Biomedical Engineering Reference
In-Depth Information
Fig. 11.14
Normal walk of female test person (59 kg): (
left
) the vertical component F
z
in N vs.
time in s of hip contact forces (Spaepen, Private communication, 2007).
Right
: the derivative of
force with respect to time. Reprinted with permission of Prof. A. Spaepen (Dept. Kinesiology,
KULeuven)
The transformation of data of Fig.
11.14
for dF /dt to d/dt may look theoreti-
cally simple but in practice it is not. The transfer of force through a system of joint
fluid (non-Newtonian), cartilage, cancellous bone (non-Hookean) to the cortex of
the femur is complex. Detailed analysis is beyond the scope of the chapter but in
a first approximation the following relation sounds reasonable: dF /dt
kd/dt .
The proportionality factor k is definitely not a constant but a complex function
of the stress-strain behavior of the proximal femur
ensemble
and, as we do not
know the mechanical characteristics of that
ensemble
, k cannot be calculated. Any-
way, inspection of the first derivative given in Fig.
11.14
allows to accept that strain
rate changes, as mentioned above for doubling the stress, are biologically sound or
even common: from dF /dt values passing through zero up to 25.000 N . s
1
within
a lapse of time less than 0.2 s should be a perturbation of comparable order of
magnitude.
Conclusion of the foregoing discussion? A prosthesis to match the properties of
the implant site is in urgent need of a material performing in a much more complex
way than, say, a polyacetal can offer. Before proposing a remedy (Sect.
11.8
), first
something about dashpots, plungers and the world of Heraclitus.
11.7
Heraclitus, 2500 Years Old and Still Alive
Hitting billiard balls deform slightly during the impact. The deformation is imme-
diately and entirely restored after that tiny moment the intimate contact lasts:
billiard balls act as nearly ideally elastic bodies,
ideal spring
, and deform reversibly
