In the example displayed in Figure 1, the upper extremity is moving free of an external contact force during an arm-elevation task performed by a preoperative reverse total shoulder arthroplasty (RTSA) patient. RTSA is being used increasingly to treat irreparable rotator cuff tears. However, RTSA and other shoulder replacements are revised at a rate of approximately 9% because of loosening or dislocation.^8,9 Loosening or dislocation of an implant could suggest that either implants are not fixated properly (eg, misaligned) or not designed adequately to withstand loading conditions in vivo. Therefore, it is of particular interest to calculate shoulder kinetics during activities of daily living in patients before versus after RTSA. To do so, mathematical models are developed of each patient’s body segments and their 3D motion is measured to estimate joint kinetics throughout the duration of tasks of interest. However, for simplicity, in Figure 1, the analysis is executed at a single “quasi-static” time, which assumes that linear and angular accelerations are negligible. An additional useful simplification is conducting this analysis in 2D to align the determined net joint forces and torques with primary lines of action of certain muscles and ligaments (in Figure 1, the mediolateral axes of the hand, forearm, and upper arm are aligned with the X-Y coordinate system plane).

The first step in joint kinetics is to mathematically isolate each body segment of interest from the rest of the body or environment, as a “free body.” In Figure 1, upper extremity joint kinetics are determined by treating the upper arm, forearm, and hand as free bodies that forces and torques act upon. A body segment or collection of body segments can be treated as free bodies (eg, whole-body, foot, leg-system). Known joint forces and torques include gravity and the contact with the environment. Unknown joint forces and torques are determined by using physical laws of rigid body dynamics (Eqn. 1,2). As demonstrated in this example, free body analysis is typically first applied to distal body segments and joints, and then toward proximal body segments and joints. If studying the lower extremity, joint kinetics are also calculated from
distal to proximal (“from the ground, up”). First, if the lower extremity is in contact with the ground at the time of interest, an external force known as the ground reaction force (often measured) is applied at a known location on the foot. This ground reaction force is included in the free body diagram of the foot to calculate ankle joint kinetics. Then, the ankle joint kinetics are used within the free body diagram of the shank to calculate knee joint kinetics. Finally, the free body diagram of the thigh is used to calculate hip joint kinetics. It is important to note that upper extremity joint kinetics can include an external force, depending on how the upper extremity interacts with the environment (eg, during push-ups, carrying a load, using an assistive device).

In the arm elevation example, it was determined that there was a radial flexor torque at the wrist, a valgus torque at the elbow, and an elevator/abductor torque at the shoulder. These types of joint torques generally make sense to describe upper extremity joint actions during an arm raise against gravity. This type of information contextualizes the muscle activation patterns or comparison of loading patterns (eg, within-patient before vs after surgery, or across patients). By using devices for measuring accelerations, the arm elevation analysis can be expanded to 3D, which can aid in comparing patients’ kinetics before and after RTSA and significantly influence clinical practices. For instance, knowing the joint kinetics used during activities of daily living may eventually reduce the rate of RTSA revision by better informing the implant design process or implant centering procedures. Furthermore, the joint kinetics used by each patient during activities of daily living can help create a “functional profile” to personalize rehabilitation practices.

During joint kinetics analysis, body segments are typically assumed to be adequately represented using parameters (including mass and moment of inertia)
from cadaver studies, scaled by the person’s body weight and measured segment length.¹⁰ However, other approaches can use personalized parameters from segment volume determined by optical motion capture^11,12 or image-based systems (eg, DXA-scans¹³). These techniques offer unique insights when studying populations whose segment parameters stray from the cadaveric study populations (eg, children, obese, athletes) or during experiments that push the boundary of rigid body assumptions (eg, high impact loading accompanied by excessive soft-tissue motion).

Joint kinetic analysis is used in other orthopaedic contexts and scales, including (but not limited to) studies of gait analysis with or without instrumented implants,³ cadaveric studies of spine vertebrae,¹⁴ fluoroscopy studies of knee loads during inclined gait,¹⁵ wheelchair propulsion,² and in sport.^4,5,6,7 In addition to novel applications, emerging joint kinetics approaches attempt to understand aspects of human movement that traditional techniques fail to capture. This includes calculating and expressing joint kinetics using more functionally derived axes, for instance, relative to an “arm plane” or “leg plane” (or relative to the proximal segment to account for adjacent segments that may not be aligned with one another).^2,4,7 Further background information about joint kinetics can be found in other classic biomechanics resources.¹⁶ The following section discusses deformable mechanics, when loads applied at the tissue level (ie, articular cartilage, ligaments, tendons, and bone) lead to deformations that describe tissue mechanical behavior and function.

The structural properties of tissue determine its ability to resist loads and deformation when considering the material and geometry. For example, the structural properties of a bone-ligament-bone complex can be determined in response to a tensile load to assess its load-elongation behavior. A tensile force is applied to the complex, causing the tissue to stretch until it ruptures. While loading is applied, the corresponding increase in length in the complex is measured. The resulting nonlinear load-elongation curve that is typical of biologic soft tissues provides information about the structural properties of the tissue complex, such as its stiffness—resistance to deformation—and ultimate load at failure—maximum load-bearing capacity. These parameters are important to define for healthy tissue because, clinically, they can factor into the decision for the replacement graft type used for surgery.

It is also important to understand the mechanical response of an individual tissue or material, which is independent of specimen geometry, by using normalized load and deformation parameters. Measuring the mechanical properties of tissues, such as ligaments, can be used to evaluate the quality of the tissue when making comparisons between normal, injured, and healing states and are represented by the stress-strain relationship. Stress is defined as the amount of force applied per unit area. Strain is considered is defined as the change in length per unit length. Similar to load-elongation measurements, stress-strain relationships are obtained experimentally during tensile, compressive, or shear loading of tissue.

A typical stress-strain curve for biologic tissues consists of four distinct regions (Figure 2):