Development and implementation of a coupled computational muscle force optimization bone shape adaptation modeling method

Abstract

Improved methods to analyze and compare the muscle-based influences that drive bone strength adaptation can aid in the understanding of the wide array of experimental observations about the effectiveness of various mechanical countermeasures to losses in bone strength that result from age, disuse, and reduced gravity environments. The coupling of gradient-based and gradientless numerical optimization routines with finite element methods in this work results in a modeling technique that determines the individual magnitudes of the muscle forces acting in a multisegment musculoskeletal system and predicts the improvement in the stress state uniformity and, therefore, strength, of a targeted bone through simulated local cortical material accretion and resorption. With a performance-based stopping criteria, no experimentally based or system-based parameters, and designed to include the direct and indirect effects of muscles attached to the targeted bone as well as to its neighbors, shape and strength alterations resulting from a wide range of boundary conditions can be consistently quantified. As demonstrated in a representative parametric study, the developed technique effectively provides a clearer foundation for the study of the relationships between muscle forces and the induced changes in bone strength. Its use can lead to the better control of such adaptive phenomena.

Effectiveness of various isometric exercises at improving bone strength in cortical regions prone to distal tibial stress fractures

“…Further insight into the development and prevention of tibial stress fractures can be gained by correlating the predictions of the current model to experimental observations. The exercises found beneficial in this work could be clinically implemented to study the time needed to invoke the necessary bone shape changes and examine possible rate adjustments based on resultant force magnitude, as the computational model is not time‐based and is independent of this magnitude . Additional isometric exercises studied by using this model could include the sequential alteration of the joint angles in addition to the resultant force direction.…”

“…A computational model was previously developed, which couples the determination of individual muscle force magnitudes that generate a desired resultant force by a given musculoskeletal system with the prediction of the ensuing cortical shape adaptations and used to create the tibial bone geometries “optimized” to the exercises compared in this work. The effectiveness of each of the optimized bone geometries was then compared under a single “critical design load”.…”

“…The leg system included 3‐dimensional representations of the pelvis, femur, tibia, and foot, considered their interactions at the hip, knee, and ankle joints, and included both cortical and cancellous bone tissue. A previously developed discretized model was positioned into the midstance joint configuration (Figure ) through a series of rotational and translational transformations of the femur, tibia, and foot . The diaphyseal region of the tibia, where the adaption was simulated, was represented by linear hexahedral elements so that individual nodes could be moved based on the adaptation model described above without the need to adjust the locations of the midside nodes.…”

“…The mesh varied axially from the minimum element size in the areas of muscle attachment (whose diameter was the average diameter of a tendon of the included muscles) to large elements away from these regions. Details of the mesh in other bones in the system can be found in Florio . Mesh sensitivity studies were performed on all components, with particular attention paid to the contacting interfaces at the joints and the regions where the muscle forces were applied.…”

“…The 10 major muscles responsible for the flexion and extension of the hip, knee, and ankle joints were included in this model: the gastrocnemius, the gluteus maximus, the iliacus, the long and short heads of the biceps femoris, the rectus femoris, the sartorius, the soleus, the tibialis anterior (TA), and the vastii muscle group. Details of the musculoskeletal model can be found in Florio , …”