Transient and microscale deformations and strains measured under exogenous loading by noninvasive magnetic resonance

Characterization of spatiotemporal deformation dynamics and material properties requires non-destructive methods to visualize mechanics of materials and biological tissues. Displacement-encoded magnetic resonance imaging (MRI) has emerged as a noninvasive and non-destructive technique used to quantify deformation and strains. However, the techniques are not yet applicable to a broad range of materials and load-bearing tissues. In this paper, we visualize transient and internal material deformation through the novel synchrony of external mechanical loading with rapid displacement-encoded MRI. We achieved deformation measurements in silicone gel materials with a spatial resolution of 100 μm and a temporal resolution (of 2.25 ms), set by the repetition time (TR) of the rapid MRI acquisition. Displacement and strain precisions after smoothing were 11 μm and 0.1%, respectively, approaching cellular length scales. Short (1/2 TR) echo times enabled visualization of in situ deformation in a human tibiofemoral joint, inclusive of multiple variable T(2) biomaterials. Moreover, the MRI acquisitions achieved a fivefold improvement in imaging time over previous technology, setting the stage for mechanical imaging in vivo. Our results provide a general approach for noninvasive and non-destructive measurement, at high spatial and temporal resolution, of the dynamic mechanical response of a broad range of load-bearing materials and biological tissues.     

Cell and tissue deformation measurements: Texture correlation with third-order approximation of displacement gradients

Cells remarkably are capable of large deformations during motility and when subjected to mechanical force. Measurement of mechanical deformation (i.e. displacements, strain) is critical to understand functional changes in cells and biological tissues following disease, and to elucidate basic relationships between applied force and cellular biosynthesis. Microscopy-based imaging modalities provide the ability to noninvasively visualize small cell or tissue structures and track their motion over time, often using two-dimensional (2D) digital image (texture) correlation algorithms. For the measurement of complex and nonlinear motion in cells and tissues, implementation of texture correlation algorithms with high order approximations of displacement mapping terms are needed to minimize error. Here, we extend a texture correlation algorithm with up to third-order approximation of displacement mapping terms for the measurement of cell and tissue deformation. We additionally investigate relationships between measurement error and image texture, defined by subset entropy. Displacement measurement error is significantly reduced when the order of displacement mapping terms in the texture correlation algorithm matches or exceeds the order of the deformation observed. Displacement measurement error is also inversely proportional to subset entropy, with well-defined cell and tissue structures leading to high entropy and low error. For cell and tissue studies where complex or nonlinear displacements are expected, texture correlation algorithms with high order terms are required to best characterize the observed deformation.     

A comparison of calibration methods for stereo fluoroscopic imaging systems

Stereo (biplane) fluoroscopic imaging systems are considered the most accurate and precise systems to study joint kinematics in vivo. Calibration of a biplane fluoroscopy system consists of three steps: (1) correction for spatial image distortion; (2) calculation of the focus position; and (3) calculation of the relative position and orientation of the two fluoroscopy systems with respect to each other. In this study we compared 6 methods for calibrating a biplane fluoroscopy system including a new method using a novel nested-optimization technique. To quantify bias and precision, an electronic digital caliper instrumented with two tantalum markers on radiolucent posts was imaged in three configurations, and for each configuration placed in ten static poses distributed throughout the viewing volume. Bias and precision were calculated as the mean and standard deviation of the displacement of the markers measured between the three caliper configurations. The data demonstrated that it is essential to correct for image distortion when sub-millimeter accuracy is required. We recommend calibrating a stereo fluoroscopic imaging system using an accurately machined plate and a calibration cube, which improved accuracy 2-3 times compared to the other calibration methods. Once image distortion is properly corrected, the focus position should be determined using the Direct Linear Transformation (DLT) method for its increased speed and equivalent accuracy compared to the novel nested-optimization method. The DLT method also automatically provides the 3D fluoroscopy configuration. Using the recommended calibration methodology, bias and precision of 0.09 and 0.05 mm or better can be expected for measuring inter-marker distances.     

Stress distributions and material properties determined in articular cartilage from MRI-based finite strains

The noninvasive measurement of finite strains in biomaterials and tissues by magnetic resonance imaging (MRI) enables mathematical estimates of stress distributions and material properties. Such methods allow for non-contact and patient-specific modeling in a manner not possible with traditional mechanical testing or finite element techniques. Here, we employed three constitutive (i.e. linear Hookean, and nonlinear Neo-Hookean and Mooney-Rivlin) relations with known loading conditions and MRI-based finite strains to estimate stress patterns and material properties in the articular cartilage of tibiofemoral joints. Displacement-encoded MRI was used to determine two-dimensional finite strains in juvenile porcine joints, and an iterative technique estimated stress distributions and material properties with defined constitutive relations. Stress distributions were consistent across all relations, although the stress magnitudes varied. Material properties for femoral and tibial cartilage were found to be consistent with those reported in literature. Further, the stress estimates from Hookean and Neo-Hookean, but not Mooney-Rivlin, relations agreed with finite element-based simulations. A nonlinear Neo-Hookean relation provided the most appropriate model for the characterization of complex and spatially dependent stresses using two-dimensional MRI-based finite strain. These results demonstrate the feasibility of a new and computationally efficient technique incorporating MRI-based deformation with mathematical modeling to non-invasively evaluate the mechanical behavior of biological tissues and materials.     

Three‐dimensional static optical coherence elastography based on inverse compositional Gauss‐Newton digital volume correlation

The three‐dimensional (3D) mechanical properties characterization of tissue is essential for physiological and pathological studies, as biological tissue is mostly heterogeneous and anisotropic. A digital volume correlation (DVC)‐based 3D optical coherence elastography (OCE) method is developed to measure the 3D displacement and strain tensors. The DVC algorithm includes a zero‐mean normalized cross‐correlation criterion‐based coarse search regime, an inverse compositional Gauss‐Newton fine search algorithm and a local ternary quadratic polynomial fitting strain calculation method. A 3D optical coherence tomography (OCT) scanning protocol is proposed through theoretical analysis and experimental verification. Measurement errors of the DVC‐based 3D OCE method are evaluated to be less than 2.0 μm for displacements and 0.30% for strains by rigid body motion experiments. The 3D displacements and strains of a phantom and a specimen of chicken breast tissue under compression are measured. Results of the phantom show a good agreement with theoretical analysis and tensile testing. The strains of the chicken breast tissue indicate anisotropic biomechanical properties. This study provides an effective method for 3D biomechanical property studies of soft tissue and improves the development of 3D OCE techniques.     

Precision in iterative modulation enhanced single-molecule localization microscopy

Modulation enhanced single-molecule localization microscopy (meSMLM) methods improve the localization precision by using patterned illumination to encode additional position information. Iterative meSMLM (imeSMLM) methods iteratively generate prior information on emitter positions, used to locally improve the localization precision during subsequent iterations. The Cramér-Rao lower bound cannot incorporate prior information to bound the best achievable localization precision because it requires estimators to be unbiased. By treating estimands as random variables with a known prior distribution, the Van Trees inequality (VTI) can be used to bound the best possible localization precision of imeSMLM methods. An imeSMLM method is considered, where the positions of in-plane standing-wave illumination patterns are controlled over the course of multiple iterations. Using the VTI, we analytically approximate a lower bound on the maximum localization precision of imeSMLM methods that make use of standing-wave illumination patterns. In addition, we evaluate the maximally achievable localization precision for different illumination pattern placement strategies using Monte Carlo simulations. We show that in the absence of background and under perfect modulation, the information content of signal photons increases exponentially as a function of the iteration count. However, the information increase is no longer exponential as a function of the iteration count under non-zero background, imperfect modulation, or limited mechanical resolution of the illumination positioning system. As a result, imeSMLM with two iterations reaches at most a fivefold improvement over SMLM at 8 expected background photons per pixel and 95% modulation contrast. Moreover, the information increase from imeSMLM is balanced by a reduced signal photon rate. Therefore, SMLM outperforms imeSMLM when considering an equal measurement time and illumination power per iteration. Finally, the VTI is an excellent tool for the assessment of the performance of illumination control and is therefore the method of choice for optimal design and control of imeSMLM methods.     

Functional MRI can detect changes in intratissue strains in a full thickness and critical sized ovine cartilage defect model

Functional imaging of tissue biomechanics can reveal subtle changes in local softening and stiffening associated with disease or repair, but noninvasive and nondestructive methods to acquire intratissue measures in well-defined animal models are largely lacking. We utilized displacement encoded MRI to measure changes in cartilage deformation following creation of a critical-sized defect in the medial femoral condyle of ovine (sheep) knees, a common in situ and large animal model of tissue damage and repair. We prioritized visualization of local, site-specific variation and changes in displacements and strains following defect placement by measuring spatial maps of intratissue deformation. Custom data smoothing algorithms were developed to minimize propagation of noise in the acquired MRI phase data toward calculated displacement or strain, and to improve strain measures in high aspect ratio tissue regions. Strain magnitudes in the femoral, but not tibial, cartilage dramatically increased in load-bearing and contact regions especially near the defect locations, with an average 6.7% ± 6.3%, 13.4% ± 10.0%, and 10.0% ± 4.9% increase in first and second principal strains, and shear strain, respectively. Strain heterogeneity reflected the complexity of the in situ mechanical environment within the joint, with multiple tissue contacts defining the deformation behavior. This study demonstrates the utility of displacement encoded MRI to detect increased deformation patterns and strain following disruption to the cartilage structure in a clinically-relevant, large animal defect model. It also defines imaging biomarkers based on biomechanical measures, in particular shear strain, that are potentially most sensitive to evaluate damage and repair, and that may additionally translate to humans in future studies.     

A finite element beam-model for efficient simulation of large-scale porous structures

This paper presents a new method for the generation of a beam finite element (FE) model from a three-dimensional (3D) data set acquired by micro-computed tomography (micro-CT). This method differs from classical modeling of trabecular bone because it models a specific sample only and differs from conventional solid hexahedron element-based FE approaches in its computational efficiency. The stress-strain curve, characterizing global mechanical properties of a porous structure, could be well predicted (R(2)=0.92). Furthermore, validation of the method was achieved by comparing local displacements of element nodes with the displacements directly measured by time-lapsed imaging methods of failure, and these measures were in good agreement. The presented model is a first step in modeling specific samples for efficient strength analysis by FE modeling. We believe that with upcoming high-resolution in-vivo imaging methods, this approach could lead to a novel and accurate tool in the risk assessment for osteoporotic fractures.     

Mechanical analysis of a rodent segmental bone defect model: The effects of internal fixation and implant stiffness on load transfer

Segmental bone defect animal models are often used for evaluating the bone regeneration performance of bone substituting biomaterials. Since bone regeneration is dependent on mechanical loading, it is important to determine mechanical load transfer after stabilization of the defect and to study the effects of biomaterial stiffness on the transmitted load. In this study, we assess the mechanical load transmitted over a 6 mm femur defect that is stabilized with an internal PEEK fixation plate. Subsequently, three types of selective laser melted porous titanium implants with different stiffness values were used to graft the defect (five specimens per group). In one additional group, the defect was left empty. Micro strain gauges were used to measure strain values at four different locations of the fixation plate during external loading on the femoral head. The load sharing between the fixation plate and titanium implant was highly variable with standard deviations of measured strain values between 31 and 93% of the mean values. As a consequence, no significant differences were measured between the forces transmitted through the titanium implants with different elastic moduli. Only some non-significant trends were observed in the mean strain values that, consistent with the results of a previous finite element study, implied the force transmitted through the implant increases with the implant stiffness. The applied internal fixation method does not standardize mechanical loading over the defect to enable detecting small differences in bone regeneration performances of bone substituting biomaterials. In conclusion, the fixation method requires further optimization to reduce the effects of the operative procedure and make the mechanical loading more consistent and improve the overall sensitivity of this rat femur defect model.     

Beyond the diffraction limit: far-field fluorescence imaging with ultrahigh resolution

Fluorescence microscopy is an important and extensively utilised tool for imaging biological systems. However, the image resolution that can be obtained has a limit as defined through the laws of diffraction. Demand for improved resolution has stimulated research into developing methods to image beyond the diffraction limit based on far-field fluorescence microscopy techniques. Rapid progress is being made in this area of science with methods emerging that enable fluorescence imaging in the far-field to possess a resolution well beyond the diffraction limit. This review outlines developments in far-field fluorescence methods which enable ultrahigh resolution imaging and application of these techniques to biology. Future possible trends and directions in far-field fluorescence imaging with ultrahigh resolution are also outlined.     

Development of an RSA calibration system with improved accuracy and precision

In this study, a new radiostereometric analysis (RSA) calibration cage was developed with the aim of improving the accuracy and precision of RSA. This development consisted of three steps: a numerical simulation technique was first used to design the new cage; a synthetic imaging method was then implemented to predict the performance of the designed cage before it was actually fabricated; and an experimental phantom test was finally conducted to verify the actual performance of the new cage and compare with two currently widely used cages. Accuracy was calculated as the 95% prediction intervals from regression analyses between the measured and actual displacements, and precision was defined as the standard deviation of repeated measurements. The final experimental phantom tests showed that the accuracy and precision of the new calibration cage were improved by about 40% over an existing biplanar cage and by about 70% compared to a uniplanar cage design. This new cage can be used with any skeletal joints, in either static or kinematic examination, which is helpful for the standardization of the RSA application.     

Completely monodisperse, highly repetitive proteins for bioconjugate capillary electrophoresis: development and characterization

Protein-based polymers are increasingly being used in biomaterial applications because of their ease of customization and potential monodispersity. These advantages make protein polymers excellent candidates for bioanalytical applications. Here we describe improved methods for producing drag-tags for free-solution conjugate electrophoresis (FSCE). FSCE utilizes a pure, monodisperse recombinant protein, tethered end-on to a ssDNA molecule, to enable DNA size separation in aqueous buffer. FSCE also provides a highly sensitive method to evaluate the polydispersity of a protein drag-tag and thus its suitability for bioanalytical uses. This method is able to detect slight differences in drag-tag charge or mass. We have devised an improved cloning, expression, and purification strategy that enables us to generate, for the first time, a truly monodisperse 20 kDa protein polymer and a nearly monodisperse 38 kDa protein. These newly produced proteins can be used as drag-tags to enable longer read DNA sequencing by free-solution microchannel electrophoresis.     

A new deep learning method for image deblurring in optical microscopic systems

Deconvolution is the most commonly used image processing method in optical imaging systems to remove the blur caused by the point‐spread function (PSF). While this method has been successful in deblurring, it suffers from several disadvantages, such as slow processing time due to multiple iterations required to deblur and suboptimal in cases where the experimental operator chosen to represent PSF is not optimal. In this paper, we present a deep‐learning‐based deblurring method that is fast and applicable to optical microscopic imaging systems. We tested the robustness of proposed deblurring method on the publicly available data, simulated data and experimental data (including 2D optical microscopic data and 3D photoacoustic microscopic data), which all showed much improved deblurred results compared to deconvolution. We compared our results against several existing deconvolution methods. Our results are better than conventional techniques and do not require multiple iterations or pre‐determined experimental operator. Our method has several advantages including simple operation, short time to compute, good deblur results and wide application in all types of optical microscopic imaging systems. The deep learning approach opens up a new path for deblurring and can be applied in various biomedical imaging fields.     

Measurement and Correction of Microscopic Head Motion during Magnetic Resonance Imaging of the Brain

Magnetic resonance imaging (MRI) is a widely used method for non-invasive study of the structure and function of the human brain. Increasing magnetic field strengths enable higher resolution imaging; however, long scan times and high motion sensitivity mean that image quality is often limited by the involuntary motion of the subject. Prospective motion correction is a technique that addresses this problem by tracking head motion and continuously updating the imaging pulse sequence, locking the imaging volume position and orientation relative to the moving brain. The accuracy and precision of current MR-compatible tracking systems and navigator methods allows the quantification and correction of large-scale motion, but not the correction of very small involuntary movements in six degrees of freedom. In this work, we present an MR-compatible tracking system comprising a single camera and a single 15 mm marker that provides tracking precision in the order of 10 m and 0.01 degrees. We show preliminary results, which indicate that when used for prospective motion correction, the system enables improvement in image quality at both 3 T and 7 T, even in experienced and cooperative subjects trained to remain motionless during imaging. We also report direct observation and quantification of the mechanical ballistocardiogram (BCG) during simultaneous MR imaging. This is particularly apparent in the head-feet direction, with a peak-to-peak displacement of 140 m.     

In vivo glenohumeral translation under anterior loading in an open-MRI set-up

The evaluation of the glenohumeral joint laxity requires the estimate of displacements of the humeral head centre (HHC) with respect to the glenoid. To the authors? knowledge, several studies have been conducted to estimate HHC translations in vivo but data under anterior loading conditions has not been collected yet. Aim of this study was to develop a non-invasive experimental methodology based on magnetic resonance (MR) imaging for the in vivo evaluation of the HHC translations due to an anteriorly directed force. Fourteen asymptomatic shoulders were acquired using a horizontal open MR scanner with the subjects in the supine position both at 15° and 90° of arm abduction with and without an anterior force of 20 N applied at the HHC level. When no load was applied, from 15° to 90° of arm abduction, the HHC moved, anteriorly (1.5±1.3 mm) and superiorly (1.8±1.3 mm) while smaller displacements were observed medio-laterally (0.4±0.7 mm). Under the application of the anterior force the 3D displacement of the HHC with respect to the glenoid was 1.6±1.2 mm and 1.3 ±0.7 mm, respectively at 15° and 90° of arm abduction. The level of precision associated to the GHJ translation was less than 0.33 mm along all directions i.e. one order of magnitude smaller than the relevant translations. In conclusion, the MRI-based methodology allowed for the analysis of HHC displacements under conditions of anterior loads within an acceptable level of reliability.     

Transversely isotropic elasticity imaging of cancellous bone

To measure spatial variations in mechanical properties of biological materials, prior studies have typically performed mechanical tests on excised specimens of tissue. Less invasive measurements, however, are preferable in many applications, such as patient-specific modeling, disease diagnosis, and tracking of age- or damage-related degradation of mechanical properties. Elasticity imaging (elastography) is a nondestructive imaging method in which the distribution of elastic properties throughout a specimen can be reconstructed from measured strain or displacement fields. To date, most work in elasticity imaging has concerned incompressible, isotropic materials. This study presents an extension of elasticity imaging to three-dimensional, compressible, transversely isotropic materials. The formulation and solution of an inverse problem for an anisotropic tissue subjected to a combination of quasi-static loads is described, and an optimization and regularization strategy that indirectly obtains the solution to the inverse problem is presented. Several applications of transversely isotropic elasticity imaging to cancellous bone from the human vertebra are then considered. The feasibility of using isotropic elasticity imaging to obtain meaningful reconstructions of the distribution of material properties for vertebral cancellous bone from experiment is established. However, using simulation, it is shown that an isotropic reconstruction is not appropriate for anisotropic materials. It is further shown that the transversely isotropic method identifies a solution that predicts the measured displacements, reveals regions of low stiffness, and recovers all five elastic parameters with approximately 10% error. The recovery of a given elastic parameter is found to require the presence of its corresponding strain (e.g., a deformation that generates ??? is necessary to reconstruct C????), and the application of regularization is shown to improve accuracy. Finally, the effects of noise on reconstruction quality is demonstrated and a signal-to-noise ratio (SNR) of 40 dB is identified as a reasonable threshold for obtaining accurate reconstructions from experimental data. This study demonstrates that given an appropriate set of displacement fields, level of regularization, and signal strength, the transversely isotropic method can recover the relative magnitudes of all five elastic parameters without an independent measurement of stress. The quality of the reconstructions improves with increasing contrast, magnitude of deformation, and asymmetry in the distributions of material properties, indicating that elasticity imaging of cancellous bone could be a useful tool in laboratory studies to monitor the progression of damage and disease in this tissue.     

Smooth surface meshing for automated finite element model generation from 3D image data

Finite element (FE) modelling based on data from three-dimensional high-resolution computed tomography (CT) imaging systems provides a non-invasive method to assess structural mechanics. Automated mesh generation from these voxel based image data can be achieved by direct conversion to hexahedron elements, however these model representations have jagged edges. This paper proposes an automated method to generate smoothed FE meshes from voxel-based image data. Mesh fairing processes are utilized that allow constraints that control the smoothing process, and are computationally efficient. Surfaces of the mesh on the exterior, as well as interfaces between two tissues, can be smoothed by varying fairing parameters and constraint criteria. The method was tested on a variety of real and simulated three-dimensional data sets, resulting in both hexahedron and tetrahedron meshes. It was shown that the fairing process is linearly related to the number of smoothing iterations, and that peak stresses are reduced in FE simulations of the smoothed models. Although developed for micro-CT data sets, this fast and reliable mesh smoothing method could be applied to any three-dimensional image data where node and element connectivity have been defined.     

Drug metabolite profiling and identification by high-resolution mass spectrometry

Mass spectrometry plays a key role in drug metabolite identification, an integral part of drug discovery and development. The development of high-resolution (HR) MS instrumentation with improved accuracy and stability, along with new data processing techniques, has improved the quality and productivity of metabolite identification processes. In this minireview, HR-MS-based targeted and non-targeted acquisition methods and data mining techniques (e.g. mass defect, product ion, and isotope pattern filters and background subtraction) that facilitate metabolite identification are examined. Methods are presented that enable multiple metabolite identification tasks with a single LC/HR-MS platform and/or analysis. Also, application of HR-MS-based strategies to key metabolite identification activities and future developments in the field are discussed.     

Direct noninvasive measurement and numerical modeling of depth-dependent strains in layered agarose constructs

Biomechanical factors play an important role in the growth, regulation, and maintenance of engineered biomaterials and tissues. While physical factors (e.g. applied mechanical strain) can accelerate regeneration, and knowledge of tissue properties often guide the design of custom materials with tailored functionality, the distribution of mechanical quantities (e.g. strain) throughout native and repair tissues is largely unknown. Here, we directly quantify distributions of strain using noninvasive magnetic resonance imaging (MRI) throughout layered agarose constructs, a model system for articular cartilage regeneration. Bulk mechanical testing, giving both instantaneous and equilibrium moduli, was incapable of differentiating between the layered constructs with defined amounts of 2% and 4% agarose. In contrast, MRI revealed complex distributions of strain, with strain transfer to softer (2%) agarose regions, resulting in amplified magnitudes. Comparative studies using finite element simulations and mixture (biphasic) theory confirmed strain distributions in the layered agarose. The results indicate that strain transfer to soft regions is possible in vivo as the biomaterial and tissue changes during regeneration and maturity. It is also possible to modulate locally the strain field that is applied to construct-embedded cells (e.g. chondrocytes) using stratified agarose constructs.