Overcoming the limitations of the Harmonic Ratio for the reliable assessment of gait symmetry

The Harmonic Ratio (HR) is an index based on the spectral analysis of lower trunk accelerations that is commonly used to assess the quality of gait. However, it presents several issues concerning reliability and interpretability. As a consequence, the literature provides very different values albeit corresponding to the same populations. In the present work, an improved harmonic ratio (iHR) was defined, relating the power of the intrinsic harmonics (i.e. associated with the symmetric component of gait) to the total power of the signal for each stride, leading to a normalised index ranging from 0 to 100%. The effect of the considered number of harmonics and strides on the estimate of both HR and iHR was assessed. The gait of three groups of volunteers was investigated: young healthy adults, elderly women and male trans-femoral amputees. Both HR and iHR were able to discriminate gait deviations from the gait of young healthy adults. Moreover, iHR proved to be more robust with respect to the number of considered harmonics and strides, and to exhibit a lower inter-stride variability. Additionally, using a normalised index as iHR led to a more straightforward interpretation and improved comparability. The importance of standardised conditions for the index evaluation was unveiled, and, in order to enhance the future comparability of the index, the following guidelines were presented: considering at least 20 harmonics and 20 strides; expressing the acceleration components in a repeatable, anatomical, local system of reference; and evaluating the iHR index, rather than the traditional HR.     

3D finite element model of the diabetic neuropathic foot: A gait analysis driven approach

Diabetic foot is an invalidating complication of diabetes that can lead to foot ulcers. Three-dimensional (3D) finite element analysis (FEA) allows characterizing the loads developed in the different anatomical structures of the foot in dynamic conditions. The aim of this study was to develop a subject specific 3D foot FE model (FEM) of a diabetic neuropathic (DNS) and a healthy (HS) subject, whose subject specificity can be found in term of foot geometry and boundary conditions. Kinematics, kinetics and plantar pressure (PP) data were extracted from the gait analysis trials of the two subjects with this purpose. The FEM were developed segmenting bones, cartilage and skin from MRI and drawing a horizontal plate as ground support. Materials properties were adopted from previous literature. FE simulations were run with the kinematics and kinetics data of four different phases of the stance phase of gait (heel strike, loading response, midstance and push off). FEMs were then driven by group gait data of 10 neuropathic and 10 healthy subjects. Model validation focused on agreement between FEM-simulated and experimental PP.     

A comparison of dorsal and heel plate foot tracking methods on lower extremity dynamics

The primary method to model ankle motion during inverse dynamic calculations of the lower limb is through the use of skin-mounted markers, with the foot modeled as a rigid segment. Motion of the foot is often tracked via the use of a marker cluster triad on either the dorsum, or heel, of the foot/shoe. The purpose of this investigation was to evaluate differences in calculated lower extremity dynamics during the stance phase of gait between these two tracking techniques. In an analysis of 7 subjects, it was found that sagittal ankle angles and sagittal ankle, hip and knee moments were strongly correlated between the two conditions, however, there was a significant difference in peak ankle plantar flexion and dorsiflexion angles. Frontal ankle angles were only moderately correlated and there was a significant difference in peak ankle eversion and inversion, resulting in moderate correlations in frontal plane moments and a significant difference in peak hip adductor moments. We demonstrate that the technique used to track the foot is an important consideration in interpreting lower extremity dynamics for clinical and research purposes.     

A wearable system for pre-impact fall detection

Unique features of body segment kinematics in falls and activities of daily living (ADL) are applied to make automatic detection of a fall in its descending phase, prior to impact, possible. Fall-related injuries can thus be prevented or reduced by deploying fall impact reduction systems, such as an inflatable airbag for hip protection, before the impact. In this application, the authors propose the following hypothesis: “Thigh segments normally do not exceed a certain threshold angle to the side and forward directions in ADL, whereas this abnormal behavior occurs during a fall activity”. Torso and thigh wearable inertial sensors (3D accelerometer and 2D gyroscope) are used and the whole system is based on a body area network (BAN) for the comfort of the wearer during a long term application. The hypothesis was validated in an experiment with 21 young healthy volunteers performing both normal ADL and fall activities. Results show that falls could be detected with an average lead-time of 700 ms before the impact occurs, with no false alarms (100% specificity), a sensitivity of 95.2%. This is the longest lead-time achieved so far in pre-impact fall detection.     

A smart device inertial-sensing method for gait analysis

The purpose of this study was to establish and cross-validate a method for analyzing gait patterns determined by the center of mass (COM) through inertial sensors embedded in smart devices. The method employed an extended Kalman filter in conjunction with a quaternion rotation matrix approach to transform accelerations from the object onto the global frame. Derived by double integration, peak-to-trough changes in vertical COM position captured by a motion capture system, inertial measurement unit, and smart device were compared in terms of averaged and individual steps. The inter-rater reliability and levels of agreement for systems were discerned through intraclass correlation coefficients (ICC) and Bland–Altman plots. ICCs corresponding to inter-rater reliability were good-to-excellent for position data (ICCs,.80–.95) and acceleration data (ICCs,.54–.81). Levels of agreements were moderate for position data (LOA, 3.1–19.3%) and poor for acceleration data (LOA, 6.8%–17.8%). The Bland–Altman plots, however, revealed a small systematic error, in which peak-to-trough changes in vertical COM position were underestimated by 2.2 mm; the Kalman filter?s accuracy requires further investigation to minimize this oversight. More importantly, however, the study?s preliminary results indicate that the smart device allows for reliable COM measurements, opening up a cost-effective, user-friendly, and popular solution for remotely monitoring movement. The long-term impact of the smart device method on patient rehabilitation and therapy cannot be underestimated: not only could healthcare expenditures be curbed (smart devices being more affordable than today‘s motion sensors), but a more refined grasp of individual functioning, activity, and participation within everyday life could be attained.     

A multisegmental cross-bridge kinetics model of the myofibril

Striated muscle is a mechanical system that develops force and generates power in serving vital activities in the body. Striated muscle is a complex biological system; a single mammalian muscle fibre contains up to hundred or even more myofibrils in parallel connected via an inter-myofibril filament network. In one single myofibril thousands of sarcomeres are lined up as a series of linear motors. We recently demonstrated that half-sarcomeres (hS) in a single myofibril operate non-uniformly. We outline a mathematical framework based on cross-bridge kinetics for the simulation of the force response and length change of individual hS in a myofibril. The model describes the muscle myofibril in contraction experiments under various conditions. The myofibril is modeled as a multisegmental mechanical system of hS models, which have active and viscoelastic properties. In the first approach, a two-state cross-bridge formalism relates the hS force to the chemical kinetics of ATP hydrolysis, as first described by Huxley [1957. Muscle structure and theories of contraction. Prog. Biophys. Mol. Biol. 7, 255-318]. Two possible types of biological variability are introduced and modeled. Numerical simulations of a myofibril composed of four to eight hS show a non-uniform hS length distribution and complex internal dynamics upon activation. We demonstrate that the steady-state approximation holds only in restricted time zones during activation. Simulations of myofibril contraction experiments that reproduce the classic steady-state force-length and force-velocity relationships, strictly constrained or “clamped” in either end-held isometric or isotonic contraction conditions, reveal a small but conspicuous effect of hS dynamics on force.     

Computational techniques for using insole pressure sensors to analyse three-dimensional joint kinetics

This study evaluated the feasibility of using insole pressure sensors together with whole body dynamics to analyse joint kinetics while running. Local affine transformations of shoe kinematics were first used to track the position of insole sensors during locomotion. Centre of pressure estimates derived from the insoles were within 10 mm of forceplate measures through much of stance, while vertical force estimates were within 15% of peak forceplate recordings. Insole data were then coupled with a least squares whole body dynamic model to obtain shear force estimates that were comparable to forceplate records during running. We demonstrated that these techniques provide a viable approach for analysing joint kinetics when running on uninstrumented surfaces.     

A quenched-flow apparatus which allows the measurement of the kinetics of a reaction in one stroke

A chemical quenched-flow apparatus is described which measures, in a unique stroke, enough data points (8–11) for establishing the kinetics curve of a reaction. Only very small volumes of reaction solutions (2 × 500 μl) are required. The time intervals between which the kinetic data may be measured range from 5 to 37 ms and from 120 to 450 ms with the corresponding mixing times of 0.6 and 5 ms, respectively. This apparatus was used to investigate the pre-steady-state domain of the aminoacylation reaction of tRNA^Val by valyl-tRNA synthetase from yeast.     

A technique for the measurement of cadence using walkway vibrations

A new method has been developed to measure cadence while walking. The method uses instrumentation to detect the vibrations transmitted in the walkway surface. These vibrations are produced when a subject's foot makes initial contact with the walking surface. The method was tested against heel switches and was found to measure stride duration with RMS errors of around 1%. The vibration method requires no instrumentation to be attached to the subject, can be used with bare feet or any other footwear, is simple to use and is very robust and reliable.     

A synergistic kinetics model for enzymatic cellulose hydrolysis compared to degree-of-synergism experimental results

It is demonstrated that a two-enzyme component synergistic model can account for the observation that the degree of synergism goes through a maximum as the total enzyme concentration is increased. The degree of synergism is low at low enzyme concentration because the extent of conversion is low and therefore the cellulose chain ends, present originally, are not exhausted; thus the action of the cellobiohydrolase (CBH) is not dependent on the chain ends generated by the endoglucanase (EG). The degree of synergism declines at high enzyme concentration due to saturation of adsorption sites with CBH, thus decreasing the generation of chain ends by EG. (c) 1993 John Wiley & Sons, Inc.     

A universal homogeneous assay for high-throughput determination of binding kinetics

There is an increasing demand for assay technologies that enable accurate, cost-effective, and high-throughput measurements of drug–target association and dissociation rates. Here we introduce a universal homogeneous kinetic probe competition assay (kPCA) that meets these requirements. The time-resolved fluorescence energy transfer (TR–FRET) procedure combines the versatility of radioligand binding assays with the advantages of homogeneous nonradioactive techniques while approaching the time resolution of surface plasmon resonance (SPR) and related biosensors. We show application of kPCA for three important target classes: enzymes, protein–protein interactions, and G protein-coupled receptors (GPCRs). This method is capable of supporting early stages of drug discovery with large amounts of kinetic information.     

The sucked-flow analyser: A simple apparatus for automatic determination of steady-state enzyme kinetics

The sucked-flow analyser is a modified stopped-flow apparatus for automatic measurements of initial rates of enzyme reactions at varying concentrations of substrate or inhibitor. The flow through the system is driven by a water suction pump and regulated by magnetic valves. Sample and reagent solution are aspired through tubes whose resistances to laminar flow determine a precise ratio of mixing in the observation cell. A minicomputer controls all operations, collects the data and calculates the results. Measurements on teh β-galactosidase and the cytochome P-450 reactions are presented.     

A new ambulatory foot pressure device for patients with sensory impairment. A system for continuous measurement of plantar pressure and a feed-back alarm

Abnormal and excessive plantar pressure is a major risk factor for the development of foot ulcers in patients with loss of protective pain sensation. Repeated pressure with each step can result in inflammation at specific points, followed by ulcer formation. Patients with peripheral nerve disease are unable to prevent the development of such lesions, which often lead to amputation. For this reason, it has been suggested that a fundamental therapeutic intervention should be the reduction of high plantar pressure. We have developed a portable, battery-operated ambulatory foot pressure device (AFPD) which has two important functions: (1) to determine the areas of high plantar pressure, and (2) to provide an acoustic alarm, adjusted to a specific pressure load, which is triggered when weight-bearing exceeds the predetermined plantar pressure. A memory of plantar pressure parameters allows for downloading of the data and sequential analysis during the investigation period. Such an alarm device could replace the lack of pain sensation and may play an important role in the prevention of ulcer development and lower extremity amputation.     

A method for determining binding kinetics applied to thiamine-binding protein

A rapid and simple method for assaying the binding activity of thiamine-binding protein is described. By this assay method, the binding characteristics of rice bran thiamine-binding protein have been evaluated with [14C]thiamine as ligand. Analysis of these data by Scatchard plot resulted in linear plots giving a dissociation constant (Kd) for thiamine of 0.55 microM and a maximum binding (Bmax) of 14.5 pmol of ligand bound/microgram of protein. Thiamine binding to the binding protein was time dependent and reached equilibrium at approximately 20 min. The Kob was 0.18 min-1 and the k1 was 1.25 X 10(5) min-1 M-1. Reversibility of thiamine binding at equilibrium was completed at 60 min with a k2 value of 0.052 min-1. The Kd calculated from the reverse rate constant was 0.42 microM. These results indicated that this binding assay method was substantially reliable and accurate.     

A capillary electrophoresis-based enzyme assay for kinetics and inhibition studies of carbonic anhydrase

In the current study, capillary electrophoresis (CE)-based enzyme assay for characterization and inhibition study of bovine carbonic anhydrase II (bCA II) was developed. The developed method is the first CE assay for carbonic anhydrase (CA). The method was optimized in order to get short analysis time, minimal sample volume consumption, and high resolution of substrate and product. The CE conditions were optimized as follows: fused-silica capillary (30 cm effective length × 75 μm i.d.), pressure injection for 5 s, 20 mM sodium borate buffer (pH 9.0), constant voltage of 15 kV, constant capillary temperature of 25 °C, and detection at 260 nm. For precise measurements, uridine was used as an internal standard during optimization of the CE methods. The limits of detection and quantification for p-nitrophenyl acetate (p-NPA) were 3.01 and 9.12 μM, respectively, whereas for p-nitrophenolate they were 2.05 and 6.22 μM, respectively. The performance of the developed method was confirmed by determination of kinetic parameters (i.e., K_m and V_max of bCA for p-NPA); the inhibition constant (K_i) was determined for furosemide, a standard inhibitor of CA. The new method proved to be fast and efficient, and it can be used for the investigation of inhibitors of all isoforms of CAs.     

A model for the effects of primary substrates on the kinetics of reductive dehalogenation

A kinetic model that describes substrate interactions during reductive dehalogenation reactions is developed. This model describes how the concentrations of primary electron-donor and -acceptor substrates affect the rates of reductive dehalogenation reactions. A basic model, which considers only exogenous electron-donor and -acceptor substrates, illustrates the fundamental interactions that affect reductive dehalogenation reaction kinetics. Because this basic model cannot accurately describe important phenomena, such as reductive dehalogenation that occurs in the absence of exogenous electron donors, it is expanded to include an endogenous electron donor and additional electron acceptor reactions. This general model more accurately reflects the behavior that has been observed for reductive dehalogenation reactions. Under most conditions, primary electron-donor substrates stimulate the reductive dehalogenation rate, while primary electron acceptors reduce the reaction rate. The effects of primary substrates are incorporated into the kinetic parameters for a Monod-like rate expression. The apparent maximum rate of reductive dehalogenation (q _{m, ap} ) and the apparent half-saturation concentration (K _ap ) increase as the electron donor concentration increases. The electron-acceptor concentration does not affect q _{m, ap} , but K _ap is directly proportional to its concentration.Definitions for model parameters RX halogenated aliphatic substrate - E-M ⁿ reduced dehalogenase - E-M ⁿ⁺² oxidized dehalogenase - [E-M ⁿ ] steady-state concentration of the reduced dehalogenase (moles of reduced dehalogenase per unit volume) - [E-M ⁿ⁺²] steady-state concentration of the oxidized dehalogenase (moles of reduced dehalogenase per unit volume) - DH₂ primary exogenous electron-donor substrate - A primary exogenous electron-acceptor substrate - A2 second primary exogenous electron-acceptor substrate - X biomass concentration (biomass per unit volume) - f fraction of biomass that is comprised of the dehalogenase (moles of dehalogenase per unit biomass) - stoichiometric coefficient for the reductive dehalogenation reaction (moles of dehalogenase oxidized per mole of halogenated substrate reduced) - stoichiometric coefficient for oxidation of the primary electron donor (moles of dehalogenase reduced per mole of donor oxidized) - stoichiometric coefficient for oxidation of the endogenous electron donor (moles of dehalogenase reduced per unit biomass oxidized) - stoichiometric coefficient for reduction of the primary electron acceptor (moles of dehalogenase oxidized per mole of acceptor reduced) - stoichiometric coefficient for reduction of the second electron acceptor (moles of dehalogenase oxidized per mole of acceptor reduced) - r _RX rate of the reductive dehalogenation reaction (moles of halogenated substrate reduced per unit volume per unit time) - r _d1 rate of oxidation of the primary exogenous electron donor (moles of donor oxidized per unit volume per unit time) - r _d2 rate of oxidation of the endogenous electron donor (biomass oxidized per unit volume per unit time) - r _a1 rate of reduction of the primary exogenous electron acceptor (moles of acceptor reduced per unit volume per unit time) - r _a2 rate of reduction of the second primary electron acceptor (moles of acceptor reduced per unit volume per unit time) - k _RX mixed second-order rate coefficient for the reductive dehalogenation reaction (volume per mole dehalogenase per unit time) - k _d1 mixed-second-order rate coefficient for oxidation of the primary electron donor (volume per mole dehalogenase per unit time) - k _d2 mixed-second-order rate coefficient for oxidation of the endogenous electron donor (volume per mole dehalogenase per unit time) - b first-order biomass decay coefficient (biomass oxidized per unit biomass per unit time) - k _a1 mixed-second-order rate coefficient for reduction of the primary electron acceptor (volume per mole dehalogenase per unit time) - k _a2 mixed-second-order rate coefficient for reduction of the second primary electron acceptor (volume per mole dehalogenase per unit time) - q _m,ap apparent maximum specific rate of reductive dehalogenation (moles of RX per unit biomass per unit time) - K _ap apparent half-saturation concentration for the halogenated aliphatic substrate (moles of RX per unit volume) - k _ap apparent pseudo-first-order rate coefficient for reductive dehalogenation (volume per unit biomass per unit time)