Sheldon Weinbaum

A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses.

A new experimentally testable hypothesis is advanced for the mechanosensory transduction mechanism by which communicating osteocytes sense the very small in vivo strains in the calcified matrix components of bone. We propose that the osteocytes, although not responsive to substantial fluid pressures, can be stimulated by relatively small fluid shear stresses acting on the membranes of their osteocytic processes. Biots porous media theory is used to relate the combined axial and bending loads applied to a whole bone to the flow past the osteocytic processes in their canaliculi. In this theory, the bone pores of interest are the proteoglycan filled fluid annuli that surround the osteocytic processes in the canaliculi. We show that previously predicted fluid pore pressure relaxation times were a hundred-fold too short for the lacunar-canalicular porosity because they neglected the fluid drag associated with proteoglycan matrix on the surface membrane of the osteocyte and its cell processes. The recent theory developed in Tsay and Weinbaum [J. Fluid Mech. 226, 125-148 (1991)] for flow through cross-linked fiber filled channels is used to model the flow through this proteoglycan matrix. The predicted pore relaxation time, 1-2 s, closely corresponds to the times measured by Salzstein and Pollack [J. Biomechanics 20, 271-280 (1987)]. Furthermore, using this model, the magnitude of the predicted fluid induced shear stresses, 8-30 dyn cm-2, is shown to be similar to the fluid shear stresses measured in osteoblasts and other cells in which an intracellular Ca2+ shear stress response had been observed. This model is also used, in conjunction with anatomical data and the pore fluid pressure relaxation time data, to show that the spacing between the fibers is approximately 7 nm. The result is consistent with the notion that the canalicular pore space is filled with glycosaminoglycans that are ordered by albumin according to the model of Michel [J. Physiol. 404, 1-29 (1988)]. The new hypothesis is also shown to be consistent with the experiments of McLeod et al. [J. Biomechanics (submitted)] which suggest that high-frequency low-amplitude postural strains can maintain and even increase bone mass.

Mechanotransduction and flow across the endothelial glycocalyx

In this inaugural paper, we shall provide an overview of the endothelial surface layer or glycocalyx in several roles: as a transport barrier, as a porous hydrodynamic interface in the motion of red and white cells in microvessels, and as a mechanotransducer of fluid shearing stresses to the actin cortical cytoskeleton of the endothelial cell. These functions will be examined from a new perspective, the quasiperiodic ultrastructural model proposed in Squire et al. [Squire, J. M., Chew, M., Nneji, G., Neal, C., Barry, J. & Michel, C. (2001) J. Struct. Biol. 136, 239–255] for the 3D organization of the endothelial surface layer and its linkage to the submembranous scaffold. We shall show that the core proteins in the bush-like structures comprising the matrix have a flexural rigidity, EI, that is sufficiently stiff to serve as a molecular filter for plasma proteins and as an exquisitely designed transducer of fluid shearing stresses. However, EI is inadequate to prevent the buckling of these protein structures during the intermittent motion of red cells or the penetration of white cell microvilli. In these cellular interactions, the viscous draining resistance of the matrix is essential for preventing adhesive molecular interactions between proteins in the endothelial membrane and circulating cellular components.

A hypothesis for vulnerable plaque rupture due to stress-induced debonding around cellular microcalcifications in thin fibrous caps

In this article, we advance a hypothesis for the rupture of thin fibrous cap atheroma, namely that minute (10-μm-diameter) cellular-level microcalcifications in the cap, which heretofore have gone undetected because they lie below the visibility of current in vivo imaging techniques, cause local stress concentrations that lead to interfacial debonding. New theoretical solutions are presented for the local stress concentration around these minute spherical inclusions that predict a nearly 2-fold increase in interfacial stress that is relatively insensitive to the location of the hypothesized microinclusions in the cap. To experimentally confirm the existence of the hypothesized cellular-level microcalcifications, we examined autopsy specimens of coronary atheromatous lesions using in vitro imaging techniques whose resolution far exceeds conventional magnetic resonance imaging, intravascular ultrasound, and optical coherence tomography approaches. These high-resolution imaging modalities, which include confocal microscopy with calcium-specific staining and micro-computed tomography imaging, provide images of cellular-level calcifications within the cap proper. As anticipated, the minute inclusions in the cap are very rare compared with the numerous calcified macrophages observed in the necrotic core. Our mathematical model predicts that inclusions located in an area of high circumferential stress (>300 kPa) in the cap can intensify this stress to nearly 600 kPa when the cap thickness is <65 μm. The most likely candidates for the inclusions are either calcified macrophages or smooth muscle cells that have undergone apoptosis.

A model for strain amplification in the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix

A model is presented that provides a resolution to a fundamental paradox in bone physiology, namely, that the strains applied to whole bone (i.e., tissue level strains) are much smaller (0.04-0.3 percent) than the strains (1-10 percent) that are necessary to cause bone signaling in deformed cell cultures (Rubin and Lanyon, J. Bone Joint Surg. 66A (1984) 397-410; Fritton et al., J. Biomech. 33 (2000) 317-325). The effect of fluid drag forces on the pericellular matrix (PM), its coupling to the intracellular actin cytoskeleton (IAC) and the strain amplification that results from this coupling are examined for the first time. The model leads to two predictions, which could fundamentally change existing views. First, for the loading range 1-20MPa and frequency range 1-20Hz, it is, indeed, possible to produce cellular level strains in bone that are up to 100 fold greater than normal tissue level strains (0.04-0.3 percent). Thus, the strain in the cell process membrane due to the loading can be of the same order as the in vitro strains measured in cell culture studies where intracellular biochemical responses are observed for cells on stretched elastic substrates. Second, it demonstrates that in any cellular system, where cells are subject to fluid flow and tethered to more rigid supporting structures, the tensile forces on the cell due to the drag forces on the tethering fibers may be many times greater than the fluid shear force on the cell membrane.

A case for bone canaliculi as the anatomical site of strain generated potentials

We address the question of determining the anatomical site that is the source of the experimentally observed strain generated potentials (SGPs) in bone tissue. There are two candidates for the anatomical site that is the SGP source, the collagen-hydroxyapatite porosity and the larger size lacunar-canalicular porosity. In the past it has been argued, on the basis of experimental data and a reasonable model, that the site of the SGPs in bone is the collagen-hydroxyapatite porosity. The theoretically predicted pore radius necessary for the SGPs to reside in this porosity is 16 nm, which is somewhat larger than the pore radii estimated from gas adsorption data where the preponderance of the pores were estimated to be in the range 5-12.5 nm. However, this pore size is significantly larger than the 2 nm size of the small tracer, microperoxidase, which appears to be excluded from the mineralized matrix. In this work a similar model, but one in which the effects of fluid dynamic drag of the cell surface matrix in the bone canaliculi are included, is used to show that it is possible for the generation of SGPs to be associated with the larger size lacunar-canalicular porosity when the hydraulic drag and electrokinetic contribution of the bone fluid passage through the cell coat (glycocalyx) is considered. The consistency of the SGP data with this model is demonstrated. A general boundary condition is introduced to allow for current leakage at the bone surface. The results suggest that the current leakage is small for the in vitro studies in which the strain generated potentials have been measured.

Oncotic pressures opposing filtration across non-fenestrated rat microvessels

We hypothesized that ultrafiltrate crossing the luminal endothelial glycocalyx through infrequent discontinuities (gaps) in the tight junction (TJ) strand of endothelial clefts reduces albumin diffusive flux from tissue into the ‘protected region’ of the cleft on the luminal side of the TJ. Thus, the effective oncotic pressure difference (σ□π) opposing filtration is greater than that measured between lumen and interstitial fluid. To test this we measured σ□π across rat mesenteric microvessels perfused with albumin (50 mg ml−1) with and without interstitial albumin at the same concentration within a few micrometres of the endothelium as demonstrated by confocal microscopy. We found σ□π was near 70% of luminal oncotic pressure when the tissue concentration equalled that in the lumen. We determined size and frequency of TJ strand gaps in endothelial clefts using serial section electron microscopy. We found nine gaps in the reconstructed clefts having mean spacing of 3.59 μm and mean length of 315 nm. The mean depth of the TJ strand near gaps was 67 nm and the mean cleft path length from lumen to interstitium was 411 nm. With these parameters our three‐dimensional hydrodynamic model confirmed that fluid velocity was high at gaps in the TJ strand so that even at relatively low hydraulic pressures the albumin concentration on the tissue side of the glycocalyx was significantly lower than in the interstitium. The results conform to the hypothesis that colloid osmotic forces opposing filtration across non‐fenestrated continuous capillaries are developed across the endothelial glycocalyx and that the oncotic pressure of interstitial fluid does not directly determine fluid balance across microvascular endothelium.

Theory and Experiment for the Effect of Vascular Microstructure on Surface Tissue Heat Transfer—Part I: Anatomical Foundation and Model Conceptualization

A new theoretical model supported by ultrastructural studies and high-spatial resolution temperature measurements is presented for surface tissue heat transfer in a two-part study. In this first paper, vascular casts of the rabbit thigh prepared by the tissue clearance method were serially sectioned parallel to the skin surface to determine the detailed variation of the vascular geometry as a function of tissue depth. Simple quantitative models of the basic vascular structures observed were then analyzed in terms of their characteristic thermal relaxation lengths and a new three-layer conceptual model proposed for surface tissue heat transfer. Fine wire temperature measurements with an 80-micron average diameter thermocouple junction and spatial increments of 20 micrometers between measurement sites have shown for the first time the detailed temperature fluctuations in the microvasculature and have confirmed the fundamental assumptions of the proposed three-layer model for the deep tissue, skeletal muscle and cutaneous layers.

Mechanosensation and transduction in osteocytes

The human skeleton is a miracle of engineering, combining both toughness and light weight. It does so because bones possess cellular mechanisms wherein external mechanical loads are sensed. These mechanical loads are transformed into biological signals, which ultimately direct bone formation and/or bone resorption. Osteocytes, since they are ubiquitous in the mineralized matrix, are the cells that sense mechanical loads and transduce the mechanical signals into a chemical response. The osteocytes then release signaling molecules, which orchestrate the recruitment and activity of osteoblasts or osteoclasts, resulting in the adaptation of bone mass and structure. In this review, we highlight current insights in bone adaptation to external mechanical loading, with an emphasis on how a mechanical load placed on whole bones is translated and amplified into a mechanical signal that is subsequently sensed by the osteocytes.

A model for the role of integrins in flow induced mechanotransduction in osteyocytes

A fundamental paradox in bone mechanobiology is that tissue-level strains caused by human locomotion are too small to initiate intracellular signaling in osteocytes. A cellular-level strain-amplification model previously has been proposed to explain this paradox. However, the molecular mechanism for initiating signaling has eluded detection because none of the molecules in this previously proposed model are known mediators of intracellular signaling. In this paper, we explore a paradigm and quantitative model for the initiation of intracellular signaling, namely that the processes are attached directly at discrete locations along the canalicular wall by β3 integrins at the apex of infrequent, previously unrecognized canalicular projections. Unique rapid fixation techniques have identified these projections and have shown them to be consistent with other studies suggesting that the adhesion molecules are αvβ3 integrins. Our theoretical model predicts that the tensile forces acting on the integrins are <15 pN and thus provide stable attachment for the range of physiological loadings. The model also predicts that axial strains caused by the sliding of actin microfilaments about the fixed integrin attachments are an order of magnitude larger than the radial strains in the previously proposed strain-amplification theory and two orders of magnitude greater than whole-tissue strains. In vitro experiments indicated that membrane strains of this order are large enough to open stretch-activated cation channels.

Biomechanics: Cell Research and Applications for the Next Decade

With the recent revolution in Molecular Biology and the deciphering of the Human Genome, understanding of the building blocks that comprise living systems has advanced rapidly. We have yet to understand, however, how the physical forces that animate life affect the synthesis, folding, assembly, and function of these molecular building blocks. We are equally uncertain as to how these building blocks interact dynamically to create coupled regulatory networks from which integrative biological behaviors emerge. Here we review recent advances in the field of biomechanics at the cellular and molecular levels, and set forth challenges confronting the field. Living systems work and move as multi-molecular collectives, and in order to understand key aspects of health and disease we must first be able to explain how physical forces and mechanical structures contribute to the active material properties of living cells and tissues, as well as how these forces impact information processing and cellular decision making. Such insights will no doubt inform basic biology and rational engineering of effective new approaches to clinical therapy.