The purpose of the current study was to investigate the geometric variations in the load-bearing joints among individuals. Two existing concepts in mathematics were introduced and their application in computational biomechanics was completely novel:​ 1) computing the depth of penetration between contact objects as an indirect measure of stress;​ and 2) computing the geometric similarity using the cubic root of volumetric ratio as a scaling law. Furthermore, an alternative geometric method to finite element analysis was proposed, which should be considered as a “proof of concept”.

This study demonstrated three novel results:​ 1) contrary to the current literature, the lateral aspect of the patellofemoral joint is not the sole indicator of PFPS;​ 2) the talus bones of the ankle joints are geometrically similar within a certain range of deviation;​ and 3) A standardized sizing for the talus bone implants which can fit all patients associated with traumatic talus bone injury.