on the ability to measure tractions applied to the cell while simultaneously observing cell deformation, combined with capability to solve an elastic inverse problem to find cell stiffness and prestress distributions. We demonstrated the application of this technique by carrying out detailed mapping of the shear modulus and cytoskeletal prestress distributions of 3T3 fibroblasts, making no assumptions regarding those distributions or the correlation between them. We also showed that on the whole cell level, the average shear modulus is closely associated with the average prestress, which is consistent with the data from the literature. Data collection is a straightforward procedure that lends itself to other biochemical/biomechanical interventions. Biomechanical imaging thus offers a new tool that can be used in studies of cell biomechanics and mechanobiology where fast imaging of cell properties and prestress is desired at subcellular resolution.

Three-dimensional kinematic stress magnetic resonance image analysis shows promise for detecting altered anatomical relationships of tissues in the cervical spine associated with painful radiculopathy

For some patients with radiculopathy a source of nerve root compression cannot be identified despite positive electromyography (EMG) evidence. This discrepancy hampers the effective clinical management for these individuals. Although it has been well-established that tissues in the cervical spine move in a three-dimensional (3D) manner, the 3D motions of the neural elements and their relationship to the bones surrounding them are largely unknown even for asymptomatic normal subjects. We hypothesize that abnormal mechanical loading of cervical nerve roots during pain-provoking head positioning may be responsible for radicular pain in those cases in which there is no evidence of nerve root compression on conventional cervical magnetic resonance imaging (MRI) with the neck in the neutral position. This biomechanical imaging proof-of-concept study focused on quantitatively defining the architectural relationships between the neural and bony structures in the cervical spine using measurements derived from 3D MR images acquired in neutral and pain-provoking neck positions for subjects: (1) with radicular symptoms and evidence of root compression by conventional MRI and positive EMG, (2) with radicular symptoms and no evidence of root compression by MRI but positive EMG, and (3) asymptomatic age-matched controls. Function and pain scores were measured, along with neck range of motion, for all subjects. MR imaging was performed in both a neutral position and a pain-provoking position. Anatomical architectural data derived from analysis of the 3D MR images were compared between symptomatic and asymptomatic groups, and the symptomatic groups with and without imaging evidence of root compression. Several differences in the architectural relationships between the bone and neural tissues were identified between the asymptomatic and symptomatic groups. In addition, changes in architectural relationships were also detected between the symptomatic groups with and without imaging evidence of nerve root compression. As demonstrated in the data and a case study the 3D stress MR imaging approach provides utility to identify biomechanical relationships between hard and soft tissues that are otherwise undetected by standard clinical imaging methods. This technique offers a promising approach to detect the source of radiculopathy to inform clinical management for this pathology.

Application of numerical methods to elasticity imaging.

Elasticity imaging can be understood as the intersection of the study of biomechanical properties, imaging sciences, and physics. It was mainly motivated by the fact that pathological tissue presents an increased stiffness when compared to surrounding normal tissue. In the last two decades, research on elasticity imaging has been an international and interdisciplinary pursuit aiming to map the viscoelastic properties of tissue in order to provide clinically useful information. As a result, several modalities of elasticity imaging, mostly based on ultrasound but also on magnetic resonance imaging and optical coherence tomography, have been proposed and applied to a number of clinical applications: cancer diagnosis (prostate, breast, liver), hepatic cirrhosis, renal disease, thyroiditis, arterial plaque evaluation, wall stiffness in arteries, evaluation of thrombosis in veins, and many others. In this context, numerical methods are applied to solve forward and inverse problems implicit in the algorithms in order to estimate viscoelastic linear and nonlinear parameters, especially for quantitative elasticity imaging modalities. In this work, an introduction to elasticity imaging modalities is presented. The working principle of qualitative modalities (sonoelasticity, strain elastography, acoustic radiation force impulse) and quantitative modalities (Crawling Waves Sonoelastography, Spatially Modulated Ultrasound Radiation Force (SMURF), Supersonic Imaging) will be explained. Subsequently, the areas in which numerical methods can be applied to elasticity imaging are highlighted and discussed. Finally, we present a detailed example of applying total variation and AM-FM techniques to the estimation of elasticity.

Modelling of global boundary effects on harmonic motion imaging of soft tissues

Biomechanical imaging techniques have been developed for soft tissue characterisation and detection of breast tumours. Harmonic motion imaging (HMI) uses a focused ultrasound technology to generate a harmonic radiation force in a localised region inside a soft tissue. The resulting dynamic response is used to map the local distribution of the mechanical properties of the tissue. In this study, a finite element (FE) model is developed to investigate the effect of global boundary conditions on the dynamic response of a soft tissue during HMI. The direct-solution steady-state dynamic analysis procedure is used to compute the harmonic displacement amplitude in FE simulations. The model is parameterised in terms of boundary conditions and viscoelastic properties, and the corresponding raster-scan displacement amplitudes are captured to examine its response. The effect of the model's global dimensions on the harmonic response is also investigated. It is observed that the dynamic response of soft tissue with high viscosity is independent of the global boundary conditions for regions remote to the boundary; thus, it can be subjected to local analysis to estimate the underlying mechanical properties. However, the dynamic response is sensitive to global boundary conditions for tissue with low viscosity or regions located near to the boundary.

Solution of the time‐harmonic viscoelastic inverse problem with interior data in two dimensions

SUMMARYWe consider the problem of determining the distribution of the complex‐valued shear modulus for an incompressible linear viscoelastic material undergoing infinitesimal time‐harmonic deformation, given the knowledge of the displacement field in its interior. In particular, we focus on the two‐dimensional problems of anti‐plane shear and plane stress. These problems are motivated by applications in biomechanical imaging, where the material modulus distributions are used to detect and/or diagnose cancerous tumors. We analyze the well‐posedness of the strong form of these problems and conclude that for the solution to exist, the measured displacement field is required to satisfy rather restrictive compatibility conditions. We propose a weak, or a variational formulation, and prove the existence and uniqueness of solutions under milder conditions on measured data. This formulation is derived by weighting the original PDE for the shear modulus by the adjoint operator acting on the complex‐conjugate of the weighting functions. For this reason, we refer to it as the complex adjoint weighted equation (CAWE). We consider a straightforward finite element discretization of these equations with total variation regularization, and test its performance with synthetically generated and experimentally measured data. We find that the CAWE method is, in general, less diffusive than a corresponding least squares solution, and that the total variation regularization significantly improves its performance in the presence of noise. Copyright © 2012 John Wiley & Sons, Ltd.

Injuries in Overhead Athletes: Editorial Comment

While baseball has been played for more than 100 years, it was not until the middle of the 20th century that Dr. Bennett began writing about the unique injuries experienced by these athletes [2–4]. (In this issue, we have republished Bennett’s article from 1947 [10.1007/s11999-012-2335-2], and in 2008, we republished his article from 1959 [5].) In the 1970s and 1980s, Drs. Frank Jobe [6–8] and James Andrews [1, 9] began to specialize in the treatment of throwers and dedicated a substantial amount of time to improving the understanding of the mechanics of throwing and how those mechanics translated to the classic injuries seen. Elbow ulnar collateral ligament injuries, which at one time were career ending for pitchers, are now treated with surgical reconstruction that gets athletes back to their previous level of play more than 80% of the time [10]. The lay media suggest more than 10% of current major league baseball players have undergone ulnar collateral ligament reconstruction. The same can be said about superior labral anterior-posterior lesions, which are now treated relatively easily with arthroscopic repair. More recently, with improvements in biomechanical testing and imaging, and with the use of arthroscopy, we have been better able to classify the adaptive and pathologic findings unique to throwers. To that end, we have organized a symposium to summarize some of the current thinking as it pertains to the treatment of these athletes. The reader will see injuries to baseball players are no longer limited to the shoulder and elbow. Treating these athletes appropriately hinges on knowing what is considered a normal adaptive response to throwing and being able to discern when these adaptations become pathologic. Successful treatment also depends on understanding that the forces experienced by the body during throwing activities are not just limited to the shoulder. Clearly, the hip, scapula, and elbow are intimately involved in throwing effectively and in dissipating the stresses generated during the throwing motion. While it has been said “baseball is America’s national pastime,” it has truly become a game played by athletes of all levels all over the world. To that end, treatment of the characteristic injuries experienced by baseball players is no longer limited to the United States. Doctors from places such as Europe and Asia are becoming thought leaders in this field, and this is represented in the articles chosen for this symposium. We believe this compilation represents much of the current thinking as it pertains to preventing, diagnosing, and treating injuries that affect overhead athletes. More importantly, we believe these studies will inspire conversation and debate and act as a stimulus for future investigations. Fig. 1 Dr. Joshua S. Dines is shown Fig. 2 Dr. David W. Altchek is shown.

Biomechanical and Magnetic Resonance Imaging Evaluation of a Single- and Double-Row Rotator Cuff Repair in an In Vivo Sheep Model

To investigate the biomechanical and magnetic resonance imaging (MRI)-derived morphologic changes between single- and double-row rotator cuff repair at different time points after fixation. Eighteen mature female sheep were randomly assigned to either a single-row treatment group using arthroscopic Mason-Allen stitches or a double-row treatment group using a combination of arthroscopic Mason-Allen and mattress stitches. Each group was analyzed at 1 of 3 survival points (6 weeks, 12 weeks, and 26 weeks). We evaluated the integrity of the cuff repair using MRI and biomechanical properties using a mechanical testing machine. The mean load to failure was significantly higher in the double-row group compared with the single-row group at 6 and 12 weeks (P = .018 and P = .002, respectively). At 26 weeks, the differences were not statistically significant (P = .080). However, the double-row group achieved a mean load to failure similar to that of a healthy infraspinatus tendon, whereas the single-row group reached only 70% of the load of a healthy infraspinatus tendon. No significant morphologic differences were observed based on the MRI results. This study confirms that in an acute repair model, double-row repair may enhance the speed of mechanical recovery of the tendon-bone complex when compared with single-row repair in the early postoperative period. Double-row rotator cuff repair enables higher mechanical strength that is especially sustained during the early recovery period and may therefore improve clinical outcome.

Deformable image registration and 3D strain mapping for the quantitative assessment of cortical bone microdamage

The resistance to forming microcracks is a key factor for bone to withstand critical loads without fracturing. In this study, we investigated the initiation and propagation of microcracks in murine cortical bone by combining three-dimensional images from synchrotron radiation-based computed tomography and time-lapsed biomechanical testing to observe microdamage accumulation over time. Furthermore, a novel deformable image registration procedure utilizing digital volume correlation and demons image registration was introduced to compute 3D strain maps allowing characterization of the mechanical environment of the microcracks. The displacement and strain maps were validated in a priori tests. At an image resolution of 740 nm the spatial resolution of the strain maps was 10 μm (MTF), while the errors of the displacements and strains were 130 nm and 0.013, respectively. The strain maps revealed a complex interaction of the propagating microcracks with the bone microstructure. In particular, we could show that osteocyte lacunae play a dual role as stress concentrating features reducing bone strength, while at the same time contributing to the bone toughness by blunting the crack tip. We conclude that time-lapsed biomechanical imaging in combination with three-dimensional strain mapping is suitable for the investigation of crack initiation and propagation in many porous materials under various loading scenarios.

Kinetic fingerprint discriminates similar cell populations subjected to uniaxial cyclic tensile strain on flexible substrates

Uniaxial cyclic tensile deformation of flexible cell culture membranes has been reported to induce cell body and cytoskeleton alignment with respect to the axis of the applied mechanical stimulus. This effect was proven to be strongly dependent on the stretching frequency and amplitude. However there is only little information available on cell type-specific responses. Extension of this stretching technique by live-cell imaging allowed us to investigate the temporal behavior of cells, which enabled us to define a cell-specific kinetic fingerprint. Based on this approach, we could identify significant differences between two periodontal cell populations closely related in vivo. The orientation response was shown to be faster for periodontal ligament fibroblasts than for alveolar bone cells. These results were substantiated by our observation of altered activation levels of RhoA. With this work we could show that the combination of biomechanical stimulation and live cell imaging provides a potential tool to distinguish between morphologically and biochemically very similar cell populations and to reveal altered stimuli-dependent physiological processes, as indicated by the kinetic fingerprint on flexible substrates. Moreover, these new findings can be implemented in the development of cell type-/tissue-specific customized substrates based on soft matter biomaterials or prospective smart flexible polymers.

Hierarchical microimaging of bone structure and function

With recent advances in molecular medicine and disease treatment in osteoporosis, quantitative image processing of three-dimensional bone structures is critical in the context of bone quality assessment. Biomedical imaging technology such as MRI or CT is readily available, but few attempts have been made to expand the capabilities of these systems by integrating quantitative analysis tools and by exploring structure-function relationships in a hierarchical fashion. Nevertheless, such quantitative end points are an important factor for success in basic research and in the development of novel therapeutic strategies. CT is key to these developments, as it images and quantifies bone in three dimensions and provides multiscale biological imaging capabilities with isotropic resolutions of a few millimeters (clinical CT), a few tens of micrometers (microCT) and even as high as 100 nanometers (nanoCT). The technology enables the assessment of the relationship between microstructural and ultrastructural measures of bone quality and certain diseases or therapies. This Review focuses on presenting strategies for three-dimensional approaches to hierarchical biomechanical imaging in the study of microstructural and ultrastructural bone failure. From this Review, it can be concluded that biomechanical imaging is extremely valuable for the study of bone failure mechanisms at different hierarchical levels.