Objective
Insight into the three-dimensional (3D) healthy growth of the radius and ulna remains limited, as orthopedics rely primarily on simple two-dimensional radiographic measurements. In this study, we used statistical shape modeling (SSM) to explore 3D forearm shape variations during healthy growth and predict individual radial and ulnar anatomy over time.

Methods
We trained SSMs using CT segmentations of 117 healthy radii and 116 ulnae. Principal Component Analysis (PCA), with and without Procrustes scaling, extracted general shape variation, while we used Partial Least Squares Regression (PLSR) to create an average growth model and prediction models. We developed several methods using age, sex, bone length and/or initial anatomy to predict bone anatomy over time. The models were validated by comparing the predicted bone models to the original segmentations of follow-up samples of 22 radii and 19 ulnae. The primary outcome measure was Root Mean Squared Error (RMSE), complemented by bone length error and mean and maximum distance errors.

Results
Size differences dominated the unscaled PCA- and PLSR-based SSMs, while the scaled PCA captured more subtle shape variations. With PLSR, we extracted the longitudinal growth trajectory for boys and girls aged 4 to 18 in 3D from the cross-sectional data. Using initial anatomy and age as input, the validation samples were predicted with RMSEs of less than 1 mm. The lowest bone length errors were reached using age, sex, and bone length as predictors.

Conclusion
We successfully utilized SSM to investigate and predict healthy growth of the radius and ulna in 3D. The current models are clinically viable as reference anatomy in pre-operative planning, and the methodology shows promise to support diagnosing and treating forearm deformities.

Anterior cruciate ligament tears are a common injury, with over two million people affected annually. Typically, magnetic resonance imaging is used to diagnose the injury, but this technique is less sensitive in evaluating incomplete or concomitant injuries. Four-dimensional computed tomography is a relatively new technique that can become commonly available in the clinical setting. It allows for dynamic imaging, which may be suited for evaluating a change in knee kinematics after ACL in movements like flexion/extension. This may be used to gain insight into the function of the anterior cruciate ligament or surrounding ligaments which informs surgical decision-making and might prevent or alter intended surgeries.
This thesis aims to answer the following research question; How can four-dimensional computed tomography scans of the tibiofemoral joint made during unloaded flexion/extension movements be meaningfully visualized and can it be used to detect kinematic differences between a knee with a complete anterior cruciate ligament tear and an uninjured one? To do so, both knees of eight patients with a unilateral complete anterior cruciate ligament tear were scanned during a simultaneous flexion/ex- tension movement in the four-dimensional computed tomography scanner. A workflow was created that consists of four steps; the segmentation, the registration, the definition of anatomical coordinate systems, and the visualization of the kinematic measures in three different ways. Almost all steps of this workflow were automated and open-source programs were used where possible throughout the workflow to facilitate easy usage. However, some manual steps are still required. The kinematic measures were expressed in three different ways. First, the rotations between the anatomical coordinate systems of the femur and tibia were calculated using Euler decomposition alongside the translations. In addition, a plot of the intercondylar axes was made, which shows the movement of the mediolateral axis of the femur relative to the tibia during flexion/extension. Finally, to obtain the kinematics at the articulation surface, an OpenSim Joint and Articular Mechanics simulation was set up to simulate the movement using the patient-specific information obtained from the four-dimensional computed tomography scans. Based on this simulation, the centres of proximity were plotted for both the tibia and the femur. The distances between the subsequent centres of proximity were then evaluated for a set of flexion angles to gain insight into the type of movement occurring (e.g., roll or slip).
Minor differences for the mean translations and rotations were seen between the anterior cruciate ligament deficient and the uninjured knees. Only in the anterior-posterior translation a statistically significant (p=0.023) increase could be seen at extension and the lower flexion angles (±-5∘ to ±15∘) for the anterior cruciate ligament deficient knees. No noteworthy differences were present for all other degrees of freedom. Differences were more apparent in the plots of the intercondylar axes. Here, the increased anterior-posterior translation was more prominent for anterior cruciate ligament deficient knees than for uninjured ones. Lastly, the centres of proximity showed substantial differences among patients, obscuring the determination of a pattern to distinguish between anterior cruciate ligament deficient and uninjured knees. However, these plots did show a substantial difference compared to the plots of the intercondylar axes. This may be due to slip occurring at the articulation surface and would mean that plotting the intercondylar axes does not adequately represent the kinematics of the articular surface throughout the whole range of motion of the knee.
Overall, some minor kinematic differences during flexion/extension can be seen in the graphs of the translations and rotations and the plots of the intercondylar axes. The plots of the intercondylar axes showed the most apparent differences, but they may not represent the situation at the articulation surface. Therefore the centres of proximity are better suited to gain information about the articulation surface. Still, due to the differences among patients, a pattern to distinguish between anterior cruciate ligament deficient and uninjured knees could not be determined. Altogether, this technique may not be suited as a tool to evaluate knee injuries in all patients, but only in patients that are expected to cope very well with the injury or where a concomitant injury is expected. However, future research should still evaluate the performance of the workflow for these situations.