Validation of a full body finite element model (THUMS) for running-type impacts to the lower extremity

The purpose of this study was to determine whether modifying an existing, highly biofidelic full body finite element model [total human model for safety (THUMS)] would produce valid amplitude and temporal shock wave characteristics as it travels proximally through the lower extremity. Modifying an existing model may be more feasible than developing a new model, in terms of cost, labour and expertise. The THUMS shoe was modified to more closely simulate the material properties of a heel pad. Relative errors in force and acceleration data from experimental human pendulum impacts and simulated THUMS impacts were 22% and 54%, respectively, across the time history studied. The THUMS peak acceleration was attenuated by 57.5% and took 19.7 ms to travel proximally along the lower extremity. Although refinements may be necessary to improve force and acceleration timing, the modified THUMS represented, to a certain extent, shock wave propagation and attenuation demonstrated by living humans under controlled impact conditions.     

Transthoracic Doppler echocardiography – noninvasive diagnostic window for coronary flow reserve assessment

Background

Strain Rate Imaging shows the filling phases of the left ventricle to consist of a wave of myocardial stretching, propagating from base to apex. The propagation velocity of the strain rate wave is reduced in delayed relaxation. This study examined the relation between the propagation velocity of strain rate in the myocardium and the propagation velocity of flow during early filling.

Methods

12 normal subjects and 13 patients with treated hypertension and normal systolic function were studied. Patients and controls differed significantly in diastolic early mitral flow measurements, peak early diastolic tissue velocity and peak early diastolic strain rate, showing delayed relaxation in the patient group. There were no significant differences in EF or diastolic diameter.

Results

Strain rate propagation velocity was reduced in the patient group while flow propagation velocity was increased. There was a negative correlation (R = -0.57) between strain rate propagation and deceleration time of the mitral flow E-wave (R = -0.51) and between strain rate propagation and flow propagation velocity and there was a positive correlation (R = 0.67) between the ratio between peak mitral flow velocity/strain rate propagation velocity and flow propagation velocity.

Conclusion

The present study shows strain rate propagation to be a measure of filling time, but flow propagation to be a function of both flow velocity and strain rate propagation. Thus flow propagation is not a simple index of diastolic function in delayed relaxation.     

Modulation of the shape and speed of a chemical wave in an unstirred Belousov–Zhabotinsky reaction by a rotating magnet

The objective of this study was to observe whether a rotating magnetic field (RMF) could change the anomalous chemical wave propagation induced by a moderate‐intensity gradient static magnetic field (SMF) in an unstirred Belousov–Zhabotinsky (BZ) reaction. The application of the SMF (maximum magnetic flux density = 0.22 T, maximum magnetic flux density gradient = 25.5 T/m, and peak magnetic force product (flux density × gradient) = 4 T²/m) accelerated the propagation velocity in a two‐dimensional pattern. Characteristic anomalous patterns of the wavefront shape were generated and the patterns were dependent on the SMF distribution. The deformation and increase in the propagation velocity were diminished by the application of an RMF at a rotation rate of 1 rpm for a few minutes. Numerical simulation by means of the time‐averaged value of the magnetic flux density gradient or the MF gradient force over one rotation partially supported the experimental observations. These considerations suggest that RMF exposure modulates the chemical wave propagation and that the degree of modulation could be, at least in part, dependent on the time‐averaged MF distribution over one rotation. Bioelectromagnetics 34:220–230, 2013. © 2012 Wiley Periodicals, Inc.     

The Influence of a gradient static magnetic field on an unstirred Belousov-Zhabotinsky reaction

It is believed that static magnetic fields (SMF) cannot affect the pattern formation of the Belousov-Zhabotinsky (BZ) reaction, which has been frequently studied as a simplified experimental model of a nonequilibrium open system, because SMF produces no induced current and the magnetic force of SMF far below 1 T is too low to expect the effects on electrons in the BZ reaction. In the present study, we examined whether the velocity of chemical waves in the unstirred BZ reaction can be affected by a moderate-intensity SMF exposure depending on the spatial magnetic gradient. The SMF was generated by a parallel pair of attracting rectangular NdFeB magnets positioned opposite each other. The respective maximum values of magnetic flux density (B(max)), magnetic flux gradient (G(max)), and the magnetic force product of the magnetic flux density its gradient (a magnetic force parameter) were 206 mT, 37 mT/mm, and 3,000 mT(2)/mm. The ferroin-catalyzed BZ medium was exposed to the SMF for up to 16 min at 25 degrees C. The experiments demonstrated that the wave velocity was significantly accelerated primarily by the magnetic gradient. The propagation of the fastest wave front indicated a sigmoid increase along the peak magnetic gradient line, but not along the peak magnetic force product line. The underlying mechanisms of the SMF effects on the anomalous wave propagation could be attributed primarily to the increased concentration gradient of the paramagnetic iron ion complexes at the chemical wave fronts induced by the magnetic gradient.     

Equine cortical bone exhibits rising R-curve fracture mechanics

Previous studies of the fracture properties of cortical bone have suggested that the fracture toughness increases with crack length, which is indicative of rising R-curve behavior. Based on this indirect evidence and the similarity of bone to ceramic matrix composites, we hypothesized that bone would exhibit rising R-curve behavior in the transverse orientation and that the characteristics of the R-curves would be regionally dependent within the cortex due to variations in bone microstructure and toughening mechanisms. To test these hypotheses, we conducted R-curve experiments on specimens from equine third metacarpal bones using standard fracture mechanics testing methods. Compact type specimens from the dorsal and lateral regions in the middle of the diaphysis were oriented for crack propagation transverse to the longitudinal axis of the bone.The test results demonstrate that equine cortical bone exhibits rising R-curve behavior during transverse crack propagation as hypothesized. Statistical analyses of the crack growth initiation toughness, K0, the peak toughness, Kpeak, and the crack extension at peak toughness, deltaa, revealed significant regional differences in these characteristics. Specifically, the lateral cortex displayed higher crack growth initiation and peak toughnesses. The dorsal cortex exhibited greater crack extension at the peak of crack growth resistance. Scanning electron microscopy revealed osteon pullout on fracture surfaces from the dorsal cortex and but not in the lateral cortex. Taken together, the significant differences in R-curves and the SEM fractography indicate that the fracture mechanisms acting in equine cortical bone are regionally dependent.     

Resonance interaction of electrons with a slow transverse wave in a weakly inhomogeneous plasma

Excitation of a circularly polarized slow wave by external sources and its subsequent propagation in a weakly inhomogeneous plasma with a positive density gradient are described in terms of the adiabatic approach. It is shown that the wave dispersion is mainly determined by the ratio between the contributions of trapped and nonresonant untrapped electrons to the total wave current. The relationship between the wave amplitude and its phase velocity and the limiting phase velocity above which the wave is strongly damped are found using the energy balance equation and the dispersion relation.     

Kinematics of human spermatozoa

A microcinematographic (50 f/s) study was performed on motile human spermatozoa. Eighty percent were found to have a linear trajectory and a pseudo-sinusoidal head displacement pattern. Throughout their progression, the spermatozoa periodically rotated on their longitudinal axis at a frequency equal to that of flagellar wave formation. These waves were found always to begin on the same side of the cell and to propagate in the flattened plane of the head until the moment of rotation. At this time the wave had reached a point near the middle of the flagellum. Beyond this point, the flagellum moves out of the plane of the head. Different variables used to characterize the movement of spermatozoa included the velocity of progression, amplitude and velocity of head displacement, frequency of rotation, wave amplitude, and propagation velocity of the flagellar wave. Among these variables, it was the propagation velocity of the wave that was found to be best correlated with the velocity of spermatozoan progression. This flagellar wave exhibited two stages, one of initiation and one of propagation.     

Variation of repetitive cortical spreading depression waves is related with relative refractory period: a computational study

Cortical spreading depression (CSD) is an important experimental model for diseases such as stroke, epilepsy and migraine. Previous observations indicated that the amplitude and velocity of the typical direct current potential shift during repetitive CSD waves were varying. The recovery state of the tissue was found related with the variation of successive CSD waves. A computational model in this paper aimed to investigate the role of relative refractory period of CSD. This model simulated that continuous injection of KCl solution induced repetitive CSD waves. The first CSD wave often had a larger amplitude and faster velocity than those of the succeeding secondary waves. The relative refractory period lasted much longer than the recovery of ions turbulence. If the induction interval was long enough for recovery, a series of CSD waves would have the same profile as the first one. In the relative refractory period, an early stimulation might lead to a late initiation of CSD, i.e., “haste makes waste”. The amplitude and velocity of CSD waves were found increasing with the initiation interval and asymptotic to those of the first CSD wave. This study verified that the propagation dynamics of CSD waves is modulated by the relative refractory period. It suggested that the refractory period is critical for preventing undesirable CSD waves.     

Stress wave propagation in bone

The traveling wave characteristics for a single compressive pulse were studied in fresh and embalmed human long bones. The stress wave was generated by the longitudinal impact of a steel ball on one end of a bone and was monitored by bonded strain gages. The dynamic properties, namely velocity, attenuation coefficient and dispersion were correlated with the mineral density, porosity, and cross-sectional area of the specimens. Statistically significant relationships were found between several of these parameters. These stress wave propagation characteristics are important for our understanding of the dynamic loading of bone and they may also provide a basis for the development of noninvasive techniques for studies of diseased or fractured bone.     

Bone material properties and mineral matrix contributions to fracture risk or age in women and men

The strength of bone is related to its mass and geometry, but also to the physical properties of the tissue itself. Bone tissue is composed primarily of collagen and mineral, each of which changes with age, and each of which can be affected by pharmaceutical treatments designed to prevent or reverse the loss of bone. With age, there is a decrease in collagen content, which is associated with an increased mean tissue mineralization, but there is no difference in cross-link levels compared to younger adult bone. In osteoporosis, however, there is a decrease in the reducible collagen cross-links without an alteration in collagen concentration; this would tend to increase bone fragility. In older people, the mean tissue age (MTA) increases, causing the tissue to become more highly mineralized. The increased bone turnover following menopause may reduce global MTA, and would reduce overall tissue mineralization. Bone strength and toughness are positively correlated to bone mineral content, but when bone tissue becomes too highly mineralized, it tends to become brittle. This reduces its toughness, and makes it more prone to fracture from repeated loads and accumulated microcracking. Most approved pharmaceutical treatments for osteoporosis suppress bone turnover, increasing MTA and mineralization of the tissue. This might have either or both of two effects. It could increase bone volume from refilling of the remodeling space, reducing the risk for fracture. Alternatively, the increased MTA could increase the propensity to develop microcracks, and reduce the toughness of bone, making it more likely to fracture. There may also be changes in the morphology of the mineral crystals that could affect the homogeneity of the tissue and impact mechanical properties. These changes might have large positive or negative effects on fracture incidence, and could contribute to the paradox that both large and small increases in density have about the same effect on fracture risk. Bone mineral density measured by DXA does not discriminate between density differences caused by volume changes, and those caused by changes in mineralization. As such, it does not entirely reflect material property changes in aging or osteoporotic bone that contribute to bone's risk for fracture.     

Wave propagation characteristics in long bones to diagnose osteoporosis

A mathematical model of stress wave propagation in bone is developed assuming a long bone to be a thick-walled, long cylindrical shell filled with a fluid. The calculated phase and group velocities in adult human femurs were found to be a function of the wave number and they were different for population groups of above and below 55 yr of age. The velocities were also sex dependent, being different for males and females of the same age group. Diagnostic methods based on the measurement of wave propagation characteristics may potentially be used to measure the structural changes in long bones due to osteoporosis.     

Ion-acoustic solitons in Bi-Ion dusty plasma

The propagation of ion-acoustic solitons in a warm dusty plasma containing two ion species is investigated theoretically. Using an approach based on the Korteveg de Vries equation, it is shown that the critical value of the negative ion density that separates the domains of existence of compression and rarefaction solitons depends continuously on the dust density. A modified Korteveg de Vries equation for the critical density is derived in the higher order of the expansion in the small parameter. It is found that the nonlinear coefficient of this equation is positive for any values of the dust density and the masses of positive and negative ions. For the case where the negative ion density is close to its critical value, a soliton solution is found that takes into account both the quadratic and cubic nonlinearities. The propagation of a solitary wave of arbitrary amplitude is investigated by the quasi-potential method. It is shown that the range of dust densities around the critical value within which solitary waves with positive and negative potentials can exist simultaneously is relatively wide.     

A model of the smooth pursuit eye movement system

Human, horizontal, smooth-pursuit eye movements were recorded by the search coil method in response to Rashbass step-ramp stimuli of 5 to 30 deg/s. Eye velocity records were analyzed by measuring features such as the time, velocity and acceleration of the point of peak acceleration, the time and velocity of the peaks and troughs of ringing and steady-state velocity. These values were averaged and mean responses reconstructed. Three normal subjects were studied and their responses averaged. All showed a peak acceleration-velocity saturation. All had ringing frequencies near 3.8 Hz and the mean steady-state gain was 0.95.It is argued that a single, linear forward path with any transfer function G(s) and a 100 ms delay (latency) cannot simultaneously simulate the initial rise of acceleration and ring at 3.8 Hz based on a Bode analysis. Also such a simple negative feedback model cannot have a steady-state gain greater than 1.0; a situation that occurs frequently experimentally. L.R. Young's model, which employs internal positive feedback to eliminate the built-in unity negative feedback, was felt necessary to resolve this problem and a modification of that model is proposed which simulates the data base. Acceleration saturation is achieved by borrowing the idea of the local feedback model for saccades so that one nonlinearity can account for the acceleration-velocity saturation: the main sequence for pursuit. Motor plasticity or motor learning, recently demonstrated for pursuit, is also incorporated and simulated.It was noticed that the offset of pursuit did not show the ringing seen in the onset so this was quantified in one subject. Offset velocity could be characterized by a single exponential with a time constant of about 90 ms. This observation suggests that fixation is not pursuit at zero velocity and that the pursuit system is turned on when needed and off during fixation.     

Temporal-spatial reach parameters derived from inertial sensors correlate to neurodevelopment in toddlers born preterm

Temporal-spatial reach parameters are revealing of upper-limb function in children with motor impairments, but have not been quantified in a toddler population. This work quantitatively characterizes temporal-spatial reach in typically-developing (TD) and very-low-birth-weight (VLBW) preterm toddlers, who are at increased risk of motor impairment. 47 children born VLBW (<1500 g birth-weight; ≤32 weeks gestation) and 22 TD children completed a reaching assessment at 18–22 months of age, adjusted for prematurity. Inertial sensors containing accelerometers, gyroscopes and magnetometers were fixed to toddlers’ wrists while they reached for a cube. Reach time, path length, velocity at contact, peak velocity magnitude and timing, acceleration at contact, and peak acceleration were derived from inertial-sensor and high-speed video data. Preterm children also received the Bayley Scales of Infant Development—3rd Edition (BSID-III). Compared to TD toddlers, preterm toddlers had significantly different reach path length, velocity at contact, peak velocity magnitude and timing, acceleration at contact, and peak acceleration. Among preterm toddlers, decreased reach time (rho = −.346, p = .018), decreased time to peak velocity (r = −.390, p = .007), and increased peak acceleration (r = .298, p = .044) correlated to higher BSID-III fine motor scores. Toddlers with below-average fine motor scores had significantly higher peak and contact velocity. Preterm toddlers demonstrated substantial differences in temporal-spatial reach parameters compared to TD toddlers, and evidence indicated several reach parameters were revealing of function and may be useful as a clinical assessment.     

Influence of geometric taper on the derivation of the true propagation coefficient using a three point method

We studied the effect of geometric taper on the derivation of the true propagation coefficient from three pressures determined 10 cm apart ('three-point method'). For this purpose the true propagation coefficients of a uniform latex tube (length 50 cm, outer diameter 12.73 mm, Womersley phase velocity 6.23-6.42 ms-1 (1-10 Hz), Womersley damping coefficient 0.05-0.14 m-1 (1-10 Hz) and of a tapered latex tube (length 50 cm, outer diameter varying from 15.88 to 9.45 mm, in the middle section with same properties as the uniform tube) were determined. The real part of the true propagation coefficient (the damping coefficient) was compared with apparent damping, and with the damping coefficient calculated using Womersley's theory. The imaginary part of the true propagation coefficient (the phase coefficient) was expressed in terms of phase velocity. True phase velocity was compared with measurements of apparent phase velocity, foot-to-foot velocity, and calculations of phase velocity parameters Womersley's theory and the Moens-Korteweg equation. The results show that in the uniform tube the three-point propagation coefficient is in agreement with all other estimates. Taper causes an error in the three-point propagation coefficient. At some frequencies the damping is reversed to amplification (values up to -2 m-1) and the phase velocity may be both overestimated or underestimated (up to 50%). The overestimation of true damping as reported in the literature cannot be explained from vessel taper.     

The speed of sound through trabecular bone predicted by Biot theory

Cancellous bone is a highly porous material filled with fluid. The mechanical properties of cancellous bone determine whether the bone is normal or osteoporotic. Wave propagation can be used to measure the elastic constants of cancellous bone. Recently, poroelasticity theory has been used to predict the elastic constants of cancellous bone from the wave velocities. In this study, it is shown that the fast wave, predicted by the Biot theory, corresponds to the wave penetrating the trabeculae, while the slow wave is determined by the interaction between the trabeculae and the fluid. The trabecular shape does not affect the wave velocity significantly when using the variable, which is determined by the microstructure, and the slow wave velocity decreases after the porosity reaches 80%.     

Phase velocity measurement of flexural waves in human tibia

A method is proposed to measure the phase velocities of the first mode of flexural waves in the human tibia. Keeping in mind the dispersive nature of flexural waves in beam-like bodies, a two point measurement method was developed which enables the calculation of the phase difference of the propagating wave between two observation points for a selected frequency range. The method for dispersion analysis was tested with synthetic and observed signals for a cylinder. This was done by comparison of observed radial acceleration on the surface of a PVC-cylinder with computed synthetic signals consisting only of first mode flexural waves. An in vivo study was performed with 43 subjects. The phase velocity measurements in human tibia show a good correlation with the bone mineral content estimated by means of the Cameron-Sorenson technique (Cameron and Sorenson, 1963). The bone mineral loss is reflected by decreasing phase velocities. This indicates that phase velocity measurements of flexural waves can be used for an estimation of bone mineral content in vivo.     

Bone mineral density is inversely related to parathyroid hormone in adolescent girls.

Preventive programs aimed at maximizing peak bone mass as a way of reducing the risk of osteoporotic fractures later in life should take into account the contribution of nutritional factors to bone mass accumulation in young age. The role of calcium and energy intakes on radial mineral density was investigated in 200 healthy girls (aged 11-15 yr) simultaneously evaluating serum changes of insulin-like growth factor-I (IGF-I), parathyroid hormone (PTH) and osteocalcin (OC). Dietary calcium and energy intakes were assessed by a 3-day food record method, bone mineral density (BMD) was performed at ultradistal (ud) and proximal (pr) radial sites using dual energy X-ray absorptiometry. Calcium consumption below the levels suggested by Dietary Reference Intakes in more than 80% of population studied was not related to BMD, which in turn markedly increased in post-compared to premenarcheal girls. Interestingly, in a multiple regression analysis PTH was inversely related to BMD after adjustment for calcium intake, bone age and menarche. Serum IGF-I was positively associated to energy intakes and bone age in girls before menarche, who exhibited the highest values of OC. Our data highlighted the role of food habits in modulating some hormonal response that might influence bone mineral apposition during adolescent age. Low calcium consumption associated to enhanced PTH values, if persisting, could be responsible for reduced rate of gain in bone mineral density. Thus, to optimize bone mineralization during the critical period of rapid body growth adequate intakes of calcium and energy should be recommended.