Effect of vascular volume and edema on wave propagation in canine lungs

The velocities of longitudinal and transverse stress waves transmitted through inflated lung parenchyma depend on the lung stiffness, as defined by the bulk and shear moduli, and the lung density. We examined the relationship between stress wave velocities and lung density. A saline-filled reservoir was connected to the vessels of caudal dog lobes held inflated at 5 cmH2O transpulmonary pressure, and vascular volume and extravascular lung water were increased in steps by increasing vascular pressure. At each step, we measured the transmitted signals at locations 2 and 7 cm from an impulse surface distortion by means of microphones embedded in the lung surface. Longitudinal and transverse wave velocities were computed by using cross-correlation analysis of microphone signal pairs. Both wave velocities decreased as lung density increased: as a first approximation, wave velocities were inversely proportional to the square root of lung density. This behavior is consistent with the propagation of small-amplitude stress waves through an elastic continuum. Estimated bulk and shear moduli were 26 and 3.5 cmH2O, respectively, and were consistent with results from quasi-static deformation tests.     

Propagation of stress waves in inflated sheep lungs

If the lung is an elastic continuum, both longitudinal and transverse stress waves should be propagated in the medium with distinct velocities. In five isolated sheep lungs, we investigated the propagation of stress waves. The lungs were degassed and then inflated to a constant transpulmonary pressure (Ptp). We measured signals transmitted at locations approximately 1.5, 6, and 11 cm from an impulse surface distortion with the use of small microphones embedded in the pleural surface. Two transit times were computed from the first two significant peaks of the cross-correlation of microphone signal pairs. The "fast" wave velocities averaged 301 +/- 92, 445 +/- 80, and 577 +/- 211 (SD) cm/s for Ptp values of 5, 10, and 15 cmH2O, respectively. Corresponding "slow" wave velocities averaged 139 +/- 22, 217 +/- 36, and 255 +/- 89 cm/s. The fast waves were consistent with longitudinal waves of velocity [(K + 4G/3)/p]1/2, where bulk modulus K = 4 Ptp and shear modulus G = 0.7 Ptp. The slow waves were consistent with transverse (and/or Rayleigh) waves of velocity (G/p)1/2, with a G value of 0.9 Ptp. Measured values of K were 5 Ptp and values of G measured by indentation tests were 0.7 Ptp. Thus, stress wave velocities measured on pleural surface of isolated lungs correlated well with elastic moduli of lung parenchyma.     

The measurement and interpretation of Brillouin scattering in the lens of the eye

Brillouin scattering from hypersonic waves in the eye lenses of many animals has been observed with a multipass Fabry Perot interferometer. The measured values of speed and attenuation range widely among the different species and in different parts of any one lens. These variations correlate broadly with the observed stiffness and the densities that have been measured with a graded column. From the spectroscopic and density measurements high-frequency elastic moduli may be derived. The results are also evaluated at a macromolecular level in terms of scattering of hypersonic waves from spherical entities composed of the crystallins and their aggregates. Reasonable agreement is obtained for the hypersonic speed for lower protein concentration; the hypersonic attenuation and variation with scattering vector are consistent with the presence of large aggregates (of order 100 nm radius) in certain of the materials.     

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.     

Stress wave velocities in bovine patellar tendon.

The velocity of longitudinal stress waves in an elastic body is given by the square root of the ratio of its elastic modulus to its density. In tendinous and ligamentous tissue, the elastic modulus increases with strain and with strain rate. Therefore, it was postulated that stress wave velocity would also increase with increasing strain and strain rate. The purpose of this study was to determine the velocity of stress waves in tendinous tissue as a function of strain and to compare these values to those predicted using the elastic modulus derived from quasi-static testing. Five bovine patellar tendons were harvested and potted as bone-tendon-bone specimens. Quasi-static mechanical properties were determined in tension at a deformation rate of 100 mm/s. Impact loading was employed to determine wave velocity at various strain levels, achieved by preloading the tendon. Following impact, there was a measurable delay in force transmission across the specimen and this delay decreased with increasing tendon strain. The wave velocities at tendon strains of 0.0075, 0.015, and 0.0225 were determined to be 260 +/- 52 m/s, 360 +/- 71 m/s, and 461 +/- 94 m/s, respectively. These velocities were significantly (p < 0.01) faster than those predicted using elastic moduli derived from the quasi-static tests by 52, 45, and 41 percent, respectively. This study has documented that stress wave velocity in patellar tendon increases with increasing strain and is underestimated with a modulus estimated from quasi-static testing.     

Axial speed of sound is related to tendon's nonlinear elasticity

Axial speed of sound (SOS) measurements have been successfully applied to noninvasively evaluate tendon load, while preliminary studies showed that this technique also has a potential clinical interest in the follow up of tendon injuries. The ultrasound propagation theory predicts that the SOS is determined by the effective stiffness, mass density and Poisson's ratio of the propagating medium. Tendon stiffness characterizes the tissue's mechanical quality, but it is often measured in quasi-static condition and for entire tendon segments, so it might not be the same as the effective stiffness which determines the SOS. The objectives of the present study were to investigate the relationship between axial SOS and tendon's nonlinear elasticity, measured in standard laboratory conditions, and to evaluate if tendon's mass density and cross-sectional area (CSA) affect the SOS level. Axial SOS was measured during in vitro cycling of 9 equine superficial digital tendons. Each tendon's stiffness was characterized with a tangent modulus (the continuous derivative of the true stress/true strain curve) and an elastic modulus (the slope of this curve's linear region). Tendon's SOS was found to linearly vary with the square root of the tangent modulus during loading; tendon's SOS level was found correlated to the elastic modulus's square root and inversely correlated to the tendon's CSA, but it was not affected by tendon's mass density. These results confirm that tendon's tangent and elastic moduli, measured in laboratory conditions, are related to axial SOS and they represent one of its primary determinants.     

Fatigue evaluation of long cortical bone using ultrasonic guided waves

Bone fatigue fracture is a progressive disease due to stress concentration. This study aims to evaluate the long bone fatigue damage using the ultrasonic guided waves. Two-dimensional finite-difference time-domain method was employed to simulate the ultrasonic guided wave propagation in the long bone under different elastic modulus. The experiment was conducted on a 3.8 mm-thick bovine bone plate. The phase velocities of two fundamental guided modes, A1 and S1, were measured by using the axial transmission technique. Simulation shows that the phase velocities of guided modes A1 and S1 decrease with the increasing of the fatigue damage. After 20,000 cycles of fatigue loading on the bone plate, the average phase velocities of A1 and S1 modes were 6.6% and 5.3% respectively, lower than those of the intact bone. The study suggests that ultrasonic guided waves can be potentially used to evaluate the fatigue damage in long bones.     

Trabecular bone modulus-density relationships depend on anatomic site

One outstanding issue regarding the relationship between elastic modulus and density for trabecular bone is whether the relationship depends on anatomic site. To address this, on-axis elastic moduli and apparent densities were measured for 142 specimens of human trabecular bone from the vertebra (n=61), proximal tibia (n=31), femoral greater trochanter (n=23), and femoral neck (n=27). Specimens were obtained from 61 cadavers (mean+/-SD age=67+/-15 years). Experimental protocols were used that minimized end-artifact errors and controlled for specimen orientation. Tissue moduli were computed for a subset of 18 specimens using high-resolution linear finite element analyses and also using two previously developed theoretical relationships (Bone 25 (1999) 481; J. Elasticity 53 (1999) 125). Resultant power law regressions between modulus and density did depend on anatomic site, as determined via an analysis of covariance. The inter-site differences were among the leading coefficients (p<0.02), but not the exponents (p>0.08), which ranged 1.49-2.18. At a given density, specimens from the tibia had higher moduli than those from the vertebra (p=0.01) and femoral neck (p=0.002); those from the trochanter had higher moduli than the vertebra (p=0.02). These differences could be as large as almost 50%, and errors in predicted values of modulus increased by up to 65% when site-dependence was ignored. These results indicate that there is no universal modulus-density relationship for on-axis loading. Tissue moduli computed using methods that account for inter-site architectural variations did not differ across site (p>0.15), suggesting that the site-specificity in apparent modulus-density relationships may be attributed to differences in architecture.     

In vivo age- and sex-related creep of human lumbar motion segments and discs in pure centric tension

In vivo creep of human lumbar motion segments and discs subject to pure centric tension is presented, in terms of aging, sex and disc level. Time-related elongations of segments L3-4, L4-5 and L5-S1 were measured during the usual 20 min long traction hydrotherapy of patients, by using a computerized subaqual ultrasound measuring method [Kurutz et al., 2002a. Orvosi Hetilap 143 (13), 673-684; Kurutz et al., 2003. Journal of Bioengineering and Biomechanics 5 (1), 67-92]. Elongation of segments was considered as a change of the distance between two adjacent spinous processes. Based on these experiments, in vivo creep of human lumbar FSUs was investigated in centric tension, in terms of sex, age and disc level. Three-parameter rheological models were used to determine viscoelastic tensile moduli of human lumbar FSUs and discs. From three time-related measured elongation values, in vivo damping constants with creep functions were calculated for each segment, in terms of sex, aging and disc level. It has been demonstrated that initial elastic elongations decrease, concerning stiffness increase with aging. Similarly, tensile creep elongations decrease, damping properties increase with aging. Former observations concerning the difference in deformation propagation of men and women in time, have been verified by means of creep analysis: although males have higher initial elastic deformability, due to a smaller damping of females, the deformation propagation of women overtakes men in creep process. This tendency is more significant with aging. Increasing damping was observed in distal direction, both for males and females.     

Actin cytoskeleton stiffness grades metastatic potential of ovarian carcinoma Hey A8 cells via nanoindentation mapping

Recent studies have indicated that the nanoindentation measured stiffness of carcinoma adherent cells is in general lower than normal cells, thus suggesting that cell stiffness may serve as a bio-marker for carcinoma. However, the proper establishment of such a conclusion would require biophysical understanding of the underlying mechanism of the cell stiffness. In this work, we compared the elastic moduli of the actin cytoskeletons of Hey A8 ovarian carcinoma cells with and without metastasis (HM and NM), as measured by 2D atomic force microscopy (AFM) with low-depth nanoindentation via a rate-jump method. The results indicate clearly that HM cells showed lower actin cytoskeleton stiffness atop of their nucleus position and higher actin cytoskeleton stiffness at their rims, compared to NM cells, suggesting that the local stiffness on the cytoskeleton can reflect actin filament distribution. Immunofluorescence staining and scanning electron microscopy (SEM) also indicated that the difference in stiffness in Hey A8 cells with different metastasis is associated with their F-actin rearrangement. Finite-element modelling (FEM) shows that a migrating cell would have its actin filaments bundled together to form stress fibers, which would exhibit lower indentation stiffness than the less aligned arrangement of filaments in a non-migrating cell. The results here indicate that the actin cytoskeleton stiffness can serve as a reliable marker for grading the metastasis of adherent carcinoma cells due to their cytoskeleton change and potentially predicting the migration direction of the cells.     

Sound speed in pulmonary parenchyma

The time it takes audible sound waves to travel across a lobe of excised horse lung was measured. Sound speed, which is the slope in the relationship between transit time and distance across the lobe, was estimated by linear regression analysis. Sound-speed estimates for air-filled lungs varied between 25 and 70 m/s, depending on lung volume. These speeds are less than 5% of sound speed in tissue and less than 20% of sound speed in air. Filling the lung with helium or sulfur hexafluoride, whose free-field sound speeds are 970 and 140 m/s, respectively, changed sound speed +/- 10% relative to air filling. Reducing the ambient pressure to 0.1 atm reduced sound speed to 30% of its 1-atm value. Increasing pressure to 7 atm increased sound speed by a factor of 2.6. These results suggest that 1) translobar sound travels through the bulk of the parenchyma and not along airways or blood vessels, and 2) the parenchyma acts as an elastic continuum to audible sound. The speed of sound is given by c = (B/rho)1/2, where B is composite volumetric stiffness of the medium and rho is average density. In the physiologic state B is affected by ambient pressure and percent gas phase. The average density includes both the tissue and gas phases of the parenchyma, so it is dependent on lung volume. These results may be helpful in the quantification of clinical observations of lung sounds.     

Anisotropic propagation of Ca2+ waves in isolated cardiomyocytes.

Digital imaging microscopy of fluor-3 fluorescence was used to study the propagation of intracellular Ca2+ waves in isolated adult rat cardiomyocytes from 17 to 37 degrees C. Ca2+ waves spread in both transverse and longitudinal direction of a myocyte. Transverse propagation was pronounced in waves starting from a focus at the edge of a myocyte and in waves following an irregular, curved path (spiral waves). For the former type of waves, propagation velocities were determined. Both transverse and longitudinal wave components propagated at constant velocity ranging from 30 to 125 micron/s. Myocytes were anisotropic with respect to wave propagation: waves propagated faster in the longitudinal than in the transverse direction. The ratio between longitudinal and transverse velocity increased from 1.30 at 17 degrees C to 1.55 at 37 degrees C. Apparent activation energies for transverse and longitudinal wave propagation were estimated to be -20 kJ/mol, suggesting that these processes are limited by diffusion of Ca2+. Direction-dependent propagation velocities are interpreted to result from the highly ordered structure of the myocytes, especially from the anisotropic arrangement of diffusion obstacles such as myofilaments and mitochondria.     

Elastic properties of external cortical bone in the craniofacial skeleton of the rhesus monkey

Knowledge of elastic properties and of their variation in the cortical bone of the craniofacial skeleton is indispensable for creating accurate finite-element models to explore the biomechanics and adaptation of the skull in primates. In this study, we measured elastic properties of the external cortex of the rhesus monkey craniofacial skeleton, using an ultrasonic technique. Twenty-eight cylindrical cortical specimens were removed from each of six craniofacial skeletons of adult Macaca mulatta. Thickness, density, and a set of longitudinal and transverse ultrasonic velocities were measured on each specimen to allow calculation of the elastic properties in three dimensions, according to equations derived from Newton's second law and Hooke's law. The axes of maximum stiffness were determined by fitting longitudinal velocities measured along the perimeter of each cortical specimen to a sinusoidal function. Results showed significant differences in elastic properties between different functional areas of the rhesus cranium, and that many sites have a consistent orientation of maximum stiffness among specimens. Overall, the cortical bones of the rhesus monkey skull can be modeled as orthotropic in many regions, and as transversely isotropic in some regions, e.g., the supraorbital region. There are differences from human crania, suggesting that structural differences in skeletal form relate to differences in cortical material properties across species. These differences also suggest that we require more comparative data on elastic properties in primate craniofacial skeletons to explore effectively the functional significance of these differences, especially when these differences are elucidated through modeling approaches, such as finite-element modeling.     

Hypertonicity triggers RhoA-dependent assembly of myosin-containing striated polygonal actin networks in endothelial cells

Electrical slow waves determine the timing and force of peristaltic contractions in the stomach. Slow waves originate from a dominant pacemaker in the orad corpus and propagate actively around and down the stomach to the pylorus. The mechanism of slow-wave propagation is controversial. We tested whether Ca(2+) entry via a voltage-dependent, dihydropyridine-resistant Ca(2+) conductance is necessary for active propagation in canine gastric antral muscles. Muscle strips cut parallel to the circular muscle were studied with intracellular electrophysiological techniques using a partitioned-chamber apparatus. Slow-wave upstroke velocity and plateau amplitude decreased from the greater to the lesser curvature, and this corresponded to a decrease in the density of interstitial cells of Cajal in the lesser curvature. Slow-wave propagation velocity between electrodes impaling cells in two regions of muscle and slow-wave upstroke and plateau were measured in response to experimental conditions that reduce the driving force for Ca(2+) entry or block voltage-dependent Ca(2+) currents. Nicardipine (0.1-1 microM) did not affect slow-wave upstroke or propagation velocities. Upstroke velocity, amplitude, and propagation velocity were reduced in a concentration-dependent manner by Ni(2+) (1-100 microM), mibefradil (10-30 microM), and reduced extracellular Ca(2+) (0.5-1.5 mM). Depolarization (by 10-15 mM K(+)) or hyperpolarization (10 microM pinacidil) also reduced upstroke and propagation velocities. The higher concentrations (or lowest Ca(2+)) of these drugs and ionic conditions tested blocked slow-wave propagation. Treatment with cyclopiazonic acid to empty Ca(2+) stores did not affect propagation. These experiments show that voltage-dependent Ca(2+) entry is obligatory for the upstroke phase of slow waves and active propagation.     

Concrete density estimation of linac bunker walls using impact-echo testing

PurposeTo estimate the concrete density of a newly constructed bunker using impact-echo testing prior to the installation of the linear accelerator.MethodsA newly constructed bunker showed visible honeycombing after the removal of the construction formwork. Impact-echo testing, which is based on the propagation and reflection of elastic waves in solids, was applied to confirm the bunker shielding integrity. A mechanical impact on the bunker wall generates a stress pulse, which propagates through the wall and is reflected or refracted by voids or changes in material characteristics such as density. Surface displacements caused by the reflected waves are recorded by a transducer, located near the impact point. The resulting displacement-time curves are analysed in the frequency domain for anomalies. The dominant frequencies are related to the depths from which stress waves are reflected within the structure. If the dynamic elastic modulus and Poisson ratio of the concrete are known, then the measured velocity of the so-called P-wave can be related to the concrete density.ResultsValidation measurements on a wall with known concrete density gave an estimate within 3% of the true density. Measured velocities on the honeycombed wall ranged from 3750 m/s to 4300 m/s, corresponding to densities of 2894 kg/m³ and 2201 kg/m³ respectively, with the majority of estimated densities ranging from 2307 kg/m³ to 2544 kg/m³.A radiation survey after the installation of the linear accelerator confirmed adequate shielding.ConclusionImpact-echo testing presents a viable solution to confirm bunker shielding integrity before the installation of a linac.     

Elastic moduli of lungs during postnatal development in the piglet

Several manifestations of lung disease during infancy suggest that mechanical interdependence can be relatively high in newborn lungs. To test this possibility, we measured elastic moduli and pleural membrane tension in lungs excised from piglets ranging in age from less than 12 h to 85 days. Near maximum inflation, newborn lungs (less than 12 h, n = 6) had no detectable pleural membrane tension, although 3- to 5-day-old lungs (n = 6) had tension greater than 5,000 dyn/cm. In contrast, parenchymal recoil was greater in the newborn lungs [19.3 +/- 3.0 (SD) vs. 14.3 +/- 2.4 cmH2O at 90% of maximum inflation volume, P less than 0.01]. Shear moduli were higher (13.5 +/- 4.6 vs. 9.2 +/- 1.5 cmH2O at 15 cmH2O transpulmonary pressure, P less than 0.05) and Poisson ratios were lower in the newborn lungs as compared with the 3- to 5-day-old lungs. Postnatal lung growth between 3 and 85 days was characterized by 1) a constant shear modulus (0.6 times transpulmonary pressure); 2) decrease in the bulk modulus (from 6.8 to 5.1 times transpulmonary pressure, P less than 0.005); and 3) evidence of gas trapping at progressively higher transpulmonary pressures. Therefore, growth of parenchyma in the piglet lung is associated with reduced stiffness to volume change but with no effect on overall stiffness to shape change. Nevertheless, a relatively great stiffness to shape change occurs transiently in newborn piglet lungs.     

Sound velocity and elasticity of tetragonal lysozyme crystals by Brillouin spectroscopy

Quasilongitudinal sound velocities and the second-order elastic moduli of tetragonal hen egg-white lysozyme crystals were determined as a function of relative humidity (RH) by Brillouin scattering. In hydrated crystals the measured sound velocities in the [110] plane vary between 2.12 +/- 0.03 km/s along the [001] direction and 2.31 +/- 0.08 km/s along the [110] direction. Dehydration from 98% to 67% RH increases the sound velocities and decreases the velocity anisotropy in (110) from 8.2% to 2.0%. A discontinuity in velocity and an inversion of the anisotropy is observed with increasing dehydration providing support for the existence of a structural transition below 88% RH. Brillouin linewidths can be described by a mechanical model in which the phonon is coupled to a relaxation mode of hydration water with a single relaxation time of 55 +/- 5 ps. At equilibrium hydration (98% RH) the longitudinal moduli C(11) + C(12) + 2C(66) = 12.81 +/- 0.08 GPa, C(11) = 5.49 +/- 0.03 GPa, and C(33) = 5.48 +/- 0.05 GPa were directly determined. Inversion of the measured sound velocities in the [110] plane constrains the combination C(44) + (1/2)C(13) to 2.99 +/- 0.05 GPa. Further constraints on the elastic tensor are obtained by combining the Brillouin quasilongitudinal results with axial compressibilities determined from high-pressure x-ray diffraction. We constrain the adiabatic bulk modulus to the range 2.7-5.3 GPa.     

Anatomical variation of orthotropic elastic moduli of the proximal human tibia

The anatomical variation of orthotropic elastic moduli of the cancellous bone from three human proximal tibiae was investigated using an ultrasonic technique. With this technique, it was possible to measure three orthogonal elastic moduli and three shear moduli from cubic specimens of cancellous bone as small as 8 mm per side. Correlation with mechanical tensile testing has shown this technique to offer a precise measure of cancellous modulus (Eten = 0.94Eult + 144.6 MPa, r2 = 0.96, n = 34). The cancellous bone of the proximal tibia was found to be very inhomogeneous, with the axial modulus ranging between 340 and 3350 MPa. A course map is presented, showing measured Young's moduli as a function of anatomical position. The anisotropy of the cancellous bone, determined by the relative differences between the three orthogonal moduli, was shown to be relatively constant over the entire range of cancellous densities tested. The relationship between the axial elastic modulus and the apparent density was found to be approximately linear, as reported by others for proximal tibial cancellous bone.     

A comparison of cortical elastic properties in the craniofacial skeletons of three primate species and its relevance to the study of human evolution

When a force is applied to an object, the resulting pattern of strain is a function of both the object's geometry and its elastic properties. Thus, knowledge of elastic properties in craniofacial cortical bone is indispensable for exploring the biomechanics and adaptation of primate skulls. However, elastic properties, such as density and stiffness, cannot be measured in all species, particularly extinct species known only from fossils. In order for advanced engineering techniques such as finite element analysis (FEA) to be applied to questions of primate and hominid craniofacial functional morphology, it is important to understand interspecific patterns of variation in elastic properties. We hypothesized that closely related species would have similar patterns of bone elastic properties, and that similarities with extant species should allow reasonable predictions of elastic properties in the skeletons of extinct primate species. In this study, we tested this hypothesis by measuring elastic properties in five areas of the external cortex of the baboon craniofacial skeleton using an ultrasonic technique, and by comparing the results to existing data from macaque and human crania. Results showed that cortical density, thickness, elastic and shear moduli, and anisotropy varied among areas in the baboon cranium. Similar variation had previously been found in rhesus and human crania, suggesting area-specific elastic patterns in the skulls of each species. Comparison among species showed differences, suggesting species-specific patterns. These patterns were more similar between macaques and baboons for density, maximum elastic and shear stiffness, and anisotropy than between either of these and humans. This finding demonstrates that patterns of cortical elastic properties are generally similar in closely related primate species with similar craniofacial morphology. Thus, reasonable estimates of cortical bone elastic properties should be possible for extinct species through the study of phylogenetically related and functionally similar modern forms. For example, reasonable elastic property estimates of cortical bone from fossil hominid skulls should be possible once adequate information about such properties in extant great apes is added to our current data from humans, macaques, and baboons. Such data should eventually allow FEA of craniofacial function in fossil hominids.     

Mechanical wave propagation on nerve axons

The mechanical waves which may occur in or on a nerve axon are considered. It is shown that under rather general assumptions mechanical waves with phase velocities corresponding to nerve impulse propagation velocities belong to the natural modes of the axon membrane. This means that the mechanical disturbances which are connected with almost all models of nerve impulse propagation are readily supported by the axon, suggesting a possibility of interaction between electrical and mechanical events in the axon.