Validation of Bayesian analysis of compartmental kinetic models in medical imaging

IntroductionKinetic compartmental analysis is frequently used to compute physiologically relevant quantitative values from time series of images. In this paper, a new approach based on Bayesian analysis to obtain information about these parameters is presented and validated.Materials and methodsThe closed-form of the posterior distribution of kinetic parameters is derived with a hierarchical prior to model the standard deviation of normally distributed noise. Markov chain Monte Carlo methods are used for numerical estimation of the posterior distribution. Computer simulations of the kinetics of F18-fluorodeoxyglucose (FDG) are used to demonstrate drawing statistical inferences about kinetic parameters and to validate the theory and implementation. Additionally, point estimates of kinetic parameters and covariance of those estimates are determined using the classical non-linear least squares approach.Results and discussionPosteriors obtained using methods proposed in this work are accurate as no significant deviation from the expected shape of the posterior was found (one-sided P > 0.08). It is demonstrated that the results obtained by the standard non-linear least-square methods fail to provide accurate estimation of uncertainty for the same data set (P < 0.0001).ConclusionsThe results of this work validate new methods for a computer simulations of FDG kinetics. Results show that in situations where the classical approach fails in accurate estimation of uncertainty, Bayesian estimation provides an accurate information about the uncertainties in the parameters. Although a particular example of FDG kinetics was used in the paper, the methods can be extended for different pharmaceuticals and imaging modalities.     

Method for the estimation of a double hinge kinematic model for the trapeziometacarpal joint using MR imaging

In this paper, we propose a method to estimate the parameters of a double hinge model of the trapeziometacarpal joint (TMC) by MRI-based motion analysis. The model includes two non-orthogonal and non-intersecting rotation axes accounting for flexion–extension (F–E) and adduction–abduction (A–A). We evaluated the quality of the estimated model parameters in the prediction of the relative motion of the first metacarpal bone with respect to the trapezium. As a result, we obtained that: (a) the estimated location and orientation of the F–E and A–A axes were in agreement with previous in vitro studies, (b) the motion of the first metacarpal predicted by the 2 degrees of freedom (2DoF) model exhibits a maximum surface distance error in the range of about 2 mm and (c) four thumb postures at the boundary of the TMC range of motion are sufficient to provide a good estimation of the 2DoF TMC kinematic model and good reproducibility (～1.7 mm) of the real thumb motion at TMC level.     

Functional analysis of the rabbit temporomandibular joint using dynamic biplane imaging

The dynamic function of the rabbit temporomandibular joint (TMJ) was analyzed through non-invasive, three-dimensional skeletal kinematics, providing essential knowledge for understanding normal joint motion. The objective of this study was to evaluate and determine repeatable measurements of rabbit TMJ kinematics. Maximal distances, as well as paths were traced and analyzed for the incisors and for the condyle–fossa relationship. From one rabbit to another, the rotations and translations of both the incisors and the condyle relative to the fossa contained multiple clear, repeatable patterns. The slope of the superior/inferior incisor distance with respect to the rotation about the transverse axis was repeatable to 0.14 mm/deg and the right/left incisor distance with respect to the rotation about the vertical axis was repeatable to 0.03 mm/deg. The slope of the superior/inferior condylar translation with respect to the rotational movement about the transverse axis showed a consistent relationship to within 0.05 mm/deg. The maximal translations of the incisors and condyles were also consistent within and between rabbits. With an understanding of the normal mechanics of the TMJ, kinematics can be used to compare and understand TMJ injury and degeneration models.     

Use of dual Euler angles to quantify the three-dimensional joint motion and its application to the ankle joint complex

This paper presents a modified Euler angles method, dual Euler angles approach, to describe general spatial human joint motions. In dual Euler angles approach, the three-dimensional joint motion is considered as three successive screw motions with respect to the axes of the moving segment coordinate system; accordingly, the screw motion displacements are represented by dual Euler angles. The algorithm for calculating dual Euler angles from coordinates of markers on the moving segment is also provided in this study. As an example, the proposed method is applied to describe motions of ankle joint complex during dorsiflexion–plantarflexion. A Flock of Birds electromagnetic tracking device (FOB) was used to measure joint motion in vivo. Preliminary accuracy tests on a gimbal structure demonstrate that the mean errors of dual Euler angles evaluated by using source data from FOB are less than 1° for rotations and 1 mm for translations, respectively. Based on the pilot study, FOB is feasible for quantifying human joint motions using dual Euler angles approach.     

MRI vs CT-based 2D-3D auto-registration accuracy for quantifying shoulder motion using biplane video-radiography

Biplane 2D-3D registration approaches have been used for measuring 3D, in vivo glenohumeral (GH) joint kinematics. Computed tomography (CT) has become the gold standard for reconstructing 3D bone models, as it provides high geometric accuracy and similar tissue contrast to video-radiography. Alternatively, magnetic resonance imaging (MRI) would not expose subjects to radiation and provides the ability to add cartilage and other soft tissues to the models. However, the accuracy of MRI-based 2D-3D registration for quantifying glenohumeral kinematics is unknown. We developed an automatic 2D-3D registration program that works with both CT- and MRI-based image volumes for quantifying joint motions. The purpose of this study was to use the proposed 2D-3D auto-registration algorithm to describe the humerus and scapula tracking accuracy of CT- and MRI-based registration relative to radiostereometric analysis (RSA) during dynamic biplanar video-radiography. The GH kinematic accuracy (RMS error) was 0.6–1.0 mm and 0.6–2.2° for the CT-based registration and 1.4–2.2 mm and 1.2–2.6° for MRI-based registration. Higher kinematic accuracy of CT-based registration was expected as MRI provides lower spatial resolution and bone contrast as compared to CT and suffers from spatial distortions. However, the MRI-based registration is within an acceptable accuracy for many clinical research questions.     

Application of a semi-automatic cartilage segmentation method for biomechanical modeling of the knee joint

Manual segmentation of articular cartilage from knee joint 3D magnetic resonance images (MRI) is a time consuming and laborious task. Thus, automatic methods are needed for faster and reproducible segmentations. In the present study, we developed a semi-automatic segmentation method based on radial intensity profiles to generate 3D geometries of knee joint cartilage which were then used in computational biomechanical models of the knee joint. Six healthy volunteers were imaged with a 3T MRI device and their knee cartilages were segmented both manually and semi-automatically. The values of cartilage thicknesses and volumes produced by these two methods were compared. Furthermore, the influences of possible geometrical differences on cartilage stresses and strains in the knee were evaluated with finite element modeling. The semi-automatic segmentation and 3D geometry construction of one knee joint (menisci, femoral and tibial cartilages) was approximately two times faster than with manual segmentation. Differences in cartilage thicknesses, volumes, contact pressures, stresses, and strains between segmentation methods in femoral and tibial cartilage were mostly insignificant (p > 0.05) and random, i.e. there were no systematic differences between the methods. In conclusion, the devised semi-automatic segmentation method is a quick and accurate way to determine cartilage geometries; it may become a valuable tool for biomechanical modeling applications with large patient groups.     

Development and validation of a subject-specific moving-axis tibiofemoral joint model using MRI and EOS imaging during a quasi-static lunge

The aims of this study were to introduce and validate a novel computationally-efficient subject-specific tibiofemoral joint model. Subjects performed a quasi-static lunge while micro-dose radiation bi-planar X-rays (EOS Imaging, Paris, France) were captured at roughly 0°, 20°, 45°, 60°, and 90° of tibiofemoral flexion. Joint translations and rotations were extracted from this experimental data through 2D-to-3D bone reconstructions, using an iterative closest point optimization technique, and employed during model calibration and validation. Subject-specific moving-axis and hinge models for comparisons were constructed in the AnyBody Modeling System (AMS) from Magnetic Resonance Imaging (MRI)-extracted anatomical surfaces and compared against the experimental data. The tibiofemoral axis of the hinge model was defined between the epicondyles while the moving-axis model was defined based on two tibiofemoral flexion angles (0° and 90°) and the articulation modeled such that the tibiofemoral joint axis moved linearly between these two positions as a function of the tibiofemoral flexion. Outside this range, the joint axis was assumed to remain stationary. Overall, the secondary joint kinematics (ML: medial–lateral, AP: anterior-posterior, SI: superior-inferior, IE: internal-external, AA: adduction-abduction) were better approximated by the moving-axis model with mean differences and standard errors of (ML: −1.98 ± 0.37 mm, AP: 6.50 ± 0.82 mm, SI: 0.05 ± 0.20 mm, IE: 0.59 ± 0.36°, AA: 1.90 ± 0.79°) and higher coefficients of determination (R²) for each clinical measure. While the hinge model achieved mean differences and standard errors of (ML: −0.84 ± 0.45 mm, AP: 10.11 ± 0.88 mm, SI: 0.66 ± 0.62 mm, IE: −3.17 ± 0.86°, AA: 11.60 ± 1.51°).     

Kinematic motion of the anterior cruciate ligament deficient knee during functionally high and low demanding tasks

The purpose of this study was to determine whether mechanical adaptations were present in patients with anterior cruciate ligament (ACL)-deficient knees during high-demand activities. Twenty-two subjects with unilateral ACL deficiency (11 males and 11 females, 19.6 months after injury) performed five different activities at a comfortable speed (level walking, ascending and descending steps, jogging, jogging to a 90-degree side cutting toward the opposite direction of the tested side). Three-dimensional knee kinematics for the ACL-deficient knees and uninjured contralateral knees were evaluated using the Point Cluster Technique. There was no significant difference in knee flexion angle, but an offset toward the knee in less valgus and more external tibial rotation was observed in the ACL-deficient knee. The tendency was more obvious in high demand motions, and a significant difference was clearly observed in the side cutting motions. These motion patterns, with the knee in less valgus and more external tibial rotation, are proposed to be an adaptive movement to avoid pivot shift dynamically, and reveal evidence in support of a dynamic adaptive motion occurring in ACL-deficient knees.     

Sensor-to-body calibration procedure for clinical motion analysis of lower limb using magnetic and inertial measurement units

Magnetic and Inertial measurement units (MIMUs) have become exceedingly popular for ambulatory human motion analysis during the past two decades. However, measuring anatomically meaningful segment and joint kinematics requires virtual alignment of the MIMU frame with the anatomical frame of its corresponding segment. Therefore, this paper presents a simple calibration procedure, based on MIMU readouts, to align the inertial frame of the MIMU with the anatomical frames, as recommended by ISB. The proposed calibration includes five seconds of quiet standing in a neutral posture followed by ten consecutive hip flexions/extensions. This procedure will independently calibrate MIMUs attached to the pelvis, thigh, shank, and foot. The accuracy and repeatability of the calibration procedure and the 3D joint angle estimation were validated against the gold standard motion capture system by an experimental study with ten able-bodied participants. The procedure showed high test-retest repeatability in aligning the MIMU frame with its corresponding anatomical frame, i.e., the helical angle between the MIMU and anatomical frames did not significantly differ between the test and retest sessions (except for thigh MIMU). Compared to previously introduced procedures, this procedure attained the highest inter-participant repeatability (inter-participant coefficient of variations of the helical angle: 20.5–42.2%). Further, the proposed calibration would reduce the offset errors of the 3D joint angle estimation (up to 12.8 degrees on average) compared to joint angle estimation without calibration (up to 26.3 degrees on average). The proposed calibration enables MIMU to measure clinically meaningful gait kinematics.     

A video image correlation technique for the measurement of electrophoretic mobility

The electrophoretic movement of blood cells has been examined with a video image correlator using the signal from a 625 line monochrome television camera attached to the optical arrangement. The diffraction pattern of a cell produces a characteristic signal which can be detected and registered in any television scan line to form the data of the first image frame. Under the influence of an electric field, cells moved across the television field of view and after a short interval appeared on different scan lines. The detection and registering process was repeated, and a cross-correlation function between the first and second image frame was computed. This function was stored in an output buffer which was continuously updated as fresh functions were integrated with the existing contents. The mean electrophoretic mobility of a suspension of particles can be calculated from the peak position of the integrated correlation function. Using a triangle deconvolution procedure, the relative contributions of subpopulations lymphocytes prepared from peripheral blood samples were examined.     

Cross-validation of a non-invasive positron detector to measure the arterial input function for pharmacokinetic modelling in dynamic positron emission tomography

Kinetic modeling of positron emission tomography (PET) data can assess index rate of uptake, metabolism and predict disease progression more accurately than conventional static PET. However, it requires knowledge of the time-course of the arterial blood radioactivity concentration, called the arterial input function (AIF). The gold standard to acquire the AIF is by invasive means. The purpose of this study was to validate a previously developed dual readout scintillating fiber-based non-invasive positron detector, hereinafter called non-invasive detector (NID), developed to determine the AIF for dynamic PET measured from the human radial artery. The NID consisted of a 3 m long plastic scintillating fiber with each end coupled to a 5 m long transmission fiber followed by a silicon photomultiplier. The scintillating fiber was enclosed inside the grooves of a plastic cylindrical shell. Two sets of experiments were performed to test the NID against a previously validated microfluidic positron detector. A closed-loop microfluidic system combined with a wrist phantom was used. During the first experiment, the three PET radioisotopes ¹⁸F, ¹¹C and ⁶⁸Ga were tested. After optimizing the detector, a second series of tests were performed using only ¹⁸F and ¹¹C. The maximum pulse amplitude to electronic noise ratio was 52 obtained with ¹¹C. Linear regressions showed a linear relation between the two detectors. These preliminary results show that the NID can accurately detect positrons from a patient’s wrist and has the potential to non-invasively measure the AIF during a dynamic PET scan. The accuracy of these measurements needs to be determined.     

Development of a dynamic imaging method for gravitropism in pea sprouts using clinical magnetic resonance imaging system

Although magnetic resonance imaging (MRI) is a useful technique, only a few studies have investigated the dynamic behavior of small subjects using MRI owing to constraints such as experimental space and signal amount. In this study, to acquire high-resolution continuous three-dimensional gravitropism data of pea (Pisum sativum) sprouts, we developed a small-bore MRI signal receiver coil that can be used in a clinical MRI and adjusted the imaging sequence. It was expected that such an arrangement would improve signal sensitivity and improve the signal-to-noise ratio (SNR) of the acquired image. All MRI experiments were performed using a 3.0-T clinical MRI scanner. An SNR comparison using an agarose gel phantom to confirm the improved performance of the small-bore receiver coil and an imaging experiment of pea sprouts exhibiting gravitropism were performed. The SNRs of the images acquired with a standard 32-channel head coil and the new small-bore receiver coil were 5.23±0.90 and 57.75±12.53, respectively. The SNR of the images recorded using the new coil was approximately 11-fold higher than that of the standard coil. In addition, when the accuracy of MR imaging that captures the movement of pea sprout was verified, the difference in position information from the optical image was found to be small and could be used for measurements. These results of this study enable the application of a clinical MRI system for dynamic plant MRI. We believe that this study is a significant first step in the development of plant MRI technique.     

Hard X-ray index of refraction tomography of a whole rabbit knee joint: A feasibility study

We report results of the computed tomography reconstruction of the index of refraction in a whole rabbit knee joint examined at the photon energy of 51 keV. Refraction based images make it possible to delineate the bone, cartilage, and soft tissues without adjusting the contrast window width and level. Density variations, which are related to tissue composition and are not visible in absorption X-ray images, are detected in the obtained refraction based images. We discuss why refraction-based images provide better detectability of low contrast features than absorption images.     

Validation of an ambient system for the measurement of gait parameters

Fall risk in elderly people is usually assessed using clinical tests. These tests consist in a subjective evaluation of gait performed by healthcare professionals, most of the time shortly after the first fall occurrence. We propose to complement this one-time, subjective evaluation, by a more quantitative analysis of the gait pattern using a Microsoft Kinect. To evaluate the potential of the Kinect sensor for such a quantitative gait analysis, we benchmarked its performance against that of a gold-standard motion capture system, namely the OptiTrack. The “Kinect” analysis relied on a home-made algorithm specifically developed for this sensor, whereas the OptiTrack analysis relied on the “built-in” OptiTrack algorithm. We measured different gait parameters as step length, step duration, cadence, and gait speed in twenty-five subjects, and compared the results respectively provided by the Kinect and OptiTrack systems. These comparisons were performed using Bland-Altman plot (95% bias and limits of agreement), percentage error, Spearman’s correlation coefficient, concordance correlation coefficient and intra-class correlation. The agreement between the measurements made with the two motion capture systems was very high, demonstrating that associated with the right algorithm, the Kinect is a very reliable and valuable tool to analyze gait. Importantly, the measured spatio-temporal parameters varied significantly between age groups, step length and gait speed proving the most effective discriminating parameters. Kinect-monitoring and quantitative gait pattern analysis could therefore be routinely used to complete subjective clinical evaluation in order to improve fall risk assessment during rehabilitation.     

Development of a statistical shape-function model of the implanted knee for real-time prediction of joint mechanics

Outcomes of total knee arthroplasty (TKA) are dependent on surgical technique, patient variability, and implant design. Non-optimal design or alignment choices may result in undesirable contact mechanics and joint kinematics, including poor joint alignment, instability, and reduced range of motion. Implant design and surgical alignment are modifiable factors with potential to improve patient outcomes, and there is a need for robust implant designs that can accommodate patient variability. Our objective was to develop a statistical shape-function model (SFM) of a posterior stabilized implanted knee to instantaneously predict joint mechanics in an efficient manner. Finite element methods were combined with Latin hypercube sampling and regression analyses to produce modeling equations relating nine implant design and six surgical alignment parameters to tibiofemoral (TF) joint mechanics outcomes during a deep knee bend. A SFM was developed and TF contact mechanics, kinematics, and soft tissue loads were instantaneously predicted from the model. Average normalized root-mean-square error predictions were between 2.79% and 9.42%, depending on the number of parameters included in the model. The statistical shape-function model generated instantaneous joint mechanics predictions using a maximum of 130 training simulations, making it ideally suited for integration into a patient-specific design and alignment optimization pipeline. Such a tool may be used to optimize kinematic function to achieve more natural motion or minimize implant wear, and may aid the engineering and clinical communities in improving patient satisfaction and surgical outcomes.     

Three‐dimensional imaging technologies: a priority for the advancement of tissue engineering and a challenge for the imaging community

Tissue engineering/regenerative medicine (TERM) is an interdisciplinary field that applies the principle of engineering and life sciences to restore/replace damaged tissues/organs with in vitro artificially‐created ones. Research on TERM quickly moves forward. Today newest technologies and discoveries, such as 3D‐/bio‐printing, allow in vitro fabrication of ex‐novo made tissues/organs, opening the door to wide and probably never‐ending application possibilities, from organ transplant to drug discovery, high content screening and replacement of laboratory animals. Imaging techniques are fundamental tools for the characterization of tissue engineering (TE) products at any stage, from biomaterial/scaffold to construct/organ analysis. Indeed, tissue engineers need versatile imaging methods capable of monitoring not only morphological but also functional and molecular features, allowing three‐dimensional (3D) and time‐lapse in vivo analysis, in a non‐destructive, quantitative, multidimensional analysis of TE constructs, to analyze their pre‐implantation quality assessment and their fate after implantation. This review focuses on the newest developments in imaging technologies and applications in the context of requirements of the different steps of the TERM field, describing strengths and weaknesses of the current imaging approaches.

     

A technique for the measurement of cadence using walkway vibrations

A new method has been developed to measure cadence while walking. The method uses instrumentation to detect the vibrations transmitted in the walkway surface. These vibrations are produced when a subject's foot makes initial contact with the walking surface. The method was tested against heel switches and was found to measure stride duration with RMS errors of around 1%. The vibration method requires no instrumentation to be attached to the subject, can be used with bare feet or any other footwear, is simple to use and is very robust and reliable.