A mechanical model to determine the influence of masses and mass distribution on the impact force during running

Simple spring-damper-mass models have been widely used to simulate human locomotion. However, most previous models have not accounted for the effect of non-rigid masses (wobbling masses) on impact forces. A simple mechanical model of the human body developed in this study included the upper and lower bodies with each part represented by a rigid and a wobbling mass. Spring-damper units connected different masses to represent the stiffness and damping between the upper and lower bodies, and between the rigid and wobbling masses. The simulated impact forces were comparable to experimentally measured impact forces. Trends in changes of the impact forces due to changes in touch-down velocity reported in previous studies could be reproduced with the model. Simulated results showed that the impact force peaks increased with increasing rigid or wobbling masses of the lower body. The ratio of mass distribution between the rigid and wobbling mass in the lower body was also shown to affect the impact force peak, for example, the impact force peak increased with increasing rigid contribution. The variation in the masses of upper body was shown to have a minimum effect on the impact force peak, but a great effect on the active force peak (the second peak in the ground reaction force). Future studies on the dynamics and neuro-muscular control of human running are required to take into consideration the influence of individual variation in lower body masses and mass distribution.     

The influence of soft tissue movement on ground reaction forces, joint torques and joint reaction forces in drop landings

The aim of this study was to determine the effects that soft tissue motion has on ground reaction forces, joint torques and joint reaction forces in drop landings. To this end a four body-segment wobbling mass model was developed to reproduce the vertical ground reaction force curve for the first 100 ms of landing. Particular attention was paid to the passive impact phase, while selecting most model parameters a priori, thus permitting examination of the rigid body assumption on system kinetics. A two-dimensional wobbling mass model was developed in DADS (version 9.00, CADSI) to simulate landing from a drop of 43 cm. Subject-specific inertia parameters were calculated for both the rigid links and the wobbling masses. The magnitude and frequency response of the soft tissue of the subject to impulsive loading was measured and used as a criterion for assessing the wobbling mass motion. The model successfully reproduced the vertical ground reaction force for the first 100 ms of the landing with a peak vertical ground reaction force error of 1.2% and root mean square errors of 5% for the first 15 ms and 12% for the first 40 ms. The resultant joint forces and torques were lower for the wobbling mass model compared with a rigid body model, up to nearly 50% lower, indicating the important contribution of the wobbling masses on reducing system loading.     

The effect of muscle stiffness and damping on simulated impact force peaks during running.

It has been frequently reported that vertical impact force peaks during running change only minimally when changing the midsole hardness of running shoes. However, the underlying mechanism for these experimental observations is not well understood. An athlete has various possibilities to influence external and internal forces during ground contact (e.g. landing velocity, geometrical alignment, muscle tuning, etc.). The purpose of this study was to discuss one possible strategy to influence external impact forces acting on the athlete's body during running, the strategy to change muscle activity (muscle tuning). The human body was modeled as a simplified mass-spring-damper system. The model included masses of the upper and the lower bodies with each part of the body represented by a rigid and a non-rigid wobbling mass. The influence of mechanical properties of the human body on the vertical impact force peak was examined by varying the spring constants and damping coefficients of the spring-damper units that connected the various masses. Two types of shoe soles were modeled using a non-linear force deformation model with two sets of parameters based on the force-deformation curves of pendulum impact experiments. The simulated results showed that the regulation of the mechanical coupling of rigid and wobbling masses of the human body had an influence on the magnitude of the vertical impact force, but not on its loading rate. It was possible to produce the same impact force peaks altering specific mechanical properties of the system for a soft and a hard shoe sole. This regulation can be achieved through changes of joint angles, changes in joint angular velocities and/or changes in muscle activation levels in the lower extremity. Therefore, it has been concluded that changes in muscle activity (muscle tuning) can be used as a possible strategy to affect vertical impact force peaks during running.     

Component inertia modeling of segmental wobbling and rigid masses

A modification to an existing mathematical model is described, which permits the determination of subject-specific inertia parameters for wobbling and rigid masses of female body segments. The model comprises segment-specific soft tissue, bone, and lung components. A total of 59 geometric solids (40 soft tissue, 17 bone, 2 lung) were used to represent the body components. Ninety-five anthropometric measurements were collected from 7 female participants and were used to develop and evaluate the model. The success of the model is evaluated using predicted mass and mass distribution. The overall absolute accuracy in predicted whole body mass was better than 3.0%, with a maximum error of 4.9%. The appropriateness of the cadaver-based density values used in the model is addressed and the accuracy of the component inertia model in relation to uniform density models is discussed. The model offers a novel approach for determining component inertia parameters, which have been used successfully in a wobbling mass model to produce realistic kinetic analyses of drop-landings.     

Time-dependent absorption anisotropy and rotational diffusion of proteins in membranes.

The decay of flash-induced absorption anisotropy, r(t), of a chromophore in a membrane protein is closely correlated with rotational diffusion of the protein in the membrane. We develop a theory of time-dependent absorption anisotropy which is applicable to both linear chromophores and planar chromophores which have two different absorption moments at right angles to one another. The theory treats two types of rotational diffusion of membrane proteins: one is rotation of the whole protein about the normal to the plane of the membrane, and the other is restricted wobbling of the whole or part of the protein molecule. In the former case, r(t) is determined by a rotational diffusion coefficient and an angle between the absorption moment(s) and the normal to the plane of the membrane. Rotation of rigid transmembrane proteins can be described by this treatment. In the latter case, r(t) is characterized by a wobbling diffusion coefficient and the degree of orientational constraint. This treatment may be applicable to independent wobbling of the hydrophilic part of membrane proteins. We further show that, for linear and circularly degenerate chromophores, the effect of the excitation flash intensity on r(t) can be accounted for by a constant scaling factor.     

Soft tissue wobbling affects trunk dynamic response in sudden perturbations

Soft tissue wobbling reduces the transferred impact of external loads on lower limb joints. The present study investigated whether soft tissue wobbling has similar effects on trunk dynamic response to sudden perturbations. Three healthy males were subjected to a series of anteriorly directed trunk position perturbations at three different velocities while trunk kinematics and kinetics were measured. A nonlinear active-passive finite element model of the human trunk was then used to study the effects of soft tissue wobbling on trunk response. Also investigated were the effects on model predictions of including elements simulating the apparatus (rod-harness assembly) transferring motor-generated perturbations to the trunk. Predicted and measured trunk kinematics and kinetics, when accounting for the dynamic effects of both wobbling mass and rod-harness assembly, were in good agreement for all velocities especially early (<120 ms) after the perturbations (ρ>0.97). Root mean square errors in model predictions increased considerably when neglecting the aforementioned modeling considerations. The trunk wobbling mass and connecting elements between the trunk and the perturbing device, particularly during faster perturbations, substantially attenuated the transferred impact of external loads on the spine (by 33-90 N across perturbation velocities). Such reductions in the impacts transferred, in turn, reduced the predicted demands on the neuromuscular system for control and maintenance of spinal loads and stability. As such, these features should be considered in future biodynamic models of the human trunk aimed at estimating trunk neuromuscular behaviors during sudden perturbations.     

Rotational diffusion of a steroid molecule in phosphatidylcholine membranes: effects of alkyl chain length, unsaturation, and cholesterol as studied by a spin-label method

Rotational diffusion of cholestane spin-label (CSL), a sterol analogue, in various phosphatidylcholine (PC)-cholesterol membranes was systematically studied by computer simulation of steady-state ESR spectra as a function of chain length and unsaturation of alkyl chains, cholesterol mole fraction, and temperature for better understanding of phospholipid-cholesterol and cholesterol-cholesterol interactions. CSL motion in the membrane was treated as Brownian rotational diffusion of a rigid rod within the confines of a cone imposed by the membrane environment. The wobbling rotational diffusion constant of the long axis, its activation energy, and the cone angle of the confines are obtained for various membranes in the liquid-crystalline phase. The wobbling diffusion constant decreases in the order dilauroyl-PC greater than dimyristoyl-PC greater than dioleoyl-PC approximately dipalmitoyl-PC greater than distearoyl-PC greater than dioleoyl-PC/cholesterol = 3/1 greater than dioleoyl-PC/cholesterol = 1/1 membranes. Activation energy for the wobbling diffusion of the long axis of CSL is strongly dependent on alkyl chain length, unsaturation, and cholesterol mole fraction. It decreases with decrease in alkyl chain length and by introduction of unsaturation in the alkyl chains. In dioleoylphosphatidylcholine membranes, activation energy decreases by a factor of approximately 3 in the presence of 50 mol % cholesterol. Activation energy for wobbling diffusion of CSL in phosphatidylcholine membranes is smaller than the activation energy for translational diffusion of a phospholipid. The former is more dependent on alkyl chain length and unsaturation.(ABSTRACT TRUNCATED AT 250 WORDS)     

A biomechanical model for size, speed and anatomical variations of the energetic costs of running mammals

Here we propose a model of energetic costs and the muscle-tendon unit function on running mammals. The main goal is to set a simple theoretical framework which gives an understanding of the biomechanical principles behind the size, speed and anatomical variations of the energetic costs of running mammals. The model is a point-like mass withstood by a two-segment leg with an extensor muscle serially attached to a tendon. We considered withstanding body weight during the stance phase as the main role of the muscle-tendon unit during fast locomotion. The ground reaction force dependence on speed and the time of stance phase as well as other biomechanical characteristics were taken from previous empirical studies of running. At the same time, the morphological variations with body mass were taken from empirically well-established allometric equations for mammals. The metabolic cost was estimated from an empirical equation relating metabolic power with muscular force and speed in shortening and stretching. Our model predicts the pattern of mass specific metabolic rate variations with both speed and body mass. It also gives an explanation of the experimentally reported linear inverse relationship between the rate of energy used for running and the time of application of force by the foot to the ground during each stride. It also suggests an explanation of the unusual energy saving adaptations of large macropodids. It provides some predictions on the relationship, between energy costs and muscle-tendon unit characteristics, testable on further experiments.     

Manual segmentation of DXA scan images results in reliable upper and lower extremity soft and rigid tissue mass estimates

Quantification of segment soft and rigid tissue masses in living people is important for a variety of clinical and biomechanical research applications including wobbling mass modeling. Although Dual-energy X-ray Absorptiometry (DXA) is widely accepted as a valid method for this purpose, the reliability of manual segmentation from DXA scans using custom regions of interest (ROIs) has not been evaluated to date. Upper and lower extremity images of 100 healthy adults who underwent a full body DXA scan in the supine position were manually segmented by 3 measurers independently using custom ROIs. Actual tissue masses (fat mass, lean mass, bone mineral content) of the arm, arm with shoulder, forearm, forearm and hand, thigh, leg, and leg and foot segments were quantified bilaterally from the ROIs. There were significant differences between-measurers, however, percentage errors were relatively small overall (<1–5.98%). Intraclass correlation coefficients (ICCs) were very high between and within-measurers, ranging from 0.990 to 0.999 and 0.990 to 1.00 for the upper and lower extremities, respectively, suggesting excellent reliability. Between and within-measurer errors were comparable in general, and differences between the tissue types were small on average (maximum of 42 and 53 g for upper and lower extremities, respectively). These results suggest that manual segmentation of DXA images using ROIs is a reliable method of estimating soft and rigid tissues in living people.     

Virtual musculo-skeletal model for the biomechanical analysis of the upper limb

In this paper, a musculo-skeletal model of the upper limb is presented. The limb is modelled as a three-dimensional 7 degrees-of-freedom system, linked to the shoulder, which has been considered as frame. The upper limb model is made up of four links corresponding to the most important body segments: the humerus, the ulna, the radius and the hand, considered as a single rigid body. Particular attention has been paid to the modelling of joints in order to mimic all the possible arm and forearm movements (including prono-supination). The model also includes 24 muscles. The mathematical model used to describe the muscles is that proposed by Zajac in 1989, modified by the authors. The kinematic analysis has been performed including an ergonomics index to take into account the posture and joint physical limits. Moreover an optimization criterion based on minimum activation pattern has been included in order to find muscular activation coefficients. The results of the proposed methodology concerning muscular activations have been compared to those coming from processed EMG signals, which have been acquired during experimental tests.     

A comparison of the triceps surae and residual muscle moments at the ankle during cycling

The rigid linked system model and principles of inverse dynamics have been widely used to calculate residual muscle moments during various activities. EMG driven models and optimization algorithms have also been presented in the literature in efforts to estimate skeletal muscle forces and evaluate their possible contribution to the residual muscle moment. Additionally, skeletal muscle-tendon forces have been measured, directly, in both animals and humans. The purpose of this investigation was to calculate the moment produced by the triceps surae muscles and compare it to the residual muscle moment at the ankle during cycling at three power outputs (90, 180 and 270 W). Inferences were made regarding the potential contribution made by each triceps surae component to the tendon force using EMG and muscle-tendon length changes. A buckle-type transducer was surgically implanted on the right Achilles tendon of one male subject. Achilles tendon forces measured in vivo were multiplied by their corresponding moment arms to yield the triceps surae moment during the three working conditions. Moment arm lengths were obtained in a separate experiment using magnetic resonance imaging (MRI). Pedal reaction forces, body segment accelerations (determined from high speed film), and appropriate mass parameters served as input to the inverse solution. The triceps surae moment was temporally in phase with and consistently represented approximately 65% of the residual muscle moment at the ankle. These data demonstrate the feasibility of using implanted transducers in human subjects and provide a greater understanding of musculoskeletal mechanics during normal human movements.     

Himalayan porter's specialization: metabolic power, economy, efficiency and skill

Carrying heavy loads in the Himalayan region is a real challenge. Porters face extreme ranges in terrain condition, path steepness, altitude hypoxia and climate for 6-8h a day, many months a year, since they were boys. It has been previously shown that, when carrying loads on level terrain, porters' metabolic economy is higher than in Caucasians but the reasons are still unknown. We monitored Nepalese porters both during 90 km trekking in Khumbu Valley and at two different altitudes (3490 and 5050 m above sea-level), where they were compared to Caucasian mountaineers during (22%) gradient walking. Both subject groups carried a load of up to 90% body mass. The remarkably higher performance of porters during uphill locomotion (+60% in speed, +39% mechanical power) is only partly explained by the lower cost of loaded walking (-20%), being also the result of a better cardio-circulatory adaptation to altitude, which generates a higher mass-specific metabolic power (+30%). Consequently, Nepalese porters show higher efficiency, both during uphill and downhill loaded walking. Their higher economy on steep paths cannot be ascribed to a better exchange between potential and kinetic energy, as in our experiments the body centre of mass travelled monotonically uphill (or downhill). A different oscillation pattern of the loaded head-trunk segment, together with the analysis of the different components of the mechanical work during load carrying, suggests that achieved motor skills in balancing the loaded body segment above the hip could play a role in determining the better economy of porters.     

Measurement and modelling of x-direction apparent mass of the seated human body-cushioned seat system

For modelling purposes and for evaluation of driver's seat performance in the vertical direction various mechano-mathematical models of the seated human body have been developed and standardized by the ISO. No such models exist hitherto for human body sitting in an upright position in a cushioned seat upper part, used in industrial environment, where the fore-and-aft vibrations play an important role. The interaction with the steering wheel has to be taken into consideration, as well as, the position of the human body upper torso with respect to the cushioned seat back as observed in real driving conditions. This complex problem has to be simplified first to arrive at manageable simpler models, which still reflect the main problem features. In a laboratory study accelerations and forces in x-direction were measured at the seat base during whole-body vibration in the fore-and-aft direction (random signal in the frequency range between 0.3 and 30 Hz, vibration magnitudes 0.28, 0.96, and 2.03 ms(-2) unweighted rms). Thirteen male subjects with body masses between 62.2 and 103.6 kg were chosen for the tests. They sat on a cushioned driver seat with hands on a support and backrest contact in the lumbar region only. Based on these laboratory measurements a linear model of the system-seated human body and cushioned seat in the fore-and-aft direction has been developed. The model accounts for the reaction from the steering wheel. Model parameters have been identified for each subject-measured apparent mass values (modulus and phase). The developed model structure and the averaged parameters can be used for further bio-dynamical research in this field.     

Tackling environmental impacts in simple trigeneration systems operating under variable conditions

Purpose

Environmental concerns have been a growing issue when planning energy supply systems for buildings, as the energy demands (presenting seasonal and daily variations) represent one of the most energy-intensive consumptions in industrialized societies. The optimal operation corresponding to different energy demands of a trigeneration system was analyzed by an integrated methodology combining Thermoeconomic analysis and life cycle assessment, in order to adequately allocate the energy resources and the generated environmental loads to the different energy services produced.

Methods

Thermoeconomic analysis, which is usually used to allocate energy and economic costs, is herein applied to the evaluation of environmental costs and distribution of resources throughout the trigeneration system. Attention is focused on the correct allocation of energy resources and environmental loads to internal flows and final products. Appropriate rules were established to calculate energy and environmental costs.

Results and discussion

Operation of the system considered the possibilities that surplus electricity could be exported to the national grid and part of the cogenerated heat could be wasted if this resulted in a decrease of operation costs and/or environmental loads. The results obtained show a low-cost and low-emission production with respect to the separate production in different operation modes. It was observed that, in specific periods, the trigeneration system operates wasting part of the cogenerated heat, and, in other periods, part of the electricity produced is exported to the electric grid. The trigeneration system operates in these modes because it results beneficial from environmental or economic viewpoints, achieving a lower economic cost or fewer CO₂ emissions.

Conclusions

The methodology presented as well as the allocation method proposal were congruent with the objectives of installing trigeneration systems that supplied energy services with fewer emissions than those of separate production and of equally benefitting the consumers of heat, coolth (“coolth” is used as the noun form of “cool”; opposite of warmth. Not to be confused with cooling, which is the opposite of heating.) (alias cooling energy), and electricity.     

Dynamic coordinate data for describing muscle-tendon paths: a mathematical approach

When modelling the musculoskeletal system over a range of joint angles the use of fixed points to describe muscle-tendon paths has inherent limitations. These result in fewer deflection points and the use of effective insertions to accommodate both relative marker movement and avoid muscle paths contacting bony structures. Model performance is dependent on the joint angle relative to the anatomical position where the muscle-tendon paths were defined. The present study proposes a scheme for the implementation of dynamic coordinates for describing muscle-tendon paths. For each muscle-tendon element a plane is defined in which the muscle-tendon complex acts when crossing a given joint. The muscle-tendon plane is dependent on 3D segment orientations and describes one degree of freedom, while the remaining two degrees of freedom are described by polar coordinates and locate the dynamic point in the muscle-tendon plane. The dynamic approach is implemented on four muscles of the lower limb in modelled and simulated joint movements and offers a significant improvement on previous approaches based on fixed deflection points. The scheme accommodates compound 3D rotations about joint axes, is not computationally difficult or require large data sets, and does not impose limitations on the number of points that may be defined along a muscle-tendon path.     

CFD Simulation of Fish-like Body Moving in Viscous Liquid

The study of fish-like bodies moving in liquid is an interesting and challenging research subject in the fields of biolocomotion and biomimetics. Typically the effect of tail oscillation on fluid flow around such a body is highly unsteady, generating vortices and requiring detailed analysis of fluid-structure interactions. An understanding of the complexities of such flows is of interest not only to biologists but also to engineers interested in developing vehicles capable of emulating the high performance of fish propulsion and manoeuvring. In the present study, a computational fluid dynamic （CFD） simulation of a three-dimensional biomimetic fish-like body has been developed to investigate the fluid flows around this body when moving in a viscous liquid. A parametric analysis of the variables that affect the flow surrounding the body is presented, along with flow visualisations, in an attempt to quantify and qualify the effect that these variables have on the performance of the body. The analysis provided by the unsteady transient simulation of a fish-like body has allowed the flow surrounding a fish-like body undergoing periodic oscillations to be studied. The simulation produces a motion of the tail in the （x, y） plane, with the tail oscillating as a rigid body in the form of a sinusoidal wave.     

Modelling, simulation and optimisation of a human vertical jump.

This paper describes an efficient biomechanical model of the human lower limb with the aim of simulating a real human jump movement consisting of an upword propulsion, a flying and a landing phase. A multiphase optimal control technique is used to solve the muscle force sharing problem. To understand how intermuscular control coordinates limb muscle excitations, the human body is reduced to a single lower limb consisting of three rigid bodies. The biomechanical system is activated by nine muscle-tendon actuators representing the basic properties of muscles during force generation. For the calculation of the minimal muscle excitations of the jump movement, the trajectory of the hip joint is given as a rheonomic constraint and the contact forces (ground reaction forces) are determined by force plates. Based on the designed musculoskeletal model and on the differential equations of the multibody system, muscle excitations and muscle forces necessary for a vertical jump movement are calculated. The validity of the system is assessed comparing the calculated muscle excitations with the registered surface electromyogramm (EMG) of the muscles. The achieved results indicate a close relationship between the predicted and the measured parameters.     

Kinematic analysis of over-determinate biomechanical systems

In this paper, we introduce a new general method for kinematic analysis of rigid multi body systems subject to holonomic constraints. The method extends the standard analysis of kinematically determinate rigid multi body systems to the over-determinate case. This is accomplished by introducing a constrained optimisation problem with the objective function given as a function of the set of system equations that are allowed to be violated while the remaining equations define the feasible set. We show that exact velocity and acceleration analysis can also be performed by solving linear sets of equations, originating from differentiation of the Karush-Kuhn-Tucker optimality conditions. The method is applied to the analysis of an 18 degrees-of-freedom gait model where the kinematical drivers are prescribed with data from a motion capture experiment. The results show that significant differences are obtained between applying standard kinematic analysis or minimising the least-square errors on the two fully equivalent 3D gait models with only the way the experimental data is processed being different.     

Anisotropic overall and internal motions of short DNA fragments.

Anisotropic motions of DNA fragments in the size range 6-118 base pairs are studied by the steady-state fluorescence polarization of different excitation transitions in the intercalated ethidium cation. Calculated effective tumbling and twisting times are found to be shorter than predicted for overall motions of rigid DNA, indicating that internal motions and/or dye wobbling contribute to the depolarization. The data are consistent with a model where the DNA fragments are considered to be rigid against bending but torsionally flexible, and where the dye can wobble within the intercalated site. We also discuss the possibility of correlated out-of-plane motions of the dye and the DNA bases.     

Body size, body shape, and long bone strength in modern humans

To identify behaviorally significant differences in bone structure it is first necessary to control for the effects of body size and body shape. Here the scaling of cross-sectional geometric properties of long bone diaphyses with different "size" measures (bone length, body mass, and the product of bone length and body mass) are compared in two modern human populations with very different body proportions: Pecos Pueblo Amerindians and East Africans. All five major long bones (excluding the fibula) were examined. Mechanical predictions are that cortical area (axial strength) should scale with body mass, while section modulus (bending/torsional strength) should scale with the product of body mass and moment arm length. These predictions are borne out for section moduli, when moment arm length is taken to be proportional to bone length, except in the proximal femoral diaphysis, where moment arm length is proportional to mediolateral body breadth (as would be expected given the predominance of M-L bending loads in this region). Mechanical scaling of long bone bending/torsional strength is similar in the upper and lower limbs despite the fact that the upper limb is not weight-bearing. Results for cortical area are more variable, possibly due to a less direct dependence on mechanical factors. Use of unadjusted bone length alone as a "size" measure produces misleading results when body shape varies significantly, as is the case between many modern and fossil hominid samples. In such cases a correction factor for body shape should be incorporated into any "size" standardization.