A finite element model of the lower limb during stance phase of gait cycle including the muscle forces

Background

Results of finite element (FE) analyses can give insight into musculoskeletal diseases if physiological boundary conditions, which include the muscle forces during specific activities of daily life, are considered in the FE modelling. So far, many simplifications of the boundary conditions are currently made. This study presents an approach for FE modelling of the lower limb for which muscle forces were included.

Methods

The stance phase of normal gait was simulated. Muscle forces were calculated using a musculoskeletal rigid body (RB) model of the human body, and were subsequently applied to a FE model of the lower limb. It was shown that the inertial forces are negligible during the stance phase of normal gait. The contact surfaces between the parts within the knee were modelled as bonded. Weak springs were attached to the distal tibia for numerical reasons.

Results

Hip joint reaction forces from the RB model and those from the FE model were similar in magnitude with relative differences less than 16%. The forces of the weak spring were negligible compared to the applied muscle forces. The maximal strain was 0.23% in the proximal region of the femoral diaphysis and 1.7% in the contact zone between the tibia and the fibula.

Conclusions

The presented approach based on FE modelling by including muscle forces from inverse dynamic analysis of musculoskeletal RB model can be used to perform analyses of the lower limb with very realistic boundary conditions. In the present form, this model can be used to better understand the loading, stresses and strains of bones in the knee area and hence to analyse osteotomy fixation devices.

Prostate deformation during hypofractionated radiotherapy: an analysis of implanted fiducial marker displacement

BACKGROUND

To report prostate deformation during treatment, based on an analysis of fiducial marker positional differences in a large sample.

MATERIAL AND METHODS

This study included 144 patients treated with prostate stereotactic body radiation therapy after implantation in each of 4 gold fiducial markers (FMs), which were located and numbered consistently. The center of mass of the FMs was recorded for every pair of X-ray images taken during treatment. The distance between each pair of fiducials in the live X-ray images is calculated and compared with the respective distances as determined in the CT volume. The RBE is the difference between these distances. Mean RBE and intrafraction and interfraction RBE were evaluated. The intrafraction and intefraction RBE variability were defined as the standard deviation, respectively, of all RBE during 1 treatment fraction and of the mean daily RBE over the whole treatment course.

RESULTS

We analyzed 720 treatment fractions comprising 24,453 orthogonal X-ray image acquisitions. We observed a trend to higher RBE related to FM4 (apex) during treatment. The fiducial marker in the prostate apex could not be used in 16% of observations, in which RBE was > 2.5 mm. The mean RBEavg was 0.93 ± 0.39 mm (range 0.32-1.79 mm) over the 5 fractions. The RBEavg was significantly lower for the first and second fraction compared with the others (P < .001). The interfraction variability of RBEavg was 0.26 ± 0.16 mm (range 0.04-0.74 mm). The mean intrafraction variability of all FMs was 0.45 ± 0.25 mm. The highest Pearson correlation coefficient was observed between FM2 and FM3 (middle left and right prostate) (R = 0.78; P < .001). Every combination with FM4 yielded lower coefficients (range 0.66-0.71; P < .001), indicating different deformation of the prostate apex.

CONCLUSIONS

Ideally, prostate deformation is generally small, but it is very sensitive to rectal and bladder filling. We observed RBE up to 11.3 mm. The overall correlation between FMs was affected by shifts of individual fiducials, indicating that the prostate is not a "rigid" organ. Systematic change of RBE average between subsequent fractions indicates a systematic change in prostate shape.

MOSHFIT: algorithms for occlusion-tolerant mean shape and rigid motion from 3D movement data

This work addresses the use of 3D point data to measure rigid motions, in the presence of occlusion and without reference to a prior model of relative point locations. This is a problem where cluster-based measurement techniques are used (e.g. for measuring limb movements) and no static calibration trial is available. The same problem arises when performing the task known as roving capture, in which a mobile 3D movement analysis system is moved through a volume with static markers in unknown locations and the ego-motion of the system is required in order to understand biomechanical activity in the environment. To provide a solution for both of these applications, the new concept of a visibility graph is introduced, and is combined with a generalised procrustes method adapted from ones used by the biological shape statistics and computer graphics communities. Recent results on shape space manifolds are applied to show sufficient conditions for convergence to unique solution. Algorithm source code is available and referenced here. Processing speed and rate of convergence are demonstrated using simulated data. Positional and angular accuracy are shown to be equivalent to approaches which require full calibration, to within a small fraction of input resolution. Typical processing times for sub-micron convergence are found to be fractions of a second, so the method is suitable for workflows where there may be time pressure such as in sports science and clinical analysis.

Competing mechanisms for the buckling of an epithelial monolayer identified using multicellular simulation

A model using the rigid body multi-cellular framework (RBMCF) is implemented to investigate the mechanisms of buckling of an epithelial monolayer. Specifically, the deformation of a monolayer of epithelial cells which are attached to a basement membrane and the surrounding stromal tissue. The epithelial monolayer, supporting basement membrane and stromal tissue are modelled using two separate vertex dynamics models (one for the epithelial monolayer layer and one for the basement membrane and stromal tissue combined) and interactions between the two are considered using the RBMCF to ensure biologically realistic interactions. Model simulations are used to investigate the effects of cell-stromal attachment and membrane rigidity on buckling behaviour. We demonstrate that there are two competing modes of buckling, stromal deformation and stromal separation.

Hybrid triggering design for global attitude synchronization of networked rigid bodies

This paper is devoted to dealing with the problem of global attitude synchronization for quaternion-based multiple rigid bodies, regardless of the general directed topologies of networks and arbitrary initial orientations of rigid bodies. A novel canonical quaternion is constructed to represent all physical attitudes of rigid bodies such that the pseudo-synchronization of their quaternion representations (namely, the quaternions' vector parts of all rigid bodies reach agreement on some identical value, whereas their scalar parts do not) can be precluded. Moreover, to reduce unnecessary communication requirements of rigid bodies, a hybrid triggering mechanism involving both the time regulation and neighbors' non-real-time information is proposed, with which a distributed protocol is developed by leveraging the constructed canonical quaternion. It is shown that the presented protocol for rigid bodies over directed networks can simultaneously realize the global attitude synchronization and naturally exclude the Zeno behavior. In addition, these observations are also validated via the application of our hybrid triggering protocol to networked spacecraft.

Geometrical analysis for motion monitoring of rigid bodies with optical surface scanning in radiation oncology

BACKGROUND AND PURPOSE

Surface guided radiotherapy can be used to improve patient setup and for accurate intra-fraction motion monitoring in correspondence to the isocenter. For a clinical relevant motion analysis the actual displacement of the entire clinical target volume (CTV) is necessary. Therefore, the aim of this study was to develop a novel assessment method for intra-fraction motion for rigid body structures based on motion data and a geometrical analysis.

MATERIALS AND METHODS

A threshold value on the volume coverage (VC(t)) of the CTV by the planning target volume (PTV) was proposed as online motion monitoring method. Moreover, offline analysis was performed by using heat maps and by calculating VCx, the volume coverage for at least x% of treatment time. The method was applied retrospectively to patient treatment data for whole brain radiation treatment without a thermoplastic mask.

RESULTS

In 132 out of 142 fractions in total the proportion of the CTV that was inside the PTV for at least 99% of the time (VC99) was more than 95%, for a CTV-to-PTV margin of 5 mm. The source-voxel heat map showed which part of the CTV had a reduced coverage and the target heat map showed the movement of the CTV.

CONCLUSION

Instead of using an action threshold on the movements of the isocenter, a threshold on the VC(t) of the CTV by the PTV was proposed. The heat maps and resulting values of VCx can be used to adapt the VC(t) threshold or the CTV-to-PTV margin for subsequent fractions.

Analyzing the spatial motion of a rigid body subjected to constant body-fixed torques and gyrostatic moment

This paper aims to explore the rotatory spatial motion of an asymmetric rigid body (RB) under constant body-fixed torques and a nonzero first component gyrostatic moment vector (GM). Euler's equations of motion are used to derive a set of dimensionless equations of motion, which are then proposed for the stability analysis of equilibrium points. Specifically, this study develops 3D phase space trajectories for three distinct scenarios; two of them are applied constant torques that are directed on the minor and major axes, while the third one is the action of applied constant torque on the body's middle axis. Novel analytical and simulation results for both scenarios of constant torque applied along the minor and middle axes are provided in the context of separatrix surfaces, equilibrium manifolds, periodic or non-periodic solutions, and periodic solutions' extreme. Concerning the scenario of a directed torque on the major axis, a numerical solution for the problem is presented in addition to a simulation of the graphed results for the angular velocities' trajectories in various regions. Moreover, the influence of GM is examined for each case and a full modeling for the body's stability has been present. The exceptional impact of these results is evident in the development and assessment of systems involving asymmetric RBs, such as satellites and spacecraft. It may serve as a motivating factor to explore different angles within the GM in similar cases, thereby influencing various industries, including engineering and astrophysics applications.