Mechanics of intact bone marrow

Abstract

The current knowledge of bone marrow mechanics is limited to its viscous properties, neglecting the elastic contribution of the extracellular matrix. To get a more complete view of the mechanics of marrow, we characterized intact yellow porcine bone marrow using three different, but complementary techniques: rheology, indentation, and cavitation. Our analysis shows that bone marrow is elastic, and has a large amount of intra- and inter-sample heterogeneity, with an effective Young׳s modulus ranging from 0.25 to 24.7 kPa at physiological temperature. Each testing method was consistent across matched tissue samples, and each provided unique benefits depending on user needs. We recommend bulk rheology to capture the effects of temperature on tissue elasticity and moduli, indentation for quantifying local tissue heterogeneity, and cavitation rheology for mitigating destructive sample preparation. We anticipate the knowledge of bone marrow elastic properties for building in vitro models will elucidate mechanisms involved in disease progression and regenerative medicine.

Keywords: Cavitation; Contact mechanics; Indentation; Rheology; Young׳s modulus.

Figure 1. Techniques used to characterize porcine bone marrow

a: Samples were removed from the medullary cavity of femurs for rheology and indentation (left). The horizontal cross-section of the femur was used as the needle insertion point for cavitation (right). b: Rheology measurements were done between two parallel plates to obtain a storage (G′) and loss (G″) modulus with respect to increasing shear. c: Indentation is an axisymmetric compression test that records the load (shown) and displacement over time. d: Cavitation records pressure as a cavity is propagated in a substrate over time. The formation of this cavity is a function of inner needle radius and solvent-substrate surface tension. The point when the cavity collapses is recorded as the pressure of the cavitation (P_c).

Figure 2. Rheological behavior of porcine marrow

a: Representative rheological data. The storage (G′, open symbol) and loss (G″, closed symbol) modulus versus strain rate show a weakly frequency dependent material with a dominant elastic modulus. As temperature is increased from 25°C (blue) to 35°C (red), both modulus and b: complex viscosity decrease, indicating strong temperature dependence. The power law (α) fit of the complex viscosity showed that bone marrow is slightly more elastic at the higher temperature (t-test, *p<0.05).

Figure 3. Bone marrow exhibits inter- and intra- sample heterogeneity

The effective Young’s modulus (E^Eff) for a: rheology (0.1 Hz at 25°C) and b: indentation (0.03 Hz at 20°C) in matched bone samples shows strong continuity between measurements from both instruments. Data points represent different locations within the same bone sample. Statistical significance was calculated using the mean of the data (*P<0.05, **P<0.01, ***P<0.001).

Figure 4. Cavitation mirrors indentation and rheology measurements

a: The pressure of cavitation (P_c) changes as a function of needle radius, r, allowing an effective Young’s modulus (E^Eff) to be derived using Equation 4 and the y-intercept (red). The inset is a picture of the bone cross-sectional area, which is the site of needle insertion. b: The E^Eff at 20°C is similar to the modulus calculated for matched tissue samples in rheology and indentation. The solid line represents no data (n.d.) because these samples maxed out the instrument pressure sensor.