In the current athletic footwear market, there exists a range of shoe architectures that offer a variety of support and flexibility options. The importance of footwear type has proved to be significant in the prevention of acute injuries due to impact forces [1, 2]. It has been shown that impact forces have most often been implicated in overuse running injuries, such as stress fractures and plantar fasciitis [2]. Additionally, material properties of damping elements, such as shoes, have demonstrated an effect on impact forces. Athletic footwear is categorized by the attribute of flexibility. The natural flex observed in the sole determines the flexibility; a more flexible shoe flexes closer to the mid-foot region, while a shoe designed for stability will flex closer to the ball of the shoe. Prior work has quantified the material stiffness of different shoe architectures with stability shoes possessing higher material stiffness than flexible shoes [3].

Purpose: This paper proposes a new method for estimating skeletal muscle forces using a model derived from dimensional analysis. It incorporates electromyography signals and muscle force-length, force-velocity, and force frequency relationships as inputs. The purpose of this model is to provide more accurate estimates of individualized muscle forces to better predict surrounding musculoskeletal tissue and joint contact loading. Theory: The derivation begins with dimensional analysis and a selection of critical parameters that define muscle force generation. The resulting constitutive equation gives way to a unique application of inverse-dynamics, one which avoids the issue of indeterminacy when reaction moments and ligament loading are minimized in a joint. The ankle joint is used as an example for developing the equations that culminate into a system of linear equations. Discussion: A muscle force model capable of being calibrated and then used to predict joint contact and surrounding tissue loading is critical in advancing biomechanics research areas like injury prevention, performance optimization, and tissue engineering, among others. This model's foundation in dimensional analysis, along with its inclusion of electromyography signals, gives promise that it will be physiologically relevant and suitable for application-based studies.

This study evaluates the predictive ability of the skeletal muscle force model derived previously within the ankle joint complex. The model is founded in dimensional analysis, using electromyography and the muscle force-length, force-velocity, and force-frequency curves as inputs. Seventeen subjects (8 males, 9 females) performed five different exercises that activated the primary muscles crossing the ankle joint. Motion capture, force plate, and electromyography data were collected during these exercises. A constant, Km, was calculated for each muscle of each subject using four of the five exercises. The fifth exercise was used to validate the results by treating the moments due to muscle forces as known and all other components in Euler's second law as unknown. While muscle forces cannot be directly validated in vivo, methods can be developed to test these values with reasonable confidence. This study compared moments about the ankle joint due to the calculated muscle forces to the sum of the moments due to all other sources and the kinematic terms in the second Newton-Euler equation of rigid body motion. Average percent errors for each subject ranged from 4.2% to 15.5% with an average percent error across all subjects of 8.2% while maximum percent errors for each subject ranged from 33.3% to 78.0% with an overall average maximum of 52.4%. Future work will examine sensitivity analyses to identify potential simplifications to the model and solution process and will validate the model on a more complex joint.