Viscoelastic characterization of mesenchymal gap tissue and consequences for tension accumulation during distraction

Nonlinear viscoelastic analysis was used to characterize the time-dependent behavior of mesenchymal gap tissue generated during distraction osteogenes is. Six (n = 6) lengthened tibiae were harvested from New Zealand white rab bits at Is days. This gap tissue was subjected to a series of step displace ment tests of increasing magnitude, and force relaxation behavior was monit ored. Isochrones in stress-strain space were fit to odd cubic functions of strain. An analytic expression, linear in both e and e3, was developed to p redict stress accumulation within the gap tissue as a function of time duri ng distraction. Stress relaxation functions were described well by two-term Prony series. The two time constants determined from mechanical testing re sults were consistent, suggesting the presence of two fundamental physiolog ic relaxation processes. Gap tissue stresses were predicted to rise conside rably during early stages of lengthening when distraction magnitudes exceed ed the clinical norm of 0.25 mm. These differences in tension accumulation were less pronounced by the time lengthening was completed. Specifically, t hese results may in part explain clinical observations of decreased bone re generation and altered tissue proliferation and differentiation at higher d istraction rates. More generally, this work provides a framework for the ri gorous characterization of the the viscoelastic properties of biologic tiss ues ordinarily exposed to step strains.