Identification of in-vivo vibration modes of human tibiae by modal analysis

When attempting to evaluate the mechanical properties of human bones in vivo by mechanical vibration analysis, some essential requirements must be met. A quantitative relation between measured vibration parameters (e.g., natural frequency) and mechanical bone properties must be available, in-vivo vibration modes should correctly be identified and the associated natural frequencies reproducibly and accurately measured, the influence of joints and soft tissues must be known. These problems were addressed by modal analysis (i.e., experimental determination of natural frequencies, mode shapes and damping ratios) of human tibiae in the following situations: 1) dry excised tibiae, 2) fresh excised tibiae, 3) in-vivo tibiae, 4) tibiae in an amputated leg, in different steps of dissection. In the in-vivo measuring conditions used by the authors, the tibia vibration is practically free-free. Two single bending modes (at +/- 270 Hz and +/- 340 Hz, respectively), each of them corresponding with one principal direction for bending, were identified. The difference between the natural frequencies observed in vivo and those of fresh excised tibiae is almost completely caused by the effect of muscles (added mass and damping), whereas joints and skin play only a minor role. Frequency differences between fresh and dry excised tibiae are largely accounted for by the absence of bone marrow in the latter.     

Assessment of tibial stiffness by vibration testing in situ--III. Sensitivity of different modes and interpretation of vibration measurements

Post mortem vibration measurements on one human tibia during gradual transection reveal the vibration modes and frequencies of a tibia during a simulated healing. The modes are identified in a tibia in an above knee amputation specimen with the leg in two positions: hanging down with the knee flexed (90 degrees) and supported in a special designed bone clamping splint (knee flexed 45 degrees). The vibration measurements are analysed using Modal Analysis and are translated to mechanical stiffness by mathematical modelling. The single bending 'free-free' mode turned out to be more sensitive to weakening of one cross-section than the 'rigid body' and single bending 'hinged-spring' modes. The error on the assessed value of the stiffness is a multiple of the error on the measured frequencies. This multiplication factor decreases for more sensitive modes. In this experiment, the results are accurate enough to reflect the asymmetric weakening imposed upon the tibia. Attempts are made towards automatization of the measurement and analysis in order to get a system for clinical use. The actual system is still too cumbersome and time consuming for standard clinical use.     

Nonlinear analysis of the dynamics of the human balance control system during fixation and smooth pursuit of visual target

The similarity between the dynamics of the human balance control system in the frontal and sagittal planes during the fixation of visual stimulus and smooth pursuit of its sinusoidal movements in the horizontal plane with a frequency of 0.1 or 0.01 Hz (so-named fast and slow pursuit) has been investigated by the nonlinear method of analysis. The experiments were carried out according to the notion that it is possible to describe the process of orthograde standing by a two-segment model--upper and lower segments which are connected by a hip joint (other joints were fixed). It was shown that during fixation the similarity between the dynamics of orthostatic control system in the frontal plane is higher than in the sagittal plane. A slow pursuit does not influence the similarity, but a fast one decreases the similarity in the frontal plane. The indices of similarity between the dynamics of the system in the sagittal plane for all the conditions are close and do not differ significantly. The changes in similarity during fast pursuit are supposed to be connected with the different inertia of eyes and body movements. The differences between dynamic similarity in the frontal and sagittal planes are probably connected with the peculiarities of both balance control during joint fixation and AP-ML control (Winter et al., 1993) under conditions investigated.     

Development of a three-dimensional finite element model of a human tibia using experimental modal analysis.

The modal analysis of a human tibia consisted of characterizing its dynamic behavior by determining natural frequency, damping ratio and mode shapes. Two methods were used to perform the modal analysis: (1) a finite element method (structural model); (2) an experimental modal analysis (modal model). The experimental modal model was used to optimize the structural model. After optimization, differences in results between the two models were found to be due only to mechanical properties and mass distribution. The influences of boundary conditions and geometric properties (such as inertia and length) were eliminated by the finite element model itself. The percent relative error between the two methods was approximately 3%, corresponding to the standard deviation of the measured frequencies. For the frequency range considered, the mode shapes were bending modes in two different vibration planes (latero-medial and sagittal), with a slight torsion effect due to the twisted geometry of the tibia.     

Directional and frequency characteristics of auditory receptors in midges (Diptera,Chironomidae)

Individual characteristic frequencies and directional sensitivity of the Johnston’s organ auditory receptors were measured in the midges Chironomus plumosus L. using the method of positive feedback stimulation: responses of receptors recorded with a glass microelectrode from their axons in the antennal nerve were amplified and fed to the stimulating speaker. With the amplitude and the stimulating signal phase properly adjusted, the whole feedback loop fell into auto-excitation with the frequency of oscillations close to the characteristic frequency of the receptor. Three separate groups of receptors were found with mean frequencies of 180, 221, and 264 Hz. These groups differ in their directional properties: the low-frequency receptors are mostly sensitive dorsoventrally, while the directional maxima of mid- and high-frequency ones are combined to provide equal sensitivity in the plane perpendicular to the flagellum. Our data suggest that in Chironomidae a single Johnston’s organ together with the antenna can provide spatial localization of conspecific sounds and also perform the initial stages of frequency analysis.     

Effects of low-pass filter combinations on lower extremity joint moments in distance running

Inverse dynamics is a standard tool in biomechanics, which requires low-pass filtering of external force and kinematic signals. Unmatched filtering procedures are reported to affect joint moment amplitudes in high impact movements, like landing or cutting, but are also common in the analysis of distance running. We analyzed the effects of cut-off frequencies in 94 rearfoot runners at a speed of 3.5 m/s. Additionally, we investigated whether the evaluation of footwear interventions is affected by the choice of cut-off frequencies. We performed 3D inverse dynamics for the hip, knee and ankle joints using different low-pass filter cut-off frequency combinations for a recursive fourth-order Butterworth filter. We observed fluctuations of joint moment curves in the first half of stance, which were most pronounced for the most unmatched cut-off frequency combination (kinematics: 10 Hz; ground reaction forces (GRFs): 100 Hz) and for more proximal joints. Peak sagittal plane hip joint moments were altered by 94% on average. We observed a change in the ranking of subjects based on joint moment amplitude. We found significant (p < 0.001) footwear by cut-off frequency combination interaction effects for most peak joint moments. These findings highlight the importance of cut-off frequency choice in the analysis of joint moments and the assessment of footwear interventions in distance running. Based on our results, we propose to use matched cut-off frequencies around 20 Hz in order to avoid large artificial fluctuations in joint moment curves while at the same time avoiding a severe removal of physiological high-frequency signal content from the GRF signals.     

On the Quantification of SSVEP Frequency Responses in Human EEG in Realistic BCI Conditions

This article concerns one of the most important problems of brain-computer interfaces (BCI) based on Steady State Visual Evoked Potentials (SSVEP), that is the selection of the a-priori most suitable frequencies for stimulation. Previous works related to this problem were done either with measuring systems that have little in common with actual BCI systems (e.g., single flashing LED) or were presented on a small number of subjects, or the tested frequency range did not cover a broad spectrum. Their results indicate a strong SSVEP response around 10 Hz, in the range 13–25 Hz, and at high frequencies in the band of 40–60 Hz. In the case of BCI interfaces, stimulation with frequencies from various ranges are used. The frequencies are often adapted for each user separately. The selection of these frequencies, however, was not yet justified in quantitative group-level study with proper statistical account for inter-subject variability. The aim of this study is to determine the SSVEP response curve, that is, the magnitude of the evoked signal as a function of frequency. The SSVEP response was induced in conditions as close as possible to the actual BCI system, using a wide range of frequencies (5–30 Hz, in step of 1 Hz). The data were obtained for 10 subjects. SSVEP curves for individual subjects and the population curve was determined. Statistical analysis were conducted both on the level of individual subjects and for the group. The main result of the study is the identification of the optimal range of frequencies, which is 12–18 Hz, for the registration of SSVEP phenomena. The applied criterion of optimality was: to find the largest contiguous range of frequencies yielding the strong and constant-level SSVEP response.     

Der Zusammenhang zwischen Lokomotionsweise,Begattungsstellung und Penislänge bei Säugetieren1

Penis length, copulation and locomotion: Their relationship to each other in Mammals A relationship between the mode of locomotion, copulatory position and length of the male copulative organ has been found in all groups of Mammalia. In this paper particular emphasis is given to the orders of the Testiconda, while the Testiphaena receive only brief account (for explanation of terms see Frey 1991 a). Results from my previous antomical study are utilized that are essential for assessing the respective modes of locomotion (Frey 1991b). Information on penis length and copulatory position are taken from the literature and evaluated. Small and middle-sized Testiphaena, which represent the majority of mammals, are capable of a dynamic sagittal bending in the trunk, which is evidenced both in the galloping mode of locomotion and in the usual mammalian copulatory position (mounting). A sagittal bending of the trunk enables the male to bring his genital region into close proximity of the female's genital opening. In this case, a short penis is sufficient to ensure sperm transfer. The construction of the trunk in the Testiconda (excepting the Hyracoidea) entirely or nearly entirely prevents the sagittal bending. This is largely due to rigidity of the lumbar region or insufficient (dynamic) muscular control. The immobilization and/or the functional weakness of the lumbar region are derived from different anatomical conditions. 1. Shortening of the lumbar region, e.g., Tachyglossidae, Elephantidae, Sirenia; 2. Tightening of the lumbar region by tendons and muscles, e. g., Macroscelididae, Cetacea; 3. Xenarthry of the lumbar vertebrae and a double connection of the pelvis on the vertebral column, e. e., Bradypodidae, Myrmeco-phagidae; 4. The lumbar region may be flexible but the hypaxial muscles too short and weak, e. g., Tenrecinae, Soricidae, Erinaceidae. Lumbar rigidity or insufficient muscular control in the lumbar region, resulting from any of these conditions, makes copulation difficult by restricting close approximation of the male and female genitals. Most Testiconda compensate for this by having a long penis. The same also applies for large-sized Testiphaena. Although these animals have retained the ability to gallop, the flexibility of their trunk is restricted and mostly localized in a single joint due to the great body mass and the constructive constraints necessary for increased stability. A long penis is not the only way to compensate for the absence of sagittal flexion. A phylogenetic change in the copulatory posture also solves the problem as seen in the Myr-mecophagidae and Bradypodidae (both Testiconda) which are equipped with a secondarily short-enedpenis. The permanently aquatic testicondid mammals (Sirenia and Cetacea) cannot copulate in the usual mammalian mount position. This is largely due to the phylogenetic reduction and reconstruction of the extremities as well as the secondary evolution of a powerful tail. Sagittal movements of the heavily musculated tail act upon the more or less rigid trunk to provide for a “rear drive” locomotion. Both a change in the copulatory position and a long penis were necessary for these aquatic mammals. The only Testiconda in which a marked dynamic sagittal flexibility of the trunk is developed -the Hyracoidea - are characterized by a short penis. On the whole, the relationship between the mode of locomotion, copulatory position and penis length within the mammalia is confirmed. A rigid lumbar region as opposed to a sagittally flexible, presumably represents the primitive condition among mammals. All Testiconda have     

Dynamic behavior of excised dog rib cage: dependence on muscle

To assess the contribution of the rib cage to chest wall elastance and hysteresis, we measured force-displacement behavior of the isolated canine rib cage during sinusoidal forcing of the sternum in the midsagittal plane at low frequencies (0.02-2.0 Hz). Elastance of the rib cage was nearly invariant with frequency of forcing from 0.02 to 1.0 Hz and decreased with increasing amplitude. Hysteresis, the width of the force-displacement loop at middisplacement (zero displacement), was nearly constant with frequency below 1.0 Hz and increased with increasing amplitude of forcing. Removal of muscle reduced elastance and hysteresis of the rib cage substantially. The data suggest that the excised dog rib cage shows dynamic behavior similar to that of the intact human rib cage and chest wall and that respiratory muscle is responsible for a major part of the behavior of the passive chest wall. We also calculated the major and minor stiffnesses in the sagittal plane, which differed by a factor of 3-11, and their directions lay close to the dorsoventral and cephalocaudal axes, respectively. Removal of muscle reduced the stiffnesses but did not change their directions. Thus, although respiratory muscles impede motion in the sagittal plane, they do not alter its pattern.     

The evolution of jumping in frogs: Morphological evidence for the basal anuran locomotor condition and the radiation of locomotor systems in crown group anurans

Our understanding of the evolution of frog locomotion follows from the work of Emerson in which anurans are proposed to possess one of three different iliosacral configurations: 1) a lateral‐bending system found in walking and hopping frogs; 2) a fore‐aft sliding mechanism found in several locomotor modes; and 3) a sagittal‐hinge‐type pelvis posited to be related to long‐distance jumping performance. The most basal living (Ascaphus) and fossil (Prosalirus) frogs are described as sagittal‐hinge pelvic types, and it has been proposed that long‐distance jumping with a sagittal‐hinge pelvis arose early in frog evolution. We revisited osteological traits of the pelvic region to conduct a phylogenetic analysis of the relationships between pelvic systems and locomotor modes in frogs. Using two of Emerson's diagnostic traits from the sacrum and ilium and two new traits from the urostyle, we resampled the taxa originally studied by Emerson and key paleotaxa and conducted an analysis of ancestral‐character state evolution in relation to locomotor mode. We present a new pattern for the evolution of pelvic systems and locomotor modes in frogs. Character analysis shows that the lateral‐bender, walker/hopper condition is both basal and generally conserved across the Anura. Long‐distance jumping frogs do not appear until well within the Neobatrachia. The sagittal‐hinge morphology is correlated with long‐distance jumping in terrestrial frogs; however, it evolved convergently multiple times in crown group anurans with the same four pelvic traits described herein. Arboreal jumping has appeared in multiple crown lineages as well, but with divergent patterns of evolution involving each of the three pelvic types. The fore‐aft slider morph appears independently in three different locomotor modes and, thus, is a more complex system than previously thought. Finally, it appears that the advent of a bicondylar sacro‐urostylic articulation was originally related to providing axial rigidity to lateral‐bending behaviors rather than sagittal bending. J. Morphol., 2011. © 2010 Wiley‐Liss, Inc.     

Effect of whole-body vibration with different frequencies and intensities on auditory evoked potentials and heart rate in man

Auditory evoked brain potentials (AEP) and electrocardiogram (ECG) were recorded from 9 healthy male subjects during sinusoidal whole-body vibration exposure (WBV) in the longitudinal (+/- az) direction with four frequencies (1 Hz, 2 Hz, 4 Hz, and 8 Hz) and two intensities as well as under non-WBV conditions. The sequences of the different experimental conditions were arranged according to a 9 X 9 Latin Square design. The sound of the electrohydraulic vibrator was masked by a constant noise level. A subtraction technique was used to eliminate vibration-synchronous activity contaminating the electroencephalogram. The AEP amplitude N1-P2 revealed systematic effects of different WBV frequencies and intensities. The amplitude decreased along with an increase in intensity (16 dB) by about 10 per cent. It diminished increasingly with a monotonic trend in the order non-WBV, WBV 8 Hz, WBV 4 Hz, WBV 2 Hz, and WBV 1 Hz. The interbeat-interval histograms computed from the ECG exhibited the highest mean values at MBV of 1 Hz, high intensity, and the lowest ones at WBV of 4 Hz, high intensity. The AEPs are reaffirmed as an informative measure for studying the WBV effect on central nervous information processing, although the modes of action are not yet fully known. Efferent influences on the acoustic input, cross-modality interaction, sensory mismatch, and changes of central nervous activation level are discussed as potential mechanisms.     

Data Processing Techniques May Influence Numerical Results and Interpretation of Single Leg Stance Test

Purposeto evaluate how different data sampling and different analysis methods may effect numerical results and interpretation of single leg stance test using parameters derived from CoP trajectories.MethodsThirty healthy active subjects were recruited for this study on voluntary. Each participant was asked to stand as still as possible for 20 s on the dominant limb, with the supporting foot placed on the force platform. Balancing task in two conditions, with eyes open (EO) and closed (EC). Three trials were collected for each condition.Medial-lateral and anterior-posterior CoP force platform data were obtained and downsampling techniques was applied to get data at original (500 Hz), 100 Hz and 20 Hz of sampling frequencies.Time series data were then analysed to get CoP variables including medial-lateral total path, anterior-posterior total path, total path, maximal excursion for the ML plane and maximal excursion for the AP plane. Sway area was evaluated as 95% confidence ellipse area (CEA) and as 95% prediction ellipse area (PEA)Main findingsSignificant different results were obtained for the same variable evaluated at different sampling frequency. In addition, at all sampling frequencies variables were significantly different (p.<0.05) between EO and EC conditions. High correlation (>0.9) between the same CoP variable calculated at different sampling frequencies was found for all CoP variables. Regarding sway area calculation, both methods were able to distinguish between EO and EC conditions and high correlation was found between CEA and PEA methods.ConclusionOverall results of this study demonstrated the importance of reporting data processing techniques, which includes sampling frequency and variable calculation methods, as they shown to influence one leg stance CoP results, thus data analysed in different manner cannot be directly compared. However, for the variables included in the study, researchers can choose preferred data collection and data analysis methods as they all return same data analysis interpretation as long as they keep consistency in the method.     

A two-layer outer hair cell model with orthotropic piezoelectric properties: correlation of cell resonant frequencies with tuning in the cochlea

The frequency response of outer hair cells (OHCs) of different lengths is studied using a mathematical model of a two-layer cylindrical shell with orthotropic properties. Material properties in the model are determined from experimental measurements reported in the literature, and the variation of material properties with the cell length is studied. The cortical lattice's Poisson ratios are found to remain fairly constant with cell length, while its stiffness changes significantly with cell length. The natural frequencies corresponding to several modes of deformation of an OHC with intracellular and extracellular fluids are calculated from this model. Our results suggest that the best frequency in the cochlea at the position where the OHC is located corresponds to different modes of deformation of the OHC, depending on the OHC length. For short OHCs, the best frequency is close to the natural frequency of the axisymmetric mode; for long OHCs, it is close to the natural frequencies of the beam-like bending and pinched modes. Such a difference in resonant modes for short and long OHCs at the best frequency suggests that different modes of OHC elongation motility may be present in amplifying the basilar membrane motion in the high and low frequency regions of the cochlea.     

A method for the intravital measurement of interspinous kinematics.

A novel non-radiographic technique for objectively quantifying quasi-static or dynamic intervertebral motion of a spinal motion segment in vivo in human subjects is presented here. The intervertebral motion device (IMD) is an instrumented linkage transducer system which can continuously measure over time two-dimensional sagittal plane rigid-body motion. Three custom-built omega-shaped displacement transducers are utilized. The IMD is rigidly fixed to the spinous processes of the lumbar motion segment by means of two intraosseous pins. Knowing the mechanoelectrical behavior and geometric configuration of the IMD, the relative spatial motion between the vertebral bodies can be resolved into sagittal rotation, axial translation, and anterior-posterior shear translation. Static calibrations of the IMD in the ranges of +/- 4 degrees rotation and +/- 4 mm translation determined the absolute maximum errors to be 0.2 degree and 0.07 mm for rotation and translation measurements, respectively, with corresponding variances of 0.1 degrees and 0.03 mm. For use in the vibration environment, negligible motion artifact content was detected in the IMD output signals when excited at discrete frequencies of 5.0 and 8.0 Hz. The first natural frequency of the IMD, specific for this design, was measured at 16.25 Hz. This technique may be used to study in vivo the spinal kinematics in healthy lumbar motion segments and in patients suspected of having segmental instability, and can perhaps be of clinical diagnostic significance.     

Relationship between the shape and density distribution of the femur and its natural frequencies of vibration

It has been recently suggested that mechanical loads applied at frequencies close to the natural frequencies of bone could enhance bone apposition due to the resonance phenomenon. Other applications of bone modal analysis are also suggested. For the above-mentioned applications, it is important to understand how patient-specific bone shape and density distribution influence the natural frequencies of bones. We used finite element models to study the effects of bone shape and density distribution on the natural frequencies of the femur in free boundary conditions. A statistical shape and appearance model that describes shape and density distribution independently was created, based on a training set of 27 femora. The natural frequencies were then calculated for different shape modes varied around the mean shape while keeping the mean density distribution, for different appearance modes around the mean density distribution while keeping the mean bone shape, and for the 27 training femora. Single shape or appearance modes could cause up to 15% variations in the natural frequencies with certain modes having the greatest impact. For the actual femora, shape and density distribution changed the natural frequencies by up to 38%. First appearance mode that describes the general cortical bone thickness and trabecular bone density had one of the strongest impacts. The first appearance mode could therefore provide a sensitive measure of general bone health and disease progression. Since shape and density could cause large variations in the calculated natural frequencies, patient-specific FE models are needed for accurate estimation of bone natural frequencies.     

Comparative analysis of the dynamics of human postural control during fixation and pursuit of a visual target

The properties of the system maintaining the upright posture were compared in different states of the oculomotor system: during target fixation and horizontal fast and slow pursuit (0.1 and 0.01 Hz), recording the trajectories of the center of pressure in the frontal and the sagittal planes. Methods of nonlinear analysis were applied to assess the similarity in pairwise comparisons. The overall similarity of the frontal plane dynamics proved to be higher than that of the sagittal plane dynamics. However, differences were revealed in fast pursuit versus slow pursuit or fixation in the frontal but not in the sagittal plane. Such differences may reflect the different inertia of the oculomotor and the balance control systems. In general, the results are consistent with the current notions on the two orthogonal subsystems of postural control.     

Dispersive and non-dispersive waves through plants: implications for arthropod vibratory communication

Vibratory communication in arthropods is a widespread phenomenon. Arthropods living on plants have been reported to use only dispersive bending waves in the context of prey-predator, competition, social and sexual interactions. Differences in signal structure have also been postulated to work as species recognition mechanisms and speciation agents. Using two identical laser Doppler vibrometers and a wavelet analysis, we quantified the wave propagation modes in rush stems (Juncus effusus) over the whole range of frequencies used by arthropods. A non-dimensionalized analysis shows that mechanical waves propagate not only as dispersive bending waves, but also as non-dispersive waves. Our analysis implies that an arthropod can communicate through non-dispersive bending waves by either producing signals of high frequencies or by choosing large stems, two widely different options tapping into the physiological and the behavioural repertoires, respectively. Non-dispersive waves, unreported so far in insect vibratory communication in plants, present serious advantages over dispersive bending waves in terms of signal integrity and may well be much more widely used than anticipated, in particular for species recognition.     

Resonant frequencies of arms and legs identify different walking patterns

The present study is aimed at investigating changes in the coordination of arm and leg movements in young healthy subjects. It was hypothesized that with changes in walking velocity there is a change in frequency and phase coupling between the arms and the legs. In addition, it was hypothesized that the preferred frequencies of the different coordination patterns can be predicted on the basis of the resonant frequencies of arms and legs with a simple pendulum model. The kinematics of arms and legs during treadmill walking in seven healthy subjects were recorded with accelerometers in the sagittal plane at a wide range of different velocities (i.e., 0.3-1. 3m/s). Power spectral analyses revealed a statistically significant change in the frequency relation between arms and legs, i.e., within the velocity range 0.3-0.7m/s arm movement frequencies were dominantly synchronized with the step frequency, whereas from 0.8m/s onwards arm frequencies were locked onto stride frequency. Significant effects of walking speed on mean relative phase between leg and arm movements were found. All limb pairs showed a significantly more stable coordination pattern from 0.8 to 1.0m/s onwards. Results from the pendulum modelling demonstrated that for most subjects at low-velocity preferred movement frequencies of the arms are predicted by the resonant frequencies of individual arms (about 0.98Hz), whereas at higher velocities these are predicted on the basis of the resonant frequencies of the individual legs (about 0.85Hz). The results support the above-mentioned hypotheses, and suggest that different patterns of coordination, as shown by changes in frequency coupling and phase relations, can exist within the human walking mode.     

The transmission of translational seat vibration to the head--II. Horizontal seat vibration

The second part of this study of the six axes of head motion caused by translational seat vibration is concerned with the effect of fore-and-aft (x-axis) and lateral (y-axis) seat vibration. Seat-to-head transmissibilities have been determined at frequencies up to 16 Hz for each of the three translational and three rotational axes of the head during exposure to random vibration of the seat. Repeatability measures within a single subject and studies of the variability across a group of twelve subjects have been conducted with two seating conditions: a rigid seat with a backrest, and the same seat with no backrest. Fore-and-aft seat motion mainly resulted in head motion within the mid-sagittal plane (x-z plane). Without the backrest, transmissibilities for the fore-and-aft, vertical and pitch axes of the head were greatest at about 2 Hz. The backrest greatly increased head vibration at frequencies above 4 Hz and caused a second peak in the transmissibility curves at about 6 to 8 Hz. Lateral seat motion mainly caused lateral head motion with a maximum transmissibility at about 2 Hz. The backrest had little effect on the transmission of lateral vibration to the head. For both axes of excitation inter-subject variability was much greater than intra-subject variability.