In situ comparison of A-mode ultrasound tracking system and skin-mounted markers for measuring kinematics of the lower extremity

Skin-mounted marker based motion capture systems are widely used in measuring the movement of human joints. Kinematic measurements associated with skin-mounted markers are subject to soft tissue artifacts (STA), since the markers follow skin movement, thus generating errors when used to represent motions of underlying bone segments. We present a novel ultrasound tracking system that is capable of directly measuring tibial and femoral bone surfaces during dynamic motions, and subsequently measuring six-degree-of-freedom (6-DOF) tibiofemoral kinematics. The aim of this study is to quantitatively compare the accuracy of tibiofemoral kinematics estimated by the ultrasound tracking system and by a conventional skin-mounted marker based motion capture system in a cadaveric experimental scenario. Two typical tibiofemoral joint models (spherical and hinge models) were used to derive relevant kinematic outcomes. Intra-cortical bone pins equipped with optical markers were inserted in the tibial and femoral bones to serve as a reference to provide ground truth kinematics. The ultrasound tracking system resulted in lower kinematic errors than the skin-mounted markers (the ultrasound tracking system: maximum root-mean-square (RMS) error 3.44° for rotations and 4.88 mm for translations, skin-mounted markers with the spherical joint model: 6.32° and 6.26 mm, the hinge model: 6.38° and 6.52 mm). Our proposed ultrasound tracking system has the potential of measuring direct bone kinematics, thereby mitigating the influence and propagation of STA. Consequently, this technique could be considered as an alternative method for measuring 6-DOF tibiofemoral kinematics, which may be adopted in gait analysis and clinical practice.     

Nonhomogeneous strain from sparse marker arrays for analysis of transmural myocardial mechanics

BACKGROUND: Knowledge of normal cardiac kinematics is important when attempting to understand the mechanisms that impair the contractile function of the heart during disease. The complex kinematics of the heart can be studied by inserting radiopaque markers in the cardiac wall and study the pumping heart with biplane cineradiography. In order to study the local strain, the bead array was developed where small radiopaque beads are inserted along three columns transmurally in the left ventricle. METHOD: This paper suggests a straightforward method for strain computation, based on polynomial least-squares fitting and tailored for combined marker and bead array analyses. RESULTS: This polynomial method gives small errors for a realistic bead array on an analytical test case. The method delivers an explicit expression of the Lagrangian strain tensor as a polynomial function of the coordinates of material points in the reference configuration. The method suggested in this paper is validated with analytical strains on a deforming cylinder resembling the heart, compared to a previously suggested finite element method, and applied to in vivo ovine data. The errors in the estimated strain components are shown to remain unchanged on an analytical test case when evaluating the effects of one missing bead. In conclusion, the proposed strain computation method is accurate and robust, with errors smaller or comparable to the current gold standard when applied on an analytical test case.     

The effect of axial compression and distraction on cervical facet mechanics during anterior shear,flexion, axial rotation,and lateral bending motions

The subaxial cervical facets are important load-bearing structures, yet little is known about their mechanical response during physiological or traumatic intervertebral motion. Facet loading likely increases when intervertebral motions are superimposed with axial compression forces, increasing the risk of facet fracture. The aim of this study was to measure the mechanical response of the facets when intervertebral axial compression or distraction is superimposed on constrained, non-destructive shear, bending and rotation motions. Twelve C6/C7 motion segments (70 ± 13 yr, nine male) were subjected to constrained quasi-static anterior shear (1 mm), axial rotation (4°), flexion (10°), and lateral bending (5°) motions. Each motion was superimposed with three axial conditions: (1) 50 N compression; (2) 300 N compression (simulating neck muscle contraction); and, (3) 2.5 mm distraction. Angular deflections, and principal and shear surface strains, of the bilateral C6 inferior facets were calculated from motion-capture data and rosette strain gauges, respectively. Linear mixed-effects models (α = 0.05) assessed the effect of axial condition. Minimum principal and maximum shear strains were largest in the compressed condition for all motions except for maximum principal strains during axial rotation. For right axial rotation, maximum principal strains were larger for the contralateral facets, and minimum principal strains were larger for the left facets, regardless of axial condition. Sagittal deflections were largest in the compressed conditions during anterior shear and lateral bending motions, when adjusted for facet side.     

On a nonlinear theory for muscle shells: Part II--Application to the beating left ventricle

This paper specializes the nonlinear laminated-muscle-shell theory developed in Part I to cylindrical geometry and computes stresses in arteries and the beating left ventricle. The theory accounts for large strain, material nonlinearity, thick-shell effects, torsion, muscle activation, and residual strain. First, comparison with elasticity solutions for pressurized arteries shows that the accuracy of the shell theory increases as transmural stress gradients and the shell thickness decrease. Residual strain reduces the stress gradients, lowering the error in the predicted peak stress in thick-walled arteries (R/t = 2.8) from about 30 to 10 percent. Second, the canine left ventricle is modeled as a thick-walled laminated cylinder with an internal pressure. Each layer is composed of transversely isotropic muscle with a fiber orientation based on anatomical data. Using a single pseudostrain-energy density function (with time-varying coefficients) for passive and active myocardium, the model predicts strain distributions that agree fairly well with published experimental measurements. The results also show that the peak fiber stress occurs subendocardially near the beginning of ejection and that residual strains significantly alter stress gradients within each lamina, but the magnitude of the peak fiber stress changes by less than 20 percent.     

Flexible multibody simulation approach in the analysis of tibial strain during walking

Strains within the bone tissue play a major role in bone (re)modeling. These small strains can be assessed using experimental strain gage measurements, which are challenging and invasive. Further, the strain measurements are, in practise, limited to certain regions of superficial bones only, such as the anterior surface of the tibia. In this study, tibial strains occurring during walking were estimated using a numerical approach based on flexible multibody dynamics. In the introduced approach, a lower body musculoskeletal model was developed by employing motion capture data obtained from walking at a constant velocity. The motion capture data were used in inverse dynamics simulation to teach the muscles in the model to replicate the motion in forward dynamics simulation. The maximum and minimum tibial principal strains predicted by the model were 490 and -588 microstrain, respectively, which are in line with literature values from in vivo measurements. In conclusion, the non-invasive flexible multibody simulation approach may be used as a surrogate for experimental bone strain measurements and thus be of use in detailed strain estimations of bones in different applications.     

Measurement of strain in the left ventricle during diastole with cine-MRI and deformable image registration

The assessment of regional heart wall motion (local strain) can localize ischemic myocardial disease, evaluate myocardial viability, and identify impaired cardiac function due to hypertrophic or dilated cardiomyopathies. The objectives of this research were to develop and validate a technique known as hyperelastic warping for the measurement of local strains in the left ventricle from clinical cine-magnetic resonance imaging (MRI) image datasets. The technique uses differences in image intensities between template (reference) and target (loaded) image datasets to generate a body force that deforms a finite element (FE) representation of the template so that it registers with the target image. To validate the technique, MRI image datasets representing two deformation states of a left ventricle were created such that the deformation map between the states represented in the images was known. A beginning diastolic cine-MRI image dataset from a normal human subject was defined as the template. A second image dataset (target) was created by mapping the template image using the deformation results obtained from a forward FE model of diastolic filling. Fiber stretch and strain predictions from hyperelastic warping showed good agreement with those of the forward solution (R2=0.67 stretch, R2=0.76 circumferential strain, R2=0.75 radial strain, and R2=0.70 in-plane shear). The technique had low sensitivity to changes in material parameters (deltaR2= -0.023 fiber stretch, deltaR2=-0.020 circumferential strain, deltaR2=-0.005 radial strain, and deltaR2=0.0125 shear strain with little or no change in rms error), with the exception of changes in bulk modulus of the material. The use of an isotropic hyperelastic constitutive model in the warping analyses degraded the predictions of fiber stretch. Results were unaffected by simulated noise down to a signal-to-noise ratio (SNR) of 4.0 (deltaR2= -0.032 fiber stretch, deltaR2=-0.023 circumferential strain, deltaR2=-0.04 radial strain, and deltaAR2=0.0211 shear strain with little or no increase in rms error). This study demonstrates that warping in conjunction with cine-MRI imaging can be used to determine local ventricular strains during diastole.     

Limitations of methods of determining effective diffusion coefficients in cell immobilization matrices

Various techniques are available for determining the effective diffusivity D(e) of solutes such as glucose in cell immobilization matrices. Nearly all, if not all, are subject to errors and limitations as regards the ranges of temperature, pressure, and/or concentration over which they give reliable results. It is the purpose of this article to compare three of these methods, designated (a) thin disc, (b) cylinder, and (c) beads types, and to show by means of a sensitivity and error analysis of the equation used in each method that the thin-disc and cylindrical techniques give more accurate results of D(e) than does the bead method.     

Evaluating pedigree data. I. The estimation of pedigree error in the presence of marker mistyping

Pedigrees used in the analysis of genetic or medical data are usually ascertained from sources subject to a variety of errors including misidentification of individuals, faults in historical documents or record linkage, nonpaternity, and unidentified adoption. Genetic markers can be used to verify putative family and pedigree data through the search for inconsistencies, or genetic exclusions, between putative parents and offspring. The probability of observing an exclusion given the occurrence of an error depends upon the gene frequencies at the loci under study and the forms of error. In addition, inconsistencies can arise from laboratory errors in marker determination. Together, these problems make the proper statistical analysis of such data desirable. Here we give a model that specifies the combined effects of various kinds of pedigree error along with genetic marker error. This model allows the maximum-likelihood estimation of the rates of various forms of pedigree error and laboratory error from genetic marker data collected on putative families. The method is illustrated by applying it to data obtained from a South Pacific island population, Tokelau. From the observed distribution of genetic marker inconsistencies between the parents and offspring of putative families, derived from the extensive genealogy of this population, we are able to estimate that the error of a paternal link is 4%, the error of a maternal link is zero, and the overall system typing error is 1%.     

Do kinematic models reduce the effects of soft tissue artefacts in skin marker-based motion analysis? An in vivo study of knee kinematics

We investigated the effects of including kinematic constraints in the analysis of knee kinematics from skin markers and compared the result to simultaneously recorded trajectories of bone pin markers during gait of six healthy subjects. The constraint equations that were considered for the knee were spherical and revolute joints, which have been frequently used in musculoskeletal modelling. In the models, the joint centres and joint axes of rotations were optimised from the skin marker trajectories over the trial. It was found that the introduction of kinematic constraints did not reduce the error associated with soft tissue artefacts. The inclusion of a revolute joint constraint showed a statistically significant increase in the mean flexion/extension joint angle error and no statistically significant change for the two other mean joint angle errors. The inclusion of a spherical joint showed a statistically significant increase in the mean flexion/extension and abduction/adduction errors. In addition, when a spherical joint was included, a statistically significant increase in the sum of squared differences between measured marker trajectories and the trajectories of the pin markers in the models was seen. From this, it was concluded that both more advanced knee models as well as models of soft tissue artefacts should be developed before accurate knee kinematics can be calculated from skin markers.     

Pump function of the heart as an optimal control problem

In order to model the pump function of the heart the left ventricle is represented as an elastic thick-walled cylinder contracting symmetrically. The acceleration is included in the mathematical formalism describing the contraction of the myocardium and optimal control theory is used to solve the differential equation of motion of the cylindrical wall in such a way as to minimize a given performance index. Application of the equations to experimental data published in the literature is discussed. The mathematical formalism presents a new way to study the time variation of the volume ejected from the left ventricle. Methods to quantify the pump function of the heart are suggested.     

Three-dimensional finite element stress analysis of the dentate human mandible.

The biomechanical events which accompany functional loading of the human mandible are not fully understood. The techniques normally used to record them are highly invasive. Computer modelling offers a promising alternative approach in this regard, with the additional ability to predict regional stresses and strains in inaccessible locations. In this study, we built two three-dimensional finite element (FE) models of a human mandible reconstructed from tomographs of a dry dentate jaw. The first model was used for a complete mechanical characterization of physical events. It also provided comparative data for the second model, which had an increased vertical corpus depth. In both cases, boundary conditions included rigid restraints at the first right molar and endosteal cortical surfaces of the articular eminences of temporal bones. Groups of parallel multiple vectors simulated individual masticatory muscle loads. The models were solved for displacements, stresses, strains, and forces. The simulated muscle loads in the first model deformed the mandible helically upward and toward its right (working) side. The highest principal stresses occurred at the bite point, anterior aspects of the coronoid processes, symphyseal region, and right and left sides of the mandibular corpus. In general, the observed principal stresses and strains were highest on the periosteal cortical surface and alveolar bone. At the symphyseal region, maximum principal stresses and strains were highest on the lower lingual mandibular aspect, whereas minimum principal stresses and strains were highest on its upper labial side. Subcondylar principal strains and condylar forces were higher on the left (balancing or nonbiting) side than on the right mandibular side, with condylar forces more concentrated on the anteromedial aspect of the working-side condyle and on the central and lateral aspects of the left. When compared with in vivo strain data from macaques during comparable biting events, the predictive strain values from the first model were qualitatively similar. In the second model, the reduced tensile stress on the working-side, and decreased shear stress bilaterally, confirmed that lower stresses occurred on the lower mandibular border with increased jaw depth. Our results suggested that although the mandible behaved in a beam-like manner, its corpus acted more like a combination of open and closed cross sections due to the presence of tooth sockets, at least for the task modelled.(ABSTRACT TRUNCATED AT 400 WORDS)     

Direct measurement of intervertebral disc maximum shear strain in six degrees of freedom: motions that place disc tissue at risk of injury

Human intervertebral disc specimens were tested to determine the regions of largest maximum shear strain (MSS) experienced by disc tissues in each of three principal displacements and three rotations, and to identify the physiological rotations and displacements that may place the disc at greatest risk for large tissue strains and injury. Tearing of disc annulus may be initiated by large interlamellar shear strains. Nine human lumbar discs were tagged with radiographic markers on the endplates, disc periphery and with a grid of wires in the mid-transverse plane and subjected to each of the six principal displacements and rotations. Stereo-radiographs were taken in each position and digitized for reconstruction of the three-dimensional position of each marker. Maximum tissue shear strains were calculated from relative marker displacements and normalized by the input displacement or rotation. Lateral shear, compression, and lateral bending were the motions that produced the mean (95% confidence interval) largest mean MSS of 9.6 (0.7)%/mm, 9.0 (0.5)%/mm, and 5.8 (1.6)%/ degrees , respectively, and which occurred in the posterior, posterolateral and lateral peripheral regions of the disc. After taking into account the reported maximum physiological range of motion for each degree of freedom, motions producing the highest physiological MSS were lateral bending (57.8 (16.2)%) and flexion (38.3 (3.3)%), followed by lateral shear (14.4 (1.1)%) and compression (12.6 (0.7)%).     

Accuracy analysis for RSA: a computer simulation study on 3D marker reconstruction

In this paper, error analysis of three-dimensional marker coordinates reconstructed from noisy two-dimensional measurement in RSA was performed. Mathematical models to predict error propagation of focus position and object points were derived and computer simulations were performed to validate these models. Two clinical calibration cages were compared by testing the error propagation at each RSA step. The results revealed that errors of reconstructed object points were related to the focus position error, two-dimensional measurement error, position of focus and positions of object points, while errors of reconstructed focus position were determined by the two-dimensional measurement error, number of control points and location of the focus. The maximum difference between the mathematical model and the simulation for the assessment of errors of focus position was 14 microm and the maximum difference of object point positions was 1.1 microm. These differences were small and judged irrelevant, hence the simulations indicated that our models were accurate.     

Soft-tissue artefact assessment during step-up using fluoroscopy and skin-mounted markers

When measuring knee kinematics with skin-mounted markers, soft tissue and structures surrounding the knee hide the actual underlying segment kinematics. Soft-tissue artefacts can be reduced when plate-mounted markers or marker trees are used instead of individual unconstrained mounted markers. The purpose of this study was to accurately quantify the soft-tissue artefacts and to compare two marker cluster fixation methods by using fluoroscopy of knee motion after total knee arthroplasty during a step-up task. Ten subjects participated 6 months after their total knee arthroplasty. The patients were randomised into (1) a plate-mounted marker group and (2) a strap-mounted marker group. Fluoroscopic data were collected during a step-up motion. A three-dimensional model fitting technique was used to reconstruct the in vivo 3-D positions of the markers and the implants representing the bones. The measurement errors associated with the thigh were generally larger (maximum translational error: 17mm; maximum rotational error 12 degrees ) than the measurement errors for the lower leg (maximum translational error: 11mm; maximum rotational error 10 degrees ). The strap-mounted group showed significant more translational errors than the plate-mounted group for both the shank (respectively, 3+/-2.2 and 0+/-2.0mm, p = 0.025) and the thigh (2+/-2.0 and 0+/-5.9mm, p = 0.031). The qualitative conclusions based on interpretation of the calculated estimates of effects within the longitudinal mixed-effects modelling evaluation of the data for the two groups (separately) were effectively identical. The soft-tissue artefacts across knee flexion angle could not be distinguished from zero for both groups. For all cases, recorded soft-tissue artefacts were less variable within subjects than between subjects. The large soft-tissue artefacts, when using clustered skin markers, irrespective of the fixation method, question the usefulness of parameters found with external movement registration and clinical interpretation of stair data in small patient groups.     

Ventricular and arterial wall stresses based on large deformation analyses

Assuming a spherical geometry for the left ventricle and a cylindrical geometry for arteries, wall stresses and elastic stiffnesses are evaluated on the basis of a large elastic deformation theory. On the basis of canine pressure-volume data, the numerical results indicate marked gradients of stress in the endocardial layers even for thin-walled vessels, a result not predicted by the classical theory of elasticity. These high gradients of stress are due to the fact that the elastic stiffness of the wall material increases with the stress which reaches maximum levels in the endocardial layers. The high stresses may be responsible for ischemia of the left ventricle and be a triggering mechanism for atherosclerosis.     

Subject-specific finite element models implementing a maximum principal strain criterion are able to estimate failure risk and fracture location on human femurs tested in vitro

No agreement on the choice of the failure criterion to adopt for the bone tissue can be found in the literature among the finite element studies aiming at predicting fracture risk of bones. The use of stress-based criteria seems to prevail on strain-based ones, while basic bone biomechanics suggest using strain parameters to describe failure. The aim of the present combined experimental-numerical study was to verify, using subject-specific finite element models able to accurately predict strains, if a strain-based failure criterion could identify the failure patterns of bones. Three cadaver femurs were CT-scanned and subsequently fractured in a clinically relevant single-stance loading scenario. Load-displacement curves and high-speed movies were acquired to define the failure load and the location of fracture onset, respectively. Subject-specific finite element models of the three femurs were built from CT data following a validated procedure. A maximum principal strain criterion was implemented in the finite element models, and two stress-based criteria selected for comparison. The failure loads measured were applied to the models, and the computed risks of fracture were compared to the results of the experimental tests. The proposed principal strain criterion managed to correctly identify the level of failure risk and the location of fracture onset in all the modelled specimens, while Von Mises or maximum principal stress criteria did not give significant information. A maximum principal strain criterion can thus be defined a suitable candidate for the in vivo risk factor assessment on long bones.     

The effect of residual strain on the diastolic function of the left ventricle as predicted by a structural model

The unloaded heart is not stress-free. It is subjected to residual stress and strain. Their extent and influence on the global performance of the left ventricle and on local phenomena in the ventricular wall are studied by model simulation. The analysis focuses on the equatorial region of the ventricle, with an approximate thick-walled cylindrical geometry. The in vivo myocardium is considered to be incompressible, consisting of fibers embedded in a fluid matrix, with transmurally varying anisotropic microstructure in accordance with morphological characteristics.

The results show that residual strain is transmurally distributed with a pattern and magnitude which agree well with measurements. The calculated residual strains are within mean ± one standard deviation of the measured ones. Their magnitude was found to increase with increasing opening angle and with increasing wall thickness. The residual strain was found to have several effects on ventricular function: At volumes higher than the reference one it gives rise to more uniform transmural distributions of stress and intramyocardial pressure; it causes about 50% increase in the ventricular compliance at high volumes and doubles the suction of atrial blood at low volumes, thus facilitating the diastolic filling. In addition, residual strains cause bias of in vivo measured strains from their true values. This may significantly affect physiological interpretation of measured ventricular deformations.

In conclusion, the present structural analysis predicts that residual strain has favorable effect on left-ventricular diastolic performance, and gives rise to more uniform ventricular stress distribution.     

Error in the description of foot kinematics due to violation of rigid body assumptions

Kinematic data from rigid segment foot models inevitably includes errors because the bones within each segment move relative to each other. This study sought to define error in foot kinematic data due to violation of the rigid segment assumption. The research compared kinematic data from 17 different mid and forefoot rigid segment models to kinematic data of the individual bones comprising these segments. Kinematic data from a previous dynamic cadaver model study was used to derive individual bone as well as foot segment kinematics.Mean and maximum errors due to violation of the rigid body assumption varied greatly between models. The model with least error was the combination of navicular and cuboid (mean errors <=1.3°, average maximum error <=2.4°). Greatest error was seen for the model combining all the ten bones (mean errors <=4.4°, average maximum errors <=6.9°). Based on the errors reported a three segment mid and forefoot model is proposed: (1) Navicular and cuboid, (2) cuneiforms and metatarsals 1, 2 and 3, and (3) metatarsals 4 and 5. However the utility of this model will depend on the precise purpose of the in vivo foot kinematics research study being undertaken.     

Scanner influence on the mechanical response of QCT-based finite element analysis of long bones

Patient-specific QCT-based finite element (QCTFE) analyses enable highly accurate quantification of bone strength. We evaluated CT scanner influence on QCTFE models of long bones.A femur, humerus, and proximal femur without the head were scanned with K₂HPO₄ phantoms by seven CT scanners (four models) using typical clinical protocols. QCTFE models were constructed. The geometrical dimensions, as well as the QCT-values expressed in Hounsfield unit (HU) distribution was compared. Principal strains at representative regions of interest (ROIs), and maximum principal strains (associated with fracture risk) were compared. Intraclass correlation coefficients (ICCs) were calculated to evaluate strain prediction reliability for different scanners. Repeatability was examined by scanning the femur twice and comparing resulting QCTFE models.Maximum difference in geometry was 2.3%. HU histograms before phantom calibration showed wide variation between QCT scans; however, bone density histogram variability was reduced after calibration and algorithmic manipulation. Relative standard deviation (RSD) in principal strains at ROIs was <10.7%. ICC estimates between scanners were >0.9. Fracture-associated strain had 6.7%, 8.1%, and 13.3% maximum RSD for the femur, humerus, and proximal femur, respectively. The difference in maximum strain location was <2 mm. The average difference with repeat scans was 2.7%.Quantification of strain differences showed mean RSD bounded by ∼6% in ROIs. Fracture-associated strains in “regular” bones showed a mean RSD bounded by ∼8%. Strains were obtained within a ±10% difference relative to the mean; thus, in a longitudinal study only changes larger than 20% in the principal strains may be significant. ICCs indicated high reliability of QCTFE models derived from different scanners.     

Stress and strain adaptation in load-dependent remodeling of the embryonic left ventricle

Altered pressure in the developing left ventricle (LV) results in altered morphology and tissue material properties. Mechanical stress and strain may play a role in the regulating process. This study showed that confocal microscopy, three-dimensional reconstruction, and finite element analysis can provide a detailed model of stress and strain in the trabeculated embryonic heart. The method was used to test the hypothesis that end-diastolic strains are normalized after altered loading of the LV during the stages of trabecular compaction and chamber formation. Stage-29 chick LVs subjected to pressure overload and underload at stage 21 were reconstructed with full trabecular morphology from confocal images and analyzed with finite element techniques. Measured material properties and intraventricular pressures were specified in the models. The results show volume-weighted end-diastolic von Mises stress and strain averaging 50–82 % higher in the trabecular tissue than in the compact wall. The volume-weighted-average stresses for the entire LV were 115, 64, and 147 Pa in control, underloaded, and overloaded models, while strains were 11, 7, and 4 %; thus, neither was normalized in a volume-weighted sense. Localized epicardial strains at mid-longitudinal level were similar among the three groups and to strains measured from high-resolution ultrasound images. Sensitivity analysis showed changes in material properties are more significant than changes in geometry in the overloaded strain adaptation, although resulting stress was similar in both types of adaptation. These results emphasize the importance of appropriate metrics and the role of trabecular tissue in evaluating the evolution of stress and strain in relation to pressure-induced adaptation.