Digital Astronaut: Bone Remodeling Model

The previous report detailed bone response in the femoral neck due to mechanical loading and included deconditioning in the absence of skeletal loading, which was the initial work that formed the foundational model. The work involved modeling exercise induced loading analogous to an equivalent amount of walking and running and was coupled with a NASTRAN finite element model of the proximal femur which averaged the stress/strain values in the femoral neck. This allowed us to track changes in a single volumetric bone mineral density value associated with the femoral neck. The report also mentioned that the work turned to extending/developing the computational model for the full proximal femur.

Modeling the full proximal femur presented a number of challenges basically because it is a much larger region but for other reasons as well. Three major areas comprise the proximal femur, the head, trochanter, and femoral neck and structural unit (remodeling units) dimensions can vary. There will be a much wider range of stress values from skeletal loading that would make averaging the entire proximal femur less valid than the averaging done for just the femoral neck. This prompted us to consider modifying the finite element model to track element by element changes in the modulus values and volumetric changes in the bone mineral density based on stress/strain values in each element. We were unable to complete this due to mathematical difficulties. However, we were able to obtain a reference that suggests grouping elements of the finite element model into 7 main areas and treating each of these as was done for the femoral neck. We could then average the 7 results to obtain a single value for the proximal femur. It is a future idea. The newest progress in the finite element modeling is moving the development of the model from a Femap V11.1 scan to development from an actual Quantitative Computed Tomography scan of a bed rest subject’ hip. This makes the model more realistic since it matches scans where our data comes from.

Another challenge was finding structural unit (remodeling unit) dimensions for the whole proximal femur. While several references gave dimensions for the femoral neck, there does not seem to be one set of dimensions covering the whole proximal femur, or even the trochanter alone. The rib and the iliac crest are the most common skeletal sites reported in the literature because they are less invasive experimentally. We were able to find a 2009 reference that discusses the relation of femoral osteon geometry to age, sex, height, and weight. It points toward a suitable value for osteon width in the age group we are interested in.

Although the adaptation to the full proximal femur is a major effort, some testing of the code’s ability to produce results close to proximal femur data was carried out. This was done by taking the femoral neck code and making some minor changes. The changes included an alternate activation density, a slightly smaller cortical origination frequency (ages 30-50), and a slightly smaller cortical osteon width consistent with the data from a reference on the femoral neck. For a 90 day bed rest study, comparison of model prediction to experimental results showed trabecular results to be just outside of the standard error and cortical results to be within standard error.

For a validation of the model’s general trend, the code for the femoral neck model was run for a year or more to see if bone density is maintained under sufficient loading and if bone mass is lost under insufficient loading. For maintenance, the simulation was carried out that used skeletal loading equivalent to the number of walking steps that is reported in the literature to be sufficient. The result was that there was no change in bone mineral density over the duration of a year. Using the number of walking steps below the lower limit reported to be sufficient for maintenance produced results that showed a decrease in bone mineral density with a tendency toward a plateau. The simulation cannot continue indefinitely however, as the model will break down.

Finally, a computational tool was created that uses probabilistic machine learning techniques to build subject specific finite specific finite element models of the femur. The femur models were coupled with the computational bone remodeling model to predict cortical and trabecular vBMD of the exercisers at the end of a 70 day bed rest study. Stochastic optimization was used to predict the required femoral forces required to match the bone state at the end of 70 days. Applying the tool to pre and post flight data to obtain output forces might aid in the development of customized exercise regimens. A NASA Techncial Memorandum (TM) on the tool is being developed.

Funding for this project has ended and work completed will be archived for future funding.