Biomedical Engineering Reference
In-Depth Information
values found in literature, the results of the simulations have not received any va-
lidity confirmation past the 'circumstantial evidence' validation, a term the authors
used to summarize the similarity of the assumption-based prediction and biological
reality.
A different algorithm for stochastic simulation of bone adaptation via the ex-
change of discrete bone packets and an accompanying novel approach for validation
has recently been introduced (Hartmann et al.,
2011
). The study was subdivided into
the investigation of the most effective signal integration for this
in silico
model, as
well as validation of the results with quantitative backscattered electron imaging
(qBEI) data. The model assumed that resorption takes place randomly on the bone
surface, while deposition is mechanically controlled. The investigation of collective
(summed), individual (maximal) and total (the sum of the previous two) signaling
modalities indicated that using collective signal from the osteocyte network will in-
troduce effective surface tension, which the authors argue plays a key role in bone
morphogenesis and cell sorting. Validation of the simulation results against exper-
imental qBEI data centered on correlating the values of quantified material hetero-
geneity. For this purpose, the age of bone packets (voxels) has been converted to
represent corresponding mineral content (Ruffoni et al.,
2007
). When comparing
simulated structures to the experimental images, bone mineralization density dis-
tribution (BMDD) exhibited similar trends, where older bone was enclosed under
layers of younger bone. Notably, this validation method helped identify one of the
limitations of the algorithm, as it did not comply with the proposed theory that older
bone is more likely to be remodeled than younger bone (Taylor et al.,
2007
), and
was capable of remodeling only bone surface voxels.
More recently, Schulte et al. (
2011
) introduced an algorithm to simulate bone
thickening in response to cyclic mechanical loading using an open control loop. This
in silico
model is based on the assumption that a single remodeling signal submitted
as an input for the simulation is sufficient to predict the long-term outcome of the
remodeling process. Micro-CT scans of whole murine caudal vertebrae measured at
the beginning of the
in vivo
study were used as the input for the simulation and the
results computed from the time-lapsed
in vivo
images were compared to the simu-
lated time points. This approach allowed not only comparison of the morphometric
indexes and relative geometries
in vivo
and
in silico
, but also quantification and spa-
tial distribution of the errors produced by the algorithm for each individual animal.
The authors report a maximum error of 2.4 % for bone volume fraction and 5.4 %
for other morphometric parameters. In addition, similarly to the previous study, the
appropriate validation method helped detect one of the less obvious model limita-
tions, namely that in the simulation remodeling occurred rather homogeneously in
the surface layers, while a similar assessment of the
in vivo
data revealed localized
areas of stronger deposition.
Finally, a similar approach has been extended for the validation of a newly de-
veloped algorithm for bone remodeling employing Frost's mechanostat theory and
using SED values calculated after each remodeling iteration, in a closed feedback
loop (Schulte,
2011
). The growth velocity was calculated with a set of iteratively
solved non-linear equations, and the mechanical thresholds for resorption, forma-
tion or homeostasis were selected interactively. The algorithm was applied for a
