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PubMed1976

Elastic area compressibility modulus of red cell membrane.

Micropipette measurements of isotropic tension vs. area expansion in pre-swollen single human red cells gave a value of 288 +/- 50 SD dyn/cm for the elastic, area compressibility modulus of the total membrane at 25 degrees C. This elastic constant, characterizing the resistance to area expansion or compression, is about 4 X 10(4) times greater than the elastic modulus for shear rigidity; therefore, in situations where deformation of the membrane does not require large isotropic tensions (e.g., in passage through normal capillaries), the membrane can be treated by a simple constitutive relation for a two-dimensionally, incompressible material (i.e. fixed area). The tension was found to be linear and reversible for the range of area changes observed (within the experimental system resolution of 10%). The maximum fractional area expansion required to produce lysis was uniformly distributed between 2 and 4% with 3% average and 0.7% SD. By heating the cells to 50 degrees C, it appears that the structural matrix (responsible for the shear rigidity and most of the strength in isotropic tension) is disrupted and primarily the lipid bilayer resists lysis. Therefore, the relative contributions of the structural matrix and lipid bilayer to the elastic, area compressibility could be estimated. The maximum isotropic tension at 25 degrees C is 10-12 dyn/cm and at 50 degrees C is between 3 and 4 dyn/cm. From this data, the respective compressibilities are estimated at 193 dyn/cm and 95 dyn/cm for structural network and bilayer. The latter value correlates well with data on in vitro, monolayer surface pressure versus area curves at oil-water interfaces.

Cell Membrane↗
PubMed1977

Osmotic correction to elastic area compressibility measurements on red cell membrane.

In a recent article (Biophys. J. 16:585, 1976), we reported measurements of the elastic area compressibility modulus or red cell membranes using micropipette aspiration on osmotically preswollen red cells. Subsequently, we have analyzed the effects of osmotic and hydrostatic pressure driving forces across the cell membrane in conjuction with the mass conservation equation; we find that the change in cell volume due to the reversible movement of water out of the cell can produce one-third of the movement of the cell projection in the pipette tip. Since the actual volume changes is too small to measure directly (about 1% of the total cell volume), we have used an indirect experimental method to provide critical evaluation of the analysis of cell volume change versus applied pressure; this is based on the model that the change in cell volume is inversely proportional to the cellular osmotic strength. We have increased the cellular cation concentration with a drug, nystatin, and measured the elastic area compressibility modulus corrected for osmotic volume changes as a function of cellular osmotic strength. We find that the corrected elastic are compressibility modulus is independent of cellular osmotic strength, which supports the model and calculated correction for the osmotic effect. The elastic area compressibility modulus is 450 dyn/cm at 25 degrees C instead of 300 dyn/cm, determined previously.

Biological Transport↗
PubMed1984

Cell poking. Determination of the elastic area compressibility modulus of the erythrocyte membrane.

Cell poking, a new method for measuring mechanical properties of single cells was used to determine the elastic area compressibility modulus of osmotically swollen human erythrocytes. With this method we determined the force required to indent cells attached to a glass coverslip (Petersen, N.O., W. B. McConnaughey , and E. L. Elson , 1982, Proc. Natl. Acad. Sci. USA, 79:5327. Forces on the order of one millidyne and indentations on the order of one micron were detected. An analysis of these data in terms of a simplified mechanical model yielded the elastic area compressibility modulus. This analysis used a variational approach to minimize the isothermal elastic potential energy density function given by E. A. Evans and R. Skalak (Mechanics and Thermodynamics of Biomembranes, 1980, CRC Press, Boca Raton , FL). Measurements on swollen erythrocytes gave a range of values, depending in part on the osmotic conditions, of 17.9 +/- 8.2 to 34.8 +/- 12.0 mdyn /micron for the elastic area compressibility modulus at 25 degrees C. Fractional area expansion greater than 2.6 +/- 0.8% produced rapid cell lysis. These values were not corrected for the reversible movement of water across the cell membrane in response to hydrostatic pressure gradients. Our results agree reasonably with those obtained by Evans et al. (Evans, E.A., R. Waugh , and L. Melnick , 1976, Biophys. J., 16:585-595.) using micropipette aspiration under similar conditions.

Elasticity↗
PubMed1988

On the measurement of shear elastic moduli and viscosities of erythrocyte plasma membranes by transient deformation in high frequency electric fields.

We present a new method to measure the shear elastic moduli and viscosities of erythrocyte membranes which is based on the fixation and transient deformation of cells in a high-frequency electric field. A frequency domain of constant force (arising by Maxwell Wagner polarization) is selected to minimize dissipative effects. The electric force is thus calculated by electrostatic principles by considering the cell as a conducting body in a dielectric fluid and neglecting membrane polarization effects. The elongation A of the cells perpendicular to their rotational axis exhibits a linear regime (A proportional to Maxwell tension or to square of the electric field E2) at small, and a nonlinear regime (A proportional to square root of Maxwell tension or to the electric field E) at large extensions with a cross-over at A approximately 0.5 micron. The nonlinearity leads to amplitude-dependent response times and to differences of the viscoelastic response and relaxation functions. The cells exhibit pronounced yet completely reversible tip formations at large extensions. Absolute values of the shear elastic modulus, mu, and membrane viscosity, eta, are determined by assuming that field-induced stretching of the biconcave cell may be approximately described in terms of a sphere to ellipsoid deformation. The (nonlinear) elongation-vs.-force relationship calculated by the elastic theory of shells agress well with the experimentally observed curves and the values of mu = 6.1 x 10(-6) N/m and eta = 3.4 x 10(-7) Ns/m are in good agreement with the micropipette results of Evans and co-workers. The effect of physical, biochemical, and disease-induced structural changes on the viscoelastic parameters is studied. The variability of mu and eta of a cell population of a healthy donor is +/- 45%, which is mainly due to differences in the cell age. The average mu value of cells of different healthy donors scatters by +/- 18%. Osmotic deflation of the cells leads to a fivefold increase of mu and 10-fold increase of eta at 500 mosm. The shear modulus mu increases with temperature showing that the cytoskeleton does not behave as a network of entropy elastic springs. Elliptic cells of patients suffering from elliptocytosis of the Leach phenotype exhibit a threefold larger value of mu than normal discocytes of control donors. Cross-linking of the spectrin by the divalent S-H agents diamide (1 mM, 15 min incubation) leads to an eightfold increase of mu whereas eta is essentially constant. The effect of diamide is reversed after treatment with S-S bond splitting agents.

Diamide↗
PubMed1988

Change in membrane elastic modulus on activation of glucose transport system of brush border membrane vesicles studied by osmotic swelling and dynamic light scattering.

The cell membrane having a transport system is inferred to be flexible when its function is being activated. For the brush border membrane vesicles prepared from rat small intestine, which have the co-transport system of Na+ and glucose, the membrane elasticity was measured as a function of the d-glucose concentration in the presence of Na+ ions. The elastic modulus of the vesicle membrane was obtained by an osmotic swelling method. Osmolality was changed by diluting the extravesicular d-mannitol concentration. The change in the diameter of the membrane vesicle in response to an osmolality change was measured by the dynamic light-scattering method. The elastic modulus of the vesicle membrane decreased from 150 dyn/cm to 80 (45) dyn/cm with the increase of d-glucose, from 0 mM to 10(30) mM in the presence of 10 mM Na+ ions. On the other hand, in the presence of 1 mM phlorizin, a glucose-transport inhibitor, the elastic modulus remained at a constant value of 160 dyn/cm in the same range of the d-glucose concentration. This indicates that the vesicle membrane becomes flexible when its transport function is activated. In a broad osmolality range, the brush border membrane vesicle showed cycles of "swell-burst-reseal". The vesicle membrane became flexible after every cycle, namely, the modulus was 150, 120, and 55 in units of dyn/cm in the presence of 1 mM d-glucose and 50 mM Na+ ions.

Alkaline Phosphatase↗
PubMed1995

Microscopic analysis of the elastic properties of nebulin in skeletal myofibrils.

The elastic properties of nebulin were studied by measuring the elasticity of single skeletal myofibrils, from which the portion of the thin filament located at the I band had been selectively removed by treatment with plasma gelsolin under rigor conditions. In this myofibril model, a portion of each nebulin molecule at the I band was expected to be free of actin filaments and exposed. The length of the exposed portion of the nebulin molecule was controlled by performing the gelsolin treatment at various sarcomere lengths. The relation between the passive tension and extension of the exposed portion of the nebulin showed a convex curve starting from a slack length, apparently in a fashion similar to that of wool. The slack sarcomere length shifted depending on the length of the exposed portion of the nebulin, however, the relation being represented by a single master curve. The elastic modulus of nebulin was estimated to be two to three orders of magnitude smaller than that of an actin filament. Based on these results, we conclude that nebulin attaches to an actin filament in a side-by-side fashion and that it does not significantly contribute to the elastic modulus of thin filaments. The relation between the passive tension and extension of connectin (titin) was obtained for a myofibril from which thin filaments had been completely removed with gelsolin under contracting conditions; this showed a concave curve, consistent with the previous results obtained in single fibers.

Actins↗
PubMed1996

The interfacial elastic packing interactions of galactosylceramides, sphingomyelins, and phosphatidylcholines.

The interfacial elastic packing interactions of different galactosylceramides (GalCers), sphingomyelins (SMs), and phosphatidylcholines (PC) were compared by determining their elastic area compressibility moduli (Cs-1) as a function of lateral packing pressure (pi) in a Langmuir-type film balance. To assess the relative contributions of the lipid headgroups as well as those of the ceramide and diacylglycerol hydrocarbon regions, we synthesized various GalCer and SM species with identical, homogeneous acyl residues and compared their behavior to that of PCs possessing similar hydrocarbon structures. For PCs, this meant that the sn-1 acyl chain was long and saturated (e.g., palmitate) and the sn-2 chain composition was varied to match that of GalCer or SM. When at equivalent pi and in either the chain-disordered (liquid-expanded) or chain-ordered (liquid-condensed) state, GalCer films were less elastic than either SM or PC films. When lipid headgroups were identical (SM and PC), Cs-1 values (at equivalent pi) for chain-disordered SMs, but not chain-ordered SMs, were 25-30% higher than those of PCs. Typical values for fluid phase (liquid-expanded) GalCer at 30 mN/m and 24 degrees C were 158 (+/- 7) mN/m, whereas those of SM were 135 (+/- 7) mN/m and those of PC were 123 (+/- 2) mN/m. Pressure-induced transitions to chain-ordered states (liquid-condensed) resulted in significant increases (two- to fourfold) in the "in-plane" compressibility for all three lipid types. Typical Cs-1 values for chain-ordered GalCers at 30 mN/m and 24 degrees C were between 610 and 650 mN/m, whereas those of SM and of PC were very similar and were between 265 and 300 mN/m. Under fluid phase conditions, the pi-Cs-1 behavior for each lipid type was insensitive to whether the acyl chain was saturated or monounsaturated. Measurement of the Cs-1 values also provided an effective way to evaluate the two-dimensional phase transition region of SMs, GalCers, and PCs. Modest heterogeneity in the acyl composition led to transitional broadening. Our findings provide useful information regarding the in-plane elasticity of lipids that are difficult to investigate by alternative methods, i.e., micropipette aspiration technique. The results also provide insight into the stability of sphingolipid-enriched, membrane microdomains that are thought to play a role in the sorting and trafficking of proteins containing glycosylphosphatidylinositol anchors with cells.

Animals↗
PubMed1997

Titin elasticity and mechanism of passive force development in rat cardiac myocytes probed by thin-filament extraction.

Titin (also known as connectin) is a giant filamentous protein whose elastic properties greatly contribute to the passive force in muscle. In the sarcomere, the elastic I-band segment of titin may interact with the thin filaments, possibly affecting the molecule's elastic behavior. Indeed, several studies have indicated that interactions between titin and actin occur in vitro and may occur in the sarcomere as well. To explore the properties of titin alone, one must first eliminate the modulating effect of the thin filaments by selectively removing them. In the present work, thin filaments were selectively removed from the cardiac myocyte by using a gelsolin fragment. Partial extraction left behind approximately 100-nm-long thin filaments protruding from the Z-line, whereas the rest of the I-band became devoid of thin filaments, exposing titin. By applying a much more extensive gelsolin treatment, we also removed the remaining short thin filaments near the Z-line. After extraction, the extensibility of titin was studied by using immunoelectron microscopy, and the passive force-sarcomere length relation was determined by using mechanical techniques. Titin's regional extensibility was not detectably affected by partial thin-filament extraction. Passive force, on the other hand, was reduced at sarcomere lengths longer than approximately 2.1 microm, with a 33 +/- 9% reduction at 2.6 microm. After a complete extraction, the slack sarcomere length was reduced to approximately 1.7 microm. The segment of titin near the Z-line, which is otherwise inextensible, collapsed toward the Z-line in sarcomeres shorter than approximately 2.0 microm, but it was extended in sarcomeres longer than approximately 2.3 microm. Passive force became elevated at sarcomere lengths between approximately 1.7 and approximately 2.1 microm, but was reduced at sarcomere lengths of >2.3 microm. These changes can be accounted for by modeling titin as two wormlike chains in series, one of which increases its contour length by recruitment of the titin segment near the Z-line into the elastic pool.

Amino Acid Sequence↗
PubMed1997

Changes in the elastic properties of cholinergic synaptic vesicles as measured by atomic force microscopy.

Cholinergic synaptic vesicles from Torpedo californica have been probed with the atomic force microscope in aqueous buffers to map and measure their elastic properties. Elastic properties were mapped with a new atomic force microscope technique known as force mapping. Force mapping of vesicles showed that the centers of the vesicles are harder or stiffer than the peripheral areas in the three buffers that were investigated. These were an isoosmotic buffer, a hypoosmotic buffer, and an isoosmotic buffer with 5 mM CaCl2 added. The hardness of the vesicular centers was quantified by calculation of the elastic modulus. Elastic moduli were in the range of 2-13 x 10(5) Pa. Vesicular centers were hardest in calcium-containing buffer and softest in isoosmotic buffer. Hypotheses are presented for the composition and function of the hard centers.

Acetylcholine↗
PubMed1997

Bending elasticities of model membranes: influences of temperature and sterol content.

Giant liposomes obtained by electroformation and observed by phase-contrast video microscopy show spontaneous deformations originating from Brownian motion that are characterized, in the case of quasispherical vesicles, by two parameters only, the membrane tension sigma and the bending elasticity k(c). For liposomes containing dimyristoyl phosphatidylcholine (DMPC) or a 10 mol% cholesterol/DMPC mixture, the mechanical property of the membrane, k(c), is shown to be temperature dependent on approaching the main (thermotropic) phase transition temperature T(m). In the case of DMPC/cholesterol bilayers, we also obtained evidence for a relation between the bending elasticity and the corresponding temperature/cholesterol molecular ratio phase diagram. Comparison of DMPC/cholesterol with DMPC/cholesterol sulfate bilayers at 30 degrees C containing 30% sterol ratio shows that k(c) is independent of the surface charge density of the bilayer. Finally, bending elasticities of red blood cell (RBC) total lipid extracts lead to a very low k(c) at 37 degrees C if we refer to DMPC/cholesterol bilayers. At 25 degrees C, the very low bending elasticity of a cholesterol-free RBC lipid extract seems to be related to a phase coexistence, as it can be observed by solid-state (31)P-NMR. At the same temperature, the cholesterol-containing RBC lipid extract membrane shows an increase in the bending constant comparable to the one observed for a high cholesterol ratio in DMPC membranes.

Biomechanical Phenomena↗
PubMed1998

Acyl chain-length asymmetry alters the interfacial elastic interactions of phosphatidylcholines.

Phosphatidylcholines (PCs) with stearoyl (18:0) sn-1 chains and variable-length, saturated sn-2 acyl chains were synthesized and investigated using a Langmuir-type film balance. Surface pressure was monitored as a function of lipid molecular area at various constant temperatures between 10 degrees C and 30 degrees C. Over this temperature range, 18:0-10:0 PC displayed only liquid-expanded behavior. In contrast, di-14:0 PC displayed liquid-expanded behavior at 24 degrees C and 30 degrees C, but two-dimensional phase transitions were evident at 20 degrees C, 15 degrees C, and 10 degrees C. The average molecular area of 18:0-10:0 PC was larger than that of liquid-expanded di-14:0 PC at equivalent surface pressures, and the shapes of their liquid expanded isotherms were somewhat dissimilar. Analysis of the elastic moduli of area compressibility (Cs(-1)) as a function of molecular area revealed shallower slopes in the semilog plots of 18:0-10:0 PC compared to di-14:0 PC. At membrane-like surface pressures (e.g., 30 mN/m), 18:0-10:0 PC was 20-25% more elastic (in an in-plane sense) than di-14:0 PC. Other PCs with varying degrees of chain-length asymmetry (18:0-8:0 PC, 18:0-12:0 PC, 18:0-14:0 PC, 18:0-16:0 PC) were also investigated to determine whether the higher in-plane elasticity of fluid-phase 18:0-10:0 PC is a common feature of PCs with asymmetrical chain lengths. Two-dimensional phase transitions in 18:0-14:0 PC and 18:0-16:0 PC prevented meaningful comparison with other fluid-phase PCs at 30 mN/m. However, the Cs(-1) values for fluid-phase 18:0-8:0 PC and 18:0-12:0 PC were similar to that of 18:0-10:0 PC (85-90 mN/m). These values showed chain-length asymmetrical PCs to have 20-25% greater in-plane elasticity than fluid-phase PCs with mono- or diunsaturated acyl chains.

Elasticity↗
PubMed1998

The elastic rod model for DNA and its application to the tertiary structure of DNA minicircles in mononucleosomes.

Explicit solutions to the equations of equilibrium in the theory of the elastic rod model for DNA are employed to develop a procedure for finding the configuration that minimizes the elastic energy of a minicircle in a mononucleosome with specified values of the minicircle size N in base pairs, the extent w of wrapping of DNA about the histone core particle, the helical repeat h(0)b of the bound DNA, and the linking number Lk of the minicircle. The procedure permits a determination of the set Y(N, w, h(0)b) of integral values of Lk for which the minimum energy configuration does not involve self-contact, and graphs of writhe versus w are presented for such values of Lk. For the range of N of interest here, 330 < N < 370, the set Y(N, w, h(0)b) is of primary importance: when Lk is not in Y(N, w, h(0)b), the configurations compatible with Lk have elastic energies high enough to preclude the occurrence of an observable concentration of topoisomer Lk in an equilibrium distribution of topoisomers. Equilibrium distributions of Lk, calculated by setting differences in the free energy of the extranucleosomal loop equal to differences in equilibrium elastic energy, are found to be very close to Gaussian when computed under the assumption that w is fixed, but far from Gaussian when it is assumed that w fluctuates between two values. The theoretical results given suggest a method by which one may calculate DNA-histone binding energies from measured equilibrium distributions of Lk.

Base Composition↗
PubMed1999

Elasticity of the red cell membrane and its relation to hemolytic disorders: an optical tweezers study.

We have used optical tweezers to study the elasticity of red cell membranes; force was applied to a bead attached to a permeabilized spherical ghost and the force-extension relation was obtained from the response of a second bead bound at a diametrically opposite position. Interruption of the skeletal network by dissociation of spectrin tetramers or extraction of the actin junctions engendered a fourfold reduction in stiffness at low applied force, but only a twofold change at larger extensions. Proteolytic scission of the ankyrin, which links the membrane skeleton to the integral membrane protein, band 3, induced a similar effect. The modified, unlike the native membranes, showed plastic relaxation under a prolonged stretch. Flaccid giant liposomes showed no measurable elasticity. Our observations indicate that the elastic character is at least as much a consequence of the attachment of spectrin as of a continuous membrane-bound network, and they offer a rationale for formation of elliptocytes in genetic conditions associated with membrane-skeletal perturbations. The theory of Parker and Winlove for elastic deformation of axisymmetric shells (accompanying paper) allows us to determine the function BH(2) for the spherical saponin-permeabilized ghost membranes (where B is the bending modulus and H the shear modulus); taking the literature value of 2 x 10(-19) Nm for B, H then emerges as 2 x 10(-6) Nm(-1). This is an order of magnitude higher than the value reported for intact cells from micropipette aspiration. Reasons for the difference are discussed.

Biophysical Phenomena↗
PubMed2002

Role of elastic fibers in cooling-induced relaxation.

The objective of this work was to confirm the main role of elastic fibers in differing responses of certain vessels during cooling from 37 to 8 degrees C. Previous results have shown that the nature of the vessel (conduit vessel vs muscular vessel) determines the different behavior (dilatation vs contraction) of isolated vessel segments when temperature decreases from 37 to 8 degrees C. In this work, it has been demonstrated that vessels with a great amount of elastic fibers show a dilatation when cooling. On the other hand, muscular vessels with fewer elastic fibers, such as the renal artery, undergo a contraction. The output of calcium from intracellular stores causes contraction of the renal artery during cooling. In this vessel, vasodilatation occurs only when mechanisms of smooth muscle contraction are inactive, as is the case with vessels that have undergone a cold storage period of 48 h. The results presented in this work confirm that there are two main effects, which directly depend on the vessel origin. In conduit arteries, the decrease of temperature induces a vascular relaxation, dependent on the elastic component of the vessel wall. In muscular vessels, the predominant effect is cooling-induced contraction due to an increase of intracellular calcium. This cooling-induced contraction needs the vessel to be in optimal conditions with an active metabolism of the muscular cells. These results are a crucial issue in the sense of explaining several biomedical mechanisms where hypothermia is implicated. The type of vessel implicated in procedures, such as isolated organ perfusion, extracorporeal circulation, and bypass surgery, must be taken into account.

Animals↗
PubMed1998

Differences in F9 and 5.51 cell elasticity determined by cell poking and atomic force microscopy.

We studied the elasticity of both a wild type (F9) mouse embryonic carcinoma and a vinculin-deficient (5.51) cell line, which was produced by chemical mutagenesis. Using cell poking, we measured the effects of loss of vinculin on the elastic properties of these cells. F9 cells were about 20% more resistant to indentation by the cell poker (a glass stylus) than were 5.51 cells. Using the atomic force microscope to map the elasticity of wild type and vinculin-deficient cells by 128 X 128 force scans, we observed a correlation of elasticity with cell poking elastometric measurements. These findings, as well as previous atomic force, rheologic, and magnetometric measurements [Goldmann and Ezzell, Exp. Cell Res. 226 (1996) 234-237; Ezzell et al., Exp. Cell Res. 231 (1997) 14-26], indicate that vinculin is an integral part of the cytoskeletal network.

Animals↗
PubMed2001

Moment dependency of the series elastic stiffness in the human plantar flexors measured in vivo.

The moment dependency of the series elastic stiffness (SES) in the human plantar flexors was investigated in vivo with the quick release method. At an ankle moment of 100 N m produced with either voluntary or electrical stimulation we found non-significantly different SES of 506+/-72 and 529+/-125 N m rad(-1), respectively. It has recently been proposed that the amount of series elastic tissue involved in plantar flexion changes with the moment level produced by the plantar flexors (Hof, J. Biomech 31 (1998) 793). However, our results indicate that the amount of series elastic tissue involved in plantar flexions remained constant with changing moment levels. We therefore propose that the series elastic component (SEC) in human plantar flexors act as one structure or rather one combination of anatomical structures which is engaged at all muscle activation levels, and that the mechanical properties (i.e. the stress-strain function) are determined by the combined tissue mechanical properties. Additionally, our results demonstrated that the SES in the human plantar flexors at moments levels up to about isometric maximum did not reach an asymptote where the stiffness is independent of moment, i.e. SEC of the plantar flexors is, during many daily activities, loaded for the greatest part in the non-linear part of the stress-strain function.

Adult↗
PubMed2002

An alternative ultrasonic method for measuring the elastic properties of cortical bone.

We studied the elastic properties of bone to analyze its mechanical behavior. The basic principles of ultrasonic methods are now well established for varying isotropic media, particularly in the field of biomedical engineering. However, little progress has been made in its application to anisotropic materials. This is largely due to the complex nature of wave propagation in these media. In the present study, the theory of elastic waves is essential because it relates the elastic moduli of a material to the velocity of propagation of these waves along arbitrary directions in a solid. Transducers are generally placed in contact with the samples which are often cubes with parallel faces that are difficult to prepare. The ultrasonic method used here is original, a rough preparation of the bone is sufficient and the sample is rotated. Moreover, to analyze heterogeneity of the structure we measure velocities in different points on the sample. The aim of the present study was to determine in vitro the anisotropic elastic properties of cortical bones. For this purpose, our method allowed measurement of longitudinal and transverse velocities (C(L) and C(T)) in longitudinal (fiber direction) and the radial directions (orthogonal to the fiber direction) of compact bones. Young's modulus E and Poisson's ratio nu, were then deduced from the velocities measured considering the compact bone as transversely isotropic or orthotropic. The results are in line with those of other methods.

Animals↗
PubMed2003

How is the indentation modulus of bone tissue related to its macroscopic elastic response? A validation study.

This work consists of the validation of a novel approach to estimate the local anisotropic elastic constants of the bone extracellular matrix using nanoindentation. For this purpose, nanoindentation on two planes of material symmetry were analyzed and the resulting longitudinal elastic moduli compared to the moduli measured with a macroscopic tensile test. A combined lathe and tensile system was designed that allows machining and testing of cylindrical microspecimens of approximately 4mm in length and 300 microm in diameter. Three bovine specimens were tested in tension and their outer geometry and porosity assessed by synchrotron radiation microtomography. Based on the results of the traction test and the precise outer geometry, an apparent longitudinal Young's modulus was calculated. Results between 20.3 and 27.6 GPa were found that match with previously reported values for bovine compact bone. The same specimens were then characterized by nanoindentation on a transverse and longitudinal plane. A longitudinal Young's modulus for the bone matrix was then derived using the numerical scheme proposed by Swadener and Pharr and the fabric-elasticity relationship by Zysset and Curnier. Based on the matrix modulus and a power law effective volume fraction, an apparent longitudinal Young's modulus was predicted for each microspecimen. This alternative approach provided values between 19.9 and 30.0 GPa, demonstrating differences between 2% and 13% to the values provided by the initial tensile test. This study therefore raises confidence in our nanoindentation protocol of the bone extracellular matrix and supports the underlying hypotheses used to extract the anisotropic elastic constants.

Animals↗