Current research on osteoporosis detection and transcranial imaging suggests that it is necessary to find a method to calculate the speed of sound in curved bones. A popular method to find the speed of sound in bones is by the bidirectional axial transmission technique. Currently, this method assumes that the arrival time of the head wave depends linearly on the source-receiver distance. For curved bones this assumption is not valid. The arrival time of the head wave as a function of the source-receiver distance follows a curved trajectory. In this report, we attempt to find an extension to the current method that also works for curved bones, and evaluate how accurate the results of this extended method are.

This extension is based on the semblance method, that quantifies how well a certain trajectory agrees with the received data. In the first part of our project, theoretical trajectories are calculated for flat and semicircular bones. Furthermore, a numerical method is discussed to find these trajectories for arbitrary geometries. Comparing the trajectories corresponding to different velocities using the semblance methods allows for the determination of the speed of sound.

The accuracy of this extended method is evaluated by computer simulations. In these simulations, a Philips P41 Cardiac Sector Probe consisting of 96 elements was used to perform measurements on three different geometries. These geometries consisted of three different single interfaces between water (simulating soft tissue) and bone. The first interface consists of a straight interface between a 2 mm thick layer of water and a 5 mm thick layer of bone (that continues until the bottom edge of the simulation). The second simulation is the same, but the interface is rotated 2 degrees around its midpoint. In the third and fourth simulation, the interface is a semicircle with a 50 mm and 40 mm radius, respectively. The speed of sound in the bone was taken to be 3 mm/s. The received data was interpolated by a cubic interpolation with a refinement of 4. Both the bidirectional and the extended,
trajectory-based method were applied on the raw and interpolated data.

For the flat interface, the bidirectional method performed slightly better than the trajectory-based method (0.13% and 0.30% error, respectively). The same is true for the tilted interface (0.16% and 0.23% error). Interpolation did not affect the results here. For the 50 mm semicircular interface, the trajectory-based method performed much better than the bidirectional method: it had a 0.10% error compared to a 2% one. This was also true when the interpolation was applied: then the errors were 0.3% and 1.97%. Similar
improvements were seen for the 40 mm radius semicircle. The higher error of the trajectory-based method for the flat and tilted interfaces can be explained by small errors in the additional assumptions that this method makes.

One drawback of the trajectory-based method is that there can be problems interpreting the results. This can be seen in the semblance plots, which plot the semblance coefficient (how well the trajectory fits the data) against the test velocity. For the bidirectional method, these plots clearly have a single biggest peak. For the trajectory-based methods the plot contains multiple large peaks. Furthermore, for the semicircular bone this plot contains a flat peak, which can cause multiple test velocities to have approximately the same semblance. This is a problem, since it means that small changes to the experimental setup can cause big changes in the calculated velocity. Indeed, this can be seen for the trajectory-based method on the 40 mm radius semicircular bone, which has a 1.6% error without interpolation (0.43% with interpolation). Further research could examine solutions to this problem, such as increasing the window size of the semblance method, taking the average velocity over flat peaks, or using an alternative to the semblance method. Finally, we conclude that the trajectory-based method represents an improvement over the bidirectional method when examining curved bones.

In this research, a Shive wave machine is used to study (a) the velocity of waves throughout different media and (b) the transition of waves between two different media. The Shive wave machine used in this research consists of 32 parallel aluminum bars attached perpendicularly to three parallel central wires. When a perturbation is applied to one of the bars, a torsional wave is initiated in the Shive wave machine, which is mapped to a transverse wave at the extremities of the bars. The velocity of a wave in the Shive wave machine is theoretically determined by four variables: (i) The distance between the two outside wires and the central wire; (ii) the tension in the two outside wires; (iii) the distance between the bars; (iv) the moment of inertia of the bars. The transition of waves between two different media is theoretically determined by the wave velocities in the two media. The theory states that a part of the wave is reflected and a part is transmitted at the intersection between the two media. The results for (a) show that the measured velocity is higher than theoretically expected, which may be caused by an incorrect measurement of (ii). The results for (b) show that a change in (i) throughout the system does not comply with the theoretically expected ratios for reflection and transmission, whereas a change in (iv) does comply with the theoretically expected ratios.

Muscles generate force and enable movement. After excitation of a muscle the muscle fibers contract. Methods to assess muscle contraction in vivo are scarce. Electromechanical delay (EMD), defined as the time lag between muscle excitation and contraction onset, has been proposed as a measure for contraction efficiency, but provides limited insight in electromechanical muscle dynamics. The current paper proposes and evaluates a novel non-invasive method to simultaneously track the propagation of both electrical and mechanical waves in muscles using high density electromyography and ultrafast ultrasound imaging (5 kHz). The method successfully tracked the propagation of the excitation-contraction (E-C) coupling in electrically evoked twitch contractions of the Biceps Brachii in three healthy participants. The excitation wave (i.e. action potential) had a velocity of 3.90 ± 0.65 m/s and the subsequent mechanical (i.e. contraction) wave had a velocity of 3.52 ± 0.89 m/s. Both waves propagated from distal to proximal and had similar spatiotemporal characteristics, indicating that our method can track the propagation of the E-C coupling. The experimental results were compared to simulated contractions of a newly developed multisegmental muscle fiber model, consisting of 500 sarcomeres in series. Both the experiment and simulation showed evidence that excited muscle sarcomeres pull on sarcomeres that were not yet reached by the action potential. In conclusion, our method can track the electromechanical muscle dynamics with high spatio-temporal resolution. Ultimately, the method can be used to characterize E-C coupling in patients with neuromuscular disease to assess contraction efficiency, monitor the progression of the disease and determine the efficacy of new treatment options.

Ultrasound gives the opportunity to look at muscles and observe their change in length. This tool has increased the knowledge about muscle-tendon dynamics and sometimes revealed surprising muscle stretch behaviour. System identification experiments use robots to disturb the ankle and measure its torque and angle. Muscle movement is derived from the measured joint angle and their assumed relationship. This study uses plane-wave ultrasound imaging to investigate the relation between ankle angle and muscle length during system identification experiments. The first goal is to determine the feasibility of using ultrasound measurements for system identification.  The second goal is to investigate the validity of the assumption that muscle stretch is proportional to ankle angle and the effect of this assumption on the prediction of reflex size. Transient and continuous disturbances were applied to the ankle, while images of the soleus and gastrocnemius were recorded with ultrasound and processed with an image tracking algorithm. For small (1° SD) continuous perturbations ankle angle and muscle length can be assumed proportional during a relax task. However, a conclusion cannot be drawn for the position task due to the low coherence of the muscle length measurements. For transient perturbations with a high velocity (>90°/s) the muscle length showed oscillations that were not present in the ankle angle, demonstrating a non-proportional relationship. The gastrocnemius velocity predicted the size of the short latency reflex better than the perturbation velocity of the ankle robot. Using plane-wave ultrasound imaging for system identification experiments was feasible.