A mathematical model of bone remodeling, the physiological mechanism for maintenance, renewal, and repair in the adult skeleton, was developed. The model consists of three major aspects of the remodeling process:
(1) The removal and replacement of bone packets via remodeling units, which is done by the coupled action of bone cells on the same cell surface. Bone resorbing cells, osteoclasts, remove old or damaged bone. Then bone forming cells, osteoblasts, fill in new bone.
(2) The biology and physiology of the cellular dynamics of remodeling units. This includes the effects of hormones and biochemical mediators that drive the dynamics.
(3) Mechanotransduction, which describes the function of skeletal loading in maintaining bone health and strength. The model includes the release of NO and PGE2 by the sensing cells, osteocytes, as a result of cyclic loading, which can act as anabolic mediators.
The mathematical formulation that captures the aspects of the bone remodeling process consists of a system of 1st order nonlinear differential equations. The basic state variable is the rate of change of Bone Volume Fraction (BVF) of a representative volume element of a specific skeletal site or bone segment. Since a bone segment can have voids, BVF is defined as the volume of bone tissue divided by the total volume. The computational model can simulate the rate of change of BVF separately in the trabecular region (spongy interior bone) and in the cortical region (compact outer layer) by using the differences in the geometry of the remodeling units. In trabecular bone the cells remove and replace a crescent shaped hemi-osteon on the surface of trabeculae, while in cortical bone the remodeling unit is a cylindrical shaped cutting cone. Other parameter values, for example activation frequency of remodeling units, distinguish trabecular bone from cortical bone.
Given that hip and proximal femur are dynamic load bearing sights susceptible to microgravity induced demineralization and potentially debilitating fractures the initial model development focused on the femoral neck. Using average, cortical remodeling unit dimensions from experimental studies and estimates of other parameters, a computational beta model of bone loss due to skeletal unloading in the femoral neck was established.
In general, the computational simulations in time work as follows. Volumetric bone mineral density (vBMD) for cortical and trabecular regions of a skeletal site are provided by Quantitative Computed Tomography (QCT). A mapping converts vBMD to BVF through conversions to ash density. Until unloading is invoked, the equations maintain an approximate steady state or balance of the processes of bone resorption and bone formation, i.e., the rate of change of BVF is approximately zero. The balanced processes are influenced by endocrine regulation, biochemical mediations, and skeletal loading modeled in the equations. Since it eliminates any disturbances in the balance caused by disease, injury, or age related osteoporosis, the balanced assumption restricts the application of the model to the healthy adult in the age range of an astronaut. A simulation will maintain steady state until skeletal loading is decreased or the skeletal site is unloaded, which triggers a negative rate of change in BVF. Then, integration in time of the rate of change reveals a loss of BVF which is related to a loss in vBMD.
A preliminary validation of the model’s capability to represent deconditioning of the femoral neck due to unloading was carried out for control subjects in two bed rest studies.
(1) The current 70-day bed rest study (CFT70). The model results were able to match experimental values within one standard deviation of two out of three of the control subjects and the group mean for both trabecular and cortical regions. The third subject, whose experimental data did not match simulation results, was identified to have a baseline trabecular and cortical vBMD consistent with values observed in an elderly person with age related bone loss. Therefore, it may not be appropriate to use the data from this subject for validation since the DAP bone model is intended to be used for simulating bone remodeling in healthy individuals between the ages of 25 and 55 who are representative of the astronaut population. This is still under investigation.
(2) A 17 week bed rest study reported in the literature. Since spaceflight missions are much longer than 70 days and QCT data for bed rest controls is not available for more than 70 days, DXA aBMD data was collected for 18 control subjects from a 17 week bed rest study (4 months). Because the model uses vBMD and BVF, a regression method was developed to map aBMD to vBMD using total femur DXA and QCT data from a previous flight study. Comparing to experimental data, model prediction of time course change through the 120 days of mean aBMD was found to be within one standard deviation of the experimental error.
The preliminary validation results suggest that the current state of the DAP bone remodeling model is most reliable for prediction of group mean BVF, vBMD, and aBMD changes under bed rest conditions. It also shows some limited capability to predict subject specific trends in vBMD changes under bed rest conditions. These results suggest that we have laid a good foundation to establish a physiologically meaningful bone remodeling model that can simulate site specific bone adaptation due to mechanical unloading.
Building the effects of exercise induced skeletal loading in spaceflight into the bone remodeling model has progressed as follows:
A literature review was conducted that focused on methods or results for determining the stress/strain in the proximal femur due to specific exercise activities, finite element methods used in performing estimates of stress/strain, and bone models predicting time course adaption of bone to loading or any related articles. Among articles found on determining bone stress/strain from exercise, a 1996 paper entitled “Biomechanical Analysis of an Exercise Program for Forces in the Hip Joint and Femoral Neck” calculated maximum stress for walking, jogging, and eight weight training exercises. However it was limited to a specific section of inferior surface of the cortex in a cross section of the femoral neck, using elementary beam theory. A more recent 2012 dissertation from Finland university, “Flexible Multibody Approach in Bone Strain Estimation during Physical Activity: Quantifying Osteogenic Potential,” determined strain values from knee flexion, knee extension, leg press, squat, and walking but the work was restricted to the tibia. Several articles report on a finite element analysis of the stress distribution in the femoral neck and proximal femur. A 2004 article titled “Stress Fracture Analysis of the Human Femur based on Computational Biomechanics” simulates force transmitted through the hip joint during the single leg stance phase of normal running or jumping to estimate the Von Misses stress distribution in the proximal femur. A 2011 article titled “Finite Element Analysis of Femoral Neck Stress in Relation to Pelvic Width” compares maximum principle stress distribution in femoral neck for a narrow pelvic and a wide pelvic in a one-legged stance. There are inconstancies though in values used for compressive modulus and in the results. A 2011 article has a limited summary on “Estimating Lower Limb Skeletal Loading” and review techniques such as multibody dynamics and Ground Reaction Force (GRF), and inverse dynamics from commercially available software such as LifeMOD plus a finite element analysis. An important point made in this article is that estimating the magnitude of stresses and strains based on external forces only like GRF or joint moment and ignoring internal forces like muscle forces may lead to significant error in the calculations.
A through study was done on the concept of a Daily Load Stimulus (DLS) and an osteogenic potential associated with exercise induced cyclic loading. Since various formulae have been used in conducting experimental studies in humans as well as animals, a comparative study was conducted. It focused on the ability of the different expressions to relate to magnitude of stress or strain, strain rate, loading cycles or repetitions, as well as the potential to capture the effects of saturation of continuous loading and benefits of rest insertion combined with multiple shorter bouts. A NASA Technical Memorandum was written that summarizes these findings (TM NASA/TM-2014-218306 – In Press). Responses from email requests to authors and researchers in the area of time course adaptation of bone to loading from exercise or other activities was limited. Two researchers, one from the University of California, Davis, Biomedical Engineering and one from the Indiana U-Purdue U Indianapolis (IUPUI) Department of Biomedical Engineering, discussed some of the issues regarding quantification of bone loading. While adaptation due to disuse can be modeled, quantification of bone loading and response to loading is difficult and challenging.
Ultimately a finite element model (FEM) will be needed to determine the strains/stresses within the femoral neck and pass these results to the computational model to track changes in bone volume fraction. Since the biomechanical models have not progressed to the point of being able to provide estimates of forces and loads on joints at skeletal sites from exercise that can be passed to a FEM, a plan for an interim solution is being developed. Based on knowledge gaps and lack of examples of DLS formulae that have summed a daily load contribution from more than one specific exercise, development of a conceptual method of estimating load contribution is part of the plan. Translation of the conceptual load contribution via a DLS in terms of a daily strain or stress and the resulting bone remodeling response into an algorithm to be tested is another part of the plan.