Statistical shape modelling of thigh muscles on healthy young and elderly arthrosic subjects

Skeletal muscles are responsible for generating the forces required to maintain posture and to move, thus to perform any kind of activity. Muscle tissue is said to be dynamic because it is able to change its morphological features in relation to certain stimuli. Clearly, these properties change from muscle to muscle, but also within the same muscle with time. These features, especially the shape, can be altered by pathological conditions such as sarcopenia, cerebral paresis, inflammatory myopathies or arthrotic pathologies, but also in the case of a subject practicing a sport that leads to frequent stimulation of specific muscles. The study of muscle shape is therefore useful as it can provide information about a person's state of health or lifestyle. There are many studies where the shape of the muscles is studied in order to capture differences between different subject populations. However, they only take into account measures such as volume, muscle length or PCSA, which are unable to capture the complex relationships between local and global shape characteristics. A useful tool for the analysis and representation of shapes able to overcome the aforementioned limitation is Statistical Shape Modelling (SSM). In this work a statistical model of the shape of lower limb muscles, specifically of the hip and knee flexors and knee extensors, was built. In particular, the dataset consisted of 26 subjects, 20 healthy subjects aged between 20 and 40 years, and 6 elderly subjects aged between 65 and 80 years with knee arthrosis. Starting from the magnetic resonance images of the lower limbs, the muscles geometries were extracted in the form of triangular surface meshes using a semi-automatic segmentation algorithm. The three-dimensional models were given as input to Deformetrica, a computational tool that, taking as input the anatomical shapes of interest, returns the template - i.e. the mean anatomical shape - and the moment vectors, which guide the deformation of the template to obtain the specific shape of the patient. A sensitivity analysis was first conducted on the input parameters required by Deformetrica aiming to select to optimal ones by minimizing the differences between the input shapes and their reconstructions provided by the tool. Principal component analysis (PCA) was then performed on the moment vectors matrix, so that the main anatomical features of the considered muscles could be identified. The sensitivity analysis resulted in the parameters with which the minimum mean distance value between the input and reconstructed shapes was obtained, i.e. 1.7203 mm. A total of 17 PCA modes were necessary to explain at least 90% of the total variance. In conclusion, SSM allowed to analyze several muscles at the same time, using a non-parametric method with which it was possible to study local and global characteristics of the objects under examination simultaneously.