Biomechanical analysis of movement strategies in human forward trunk bending. I. Modeling

 Two behavioral goals are achieved simultaneously during forward trunk bending in humans: the bending movement per se and equilibrium maintenance. The objective of the present study was to understand how the two goals are achieved by using a biomechanical model of this task. Since keeping the center of pressure inside the support area is a crucial condition for equilibrium maintenance during the movement, we decided to model an extreme case, called “optimal bending”, in which the movement is performed without any center of pressure displacement at all, as if standing on an extremely narrow support. The “optimal bending” is used as a reference in the analysis of experimental data in a companion paper. The study is based on a three-joint (ankle, knee, and hip) model of the human body and is performed in terms of “eigenmovements”, i.e., the movements along eigenvectors of the motion equation. They are termed “ankle”, “hip”, and “knee” eigenmovements according to the dominant joint that provides the largest contribution to the corresponding eigenmovement. The advantage of the eigenmovement approach is the presentation of the coupled system of dynamic equations in the form of three independent motion equations. Each of these equations is equivalent to the motion equation for an inverted pendulum. Optimal bending is constructed as a superposition of two (hip and ankle) eigenmovements. The hip eigenmovement contributes the most to the movement kinematics, whereas the contributions of both eigenmovements into the movement dynamics are comparable. The ankle eigenmovement moves the center of gravity forward and compensates for the backward center of gravity shift that is provoked by trunk bending as a result of dynamic interactions between body segments. An important characteristic of the optimal bending is the timing of the onset of each eigenmovement: the ankle eigenmovement onset precedes that of the hip eigenmovement. Without an earlier onset of the ankle eigenmovement, forward bending on the extremely narrow support results in falling backward. This modeling approach suggests that during trunk bending, two motion units – the hip and ankle eigenmovements – are responsible for the movement and for equilibrium maintenance, respectively. Received: 1 July 1999 / Accepted in revised form: 23 October 2000     

Biomechanical properties and a kinetic simulation model of the smooth muscle I2 in the buccal mass of Aplysia

The muscle I2 is a smooth muscle from the buccal mass of the marine mollusc Aplysia californica whose neural control, in vivo kinematics, and behavioral role have been extensively analyzed. In this study, we measured the activation and contractile dynamics of the muscle in order to construct a Hill-type kinetic model of the muscle. This is the first study to our knowledge, of Aplysia muscle contractile dynamics. The isometric force-frequency relationship of I2 had a frequency threshold of about 6–8 Hz, and its force output saturated at 20–25 Hz, properties that match the high frequency (20 Hz) bursts generated by the B31/B32 neurons that innervate it. Peak isometric force was generated at about 118% of the in situ relaxed length. These results and I2's estimated in vivo kinematics suggest that it generates maximum force at the onset of protraction. The muscle tension during iso-velocity lengthening and shortening was an asymmetric function of velocity. Short range stiffness and yielding responses were observed in lengthening, whereas muscle tension decreased smoothly in shortening. These visco-elastic properties suggest that the I2 muscle can serve to brake forceful retraction movements. A Hill-type model, parameterized from the measurements, captured many of the mechanical properties of I2. Our results provide a quantitative understanding of the biomechanical significance of the muscle's neural control and provide a basis for simulation studies of the control of feeding behavior. Received: 5 February 1999 / Accepted in revised form: 18 May 1999     

Molecule capture by olfactory antennules: Mantis shrimp

 A critical step in the process of olfaction is the movement of odorant molecules from the environment to the surface of a chemosensory structure. Many marine crustaceans capture odorant molecules with arrays of chemosensory sensilla (aesthetascs) on antennules that they flick through the water. We developed a model to calculate molecule flux to the surfaces of aesthetascs in order to study how the size, aesthetasc spacing, and flick kinematics of olfactory antennules affect their performance in capturing molecules from the surrounding water. Since the three-dimensional geometry of an aesthetasc-bearing antennule is complex, dynamically-scaled physical models can often provide an efficient method of determining the fluid velocity field through the array. Here we present a method to optimize the incorporation of such measured velocity vector fields into a numerical simulation of the advection and diffusion of odorants to aesthetasc surfaces. Furthermore, unlike earlier models of odorant interception by antennae, our model incorporates odorant concentration distributions that have been measured in turbulent ambient flows. By applying our model to the example of the olfactory antennules of mantis shrimp, we learned that flicking velocity can have profound effects on odorant flux to the aesthetascs if they operate in the speed range in which the leakiness of the gaps between the aesthetascs to fluid movement is sensitive to velocity. This sensitivity creates an asymmetry in molecule fluxes between outstroke and return stroke, which results in an antennule taking discrete samples in space and time, i.e. “sniffing”. As stomatopods grow and their aesthetasc Reynolds number increases, the aesthetasc arrangement on the antennule changes in a way that maintains these asymmetries in leakiness and molecule flux between the outstroke and return stroke, allowing the individual to continue to take discrete samples as it develops. Received: 24 May 2000 / Revised version: 8 May 2001 / Published online: 7 December 2001     

In one era and out the other

A guided tour through much of photosynthesis research as I saw it, 1936–2001, is presented here. For earlier perspectives, see Myers 1974 (Plant Physiol 54: 420–426) and 1996 (Photosynth Res 50: 195–208). This revised version was published online in June 2006 with corrections to the Cover Date.     

Quantization of human motions and learning of accurate movements

This paper presents a mathematical model for the learning of accurate human arm movements. Its main features are that the movement is the superposition of smooth submovements, the intrinsic deviation of arm movements is considered, visual and kinesthetic feedback are integrated in the motion control, and the movement duration and accuracy are optimized with practice. This model is consistent with the jerky arm movements of infants, and may explain how the adult motion behavior emerges from the infant behavior. Comparison with measurements of adult movements shows that the kinematics of accurate movements are well predicted by the model. Received: 15 May 1997 / Accepted 5 December 1997     

The reported incidence of campylobacteriosis modelled as a function of earlier temperatures and numbers of cases,Montreal, Canada, 1990–2006

Previous studies have detected an effect of earlier temperatures on the incidence of campylobacteriosis in humans, but without adjustment for earlier numbers of cases of the disease. We estimated the effect of temperature on the number of cases notified by week in Montreal, Canada, from 1 January 1990 to 26 March 2006, simultaneously with the effect of the numbers of cases notified in the preceding weeks. The current campylobacteriosis count (week 0) was modelled by negative binomial regression, with earlier weekly average temperatures and earlier counts as predictors. Secular trends were accounted for by cubic spline functions and seasonal variations by sine-cosine functions. Indicator variables identified weeks with fewer than 5 working days. In the final statistical model, a 1°C increase in temperature above 10°C during any of weeks −1 to −6 was associated with a 0.8% (95% CI: 0.3% to 1.3%) increase in the current count. For each additional notified case during any of weeks −1 to −5 or −9 to −12, the increase in the current count was approximately 0.5% (95% CI: 0.2% to 1.0%). Thus, earlier temperatures and earlier counts have independent effects, that of temperatures being the larger one. The temperature effect is too small to require short term public health planning. However, in Montreal, an increase in average temperature of the order of 4.5°C, forecast by some for 2055, could produce a 23% increase in incidence, resulting in about 4,000 excess cases per year.     

Schema design and implementation of the grasp-related mirror neuron system

 Mirror neurons within a monkey's premotor area F5 fire not only when the monkey performs a certain class of actions but also when the monkey observes another monkey (or the experimenter) perform a similar action. It has thus been argued that these neurons are crucial for understanding of actions by others. We offer the hand-state hypothesis as a new explanation of the evolution of this capability: the basic functionality of the F5 mirror system is to elaborate the appropriate feedback – what we call the hand state– for opposition-space based control of manual grasping of an object. Given this functionality, the social role of the F5 mirror system in understanding the actions of others may be seen as an exaptation gained by generalizing from one's own hand to an other's hand. In other words, mirror neurons first evolved to augment the “canonical” F5 neurons (active during self-movement based on observation of an object) by providing visual feedback on “hand state,” relating the shape of the hand to the shape of the object. We then introduce the MNS1 (mirror neuron system 1) model of F5 and related brain regions. The existing Fagg–Arbib–Rizzolatti–Sakata model represents circuitry for visually guided grasping of objects, linking the anterior intraparietal area (AIP) with F5 canonical neurons. The MNS1 model extends the AIP visual pathway by also modeling pathways, directed toward F5 mirror neurons, which match arm–hand trajectories to the affordances and location of a potential target object. We present the basic schemas for the MNS1 model, then aggregate them into three “grand schemas”– visual analysis of hand state, reach and grasp, and the core mirror circuit – for each of which we present a useful implementation (a non-neural visual processing system, a multijoint 3-D kinematics simulator, and a learning neural network, respectively). With this implementation we show how the mirror system may learnto recognize actions already in the repertoire of the F5 canonical neurons. We show that the connectivity pattern of mirror neuron circuitry can be established through training, and that the resultant network can exhibit a range of novel, physiologically interesting behaviors during the process of action recognition. We train the system on the basis of final grasp but then observe the whole time course of mirror neuron activity, yielding predictions for neurophysiological experiments under conditions of spatial perturbation, altered kinematics, and ambiguous grasp execution which highlight the importance of the timingof mirror neuron activity. Received: 6 August 2001 / Accepted in revised form: 5 February 2002     

Standing sway: iterative estimation of the kinematics and dynamics of the lower extremities from force-plate measurements

In this study, a model for the estimation of the dynamics of the lower extremities in standing sway from force plate data only is presented. A three-dimensional, five-segment, four-joint model of the human body was used to describe postural standing sway dynamics. Force-plate data of the reactive forces and centers of pressure were measured bilaterally. By applying the equations of motion to these data, the transversal trajectory of the center of gravity (CG) of the body was resolved in the sagittal and coronal planes. An inverse kinematics algorithm was used to evaluate the kinematics of the body segments. The dynamics of the segments was then resolved by using the Newton-Euler equations, and the model's estimated dynamic quantities of the distal segments were compared with those actually measured. Differences between model and measured dynamics were calculated and minimized, using an iterative algorithm to re-estimate joint positioning and anthropometric properties. The above method was tested with a group of 11 able-bodied subjects, and the results indicated that the relative errors obtained in the final iteration were of the same order of magnitude as those reported for closed loop problems involved in direct kinematics measurements of human gait. Received: 22 July 1997 / Accepted in revised form: 29 January 1998     

Analysis of kinematically redundant reaching movements using the equilibrium-point hypothesis

 Six subjects performed a planar reaching arm movement to a target while unpredictable perturbations were applied to the endpoint; the perturbations consisted of pulling springs having different stiffness. Two conditions were applied; in the first, subjects had to reach for the target despite the perturbation, in the second condition, the subjects were asked to not correct the motion as a perturbation was applied. We analyzed the kinematics profiles of the three arm segments and, by means of inverse dynamics, calculated the joint torques. The framework of the equilibrium-point (EP) hypothesis, the λ model, allowed the reconstruction of the control variables, the “equilibrium trajectories”, in the “do not correct” condition for the wrist and the elbow joints as well as for the end point final position, while for the other condition, the reconstruction was less reliable. The findings support and extend to a multiple-joint planar movement, the paradigm of the EP hypothesis along with the “do not correct” instruction. Received: 3 May 1999 / Accepted in revised form: 19 May 2000     

Thermal stability of a flavoprotein assessed from associative analysis of polarized time-resolved fluorescence spectroscopy

Upon gradually heating a particular mutant of the flavoprotein NADH peroxidase, it was found from the peculiar time-resolved fluorescence anisotropy pattern of the flavin prosthetic group (FAD) that, at elevated temperature, FAD is released from the tetrameric enzyme. Since in this case a mixture of free and enzyme-bound FAD contributes to the time-dependent fluorescence anisotropy, its analysis can only be accomplished by an associative fitting model, in which specific fluorescence lifetimes of both species are linked to specific correlation times. In this letter the general approach to the associative polarized fluorescence decay analysis is described. The procedure can be used for other flavoproteins to determine the temperature at which the onset of thermal denaturation will start, leading to release of the flavin prosthetic group. Received: 20 November 1998 / Revised version: 6 April 1999 / Accepted: 8 April 1999     

Monotone travelling fronts in an age-structured reaction-diffusion model of a single species

 We consider a partially coupled diffusive population model in which the state variables represent the densities of the immature and mature population of a single species. The equation for the mature population can be considered on its own, and is a delay differential equation with a delay-dependent coefficient. For the case when the immatures are immobile, we prove that travelling wavefront solutions exist connecting the zero solution of the equation for the matures with the delay-dependent positive equilibrium state. As a perturbation of this case we then consider the case of low immature diffusivity showing that the travelling front solutions continue to persist. Our findings are contrasted with recent studies of the delayed Fisher equation. Travelling fronts of the latter are known to lose monotonicity for sufficiently large delays. In contrast, travelling fronts of our equation appear to remain monotone for all values of the delay. Received: 1 November 2001 / Revised version: 10 May 2002 / Published online: 23 August 2002 Mathematics Subject Classification (2000): 35K57, 92D25 Key words or phrases: Age-structure – Time-delay – Travelling Fronts – Reaction-diffusion     

Coalescence time for two genes from a subdivided population

In this paper a new form of the solution for the Laplace transform and moments of the distribution of the waiting time for two genes to coalescence is presented. The two genes are sampled from a subdivided population where migration rates between populations are constant in time. Equal subpopulation size is not assumed. For the special case of an island model with equal migration rates between islands, the Laplace transform of the coalescence time and the first and second moments are found explicitly. The new form of the solutions allows numerical calculation. The connection of how the results relate to a panmictic population when migration rates are large is illustrated using strong-migration-limit theory. Received: 19 April 1999 / Revised version: 22 March 2001 / Published online: 19 September 2001     

A modular artificial neural net for controlling a six-legged walking system

 A system that controls the leg movement of an animal or a robot walking over irregular ground has to ensure stable support for the body and at the same time propel it forward. To do so, it has to react adaptively to unpredictable features of the environment. As part of our study of the underlying mechanisms, we present here a model for the control of the leg movement of a 6-legged walking system. The model is based on biological data obtained from the stick insect. It represents a combined treatment of realistic kinematics and biologically motivated, adaptive gait generation. The model extends a previous algorithmic model by substituting simple networks of artificial neurons for the algorithms previously used to control leg state and interleg coordination. Each system controlling an individual leg consists of three subnets. A hierarchically superior net contains two sensory and two ‘premotor’ units; it rhythmically suppresses the output of one or the other of the two subordinate nets. These are continuously active. They might be called the ‘swing module’ and the ‘stance module’ because they are responsible for controlling the swing (return stroke) and the stance (power stroke) movements, respectively. The swing module consists of three motor units and seven sensory units. It can produce appropriate return stroke movements for a broad range of initial and final positions, can cope with mechanical disturbances of the leg movement, and is able to react to an obstacle which hinders the normal performance of the swing movement. The complete model is able to walk at different speeds over irregular surfaces. The control system rapidly reestablishes a stable gait when the movement of the legs is disturbed. Received: 13 July 1994/Accepted in revised form: 15 November 1994     

Asymptotics of Conduction Velocity Restitution in Models of Electrical Excitation in the Heart

We extend a non-Tikhonov asymptotic embedding, proposed earlier, for calculation of conduction velocity restitution curves in ionic models of cardiac excitability. Conduction velocity restitution is the simplest non-trivial spatially extended problem in excitable media, and in the case of cardiac tissue it is an important tool for prediction of cardiac arrhythmias and fibrillation. An idealized conduction velocity restitution curve requires solving a non-linear eigenvalue problem with periodic boundary conditions, which in the cardiac case is very stiff and calls for the use of asymptotic methods. We compare asymptotics of restitution curves in four examples, two generic excitable media models, and two ionic cardiac models. The generic models include the classical FitzHugh–Nagumo model and its variation by Barkley. They are treated with standard singular perturbation techniques. The ionic models include a simplified “caricature” of Noble (J. Physiol. Lond. 160:317–352, 1962) model and Beeler and Reuter (J. Physiol. Lond. 268:177–210, 1977) model, which lead to non-Tikhonov problems where known asymptotic results do not apply. The Caricature Noble model is considered with particular care to demonstrate the well-posedness of the corresponding boundary-value problem. The developed method for calculation of conduction velocity restitution is then applied to the Beeler–Reuter model. We discuss new mathematical features appearing in cardiac ionic models and possible applications of the developed method.     

Three-dimensional kinematic analysis of influence of hand orientation and joint limits on the control of arm postures and movements

The problems related to kinematic redundancy in both task and joint space were investigated for arm prehension movements in this paper. After a detailed analysis of kinematic redundancy of the arm, it is shown that the redundancy problem is ill posed only for the control of hand orientation. An experiment was then designed to investigate the influence of hand orientation on the control of arm movements. Since movements must be made within the limits of the joints, the influence of these limits was also analyzed quantitatively. The results of the experiment confirm that the increase of movement time because of the change of object orientation is due to the lengthening of the deceleration phase disproportionately to the rest of the movement. The variation of hand path due to the change of object orientation was observed as being surprisingly small for some subjects as opposed to the large range of object orientation, implying that hand path and hand orientation could be controlled separately, thus simplifying the computational problem of inverse kinematics. Moreover, the observations from the present experiment strongly suggest that a functional segmentation of the proximal and distal joints exists and that the control of wrist motion is dissociated from the rest of joint motions. The contribution of each joint in the control of arm movements could be determined through the principle of minimum energy and minimum discomfort under the constraints of the joint limits. A simplified inverse kinematics model was tested. It shows that these hypotheses can be easily implemented in a geometric algorithm and be used to predict arm prehension postures reasonably well under the constraints of joint limits. Received: 6 August 1998 / Accepted in revised form: 16 December 1998     

Analysis of an excitable dendritic spine with an activity-dependent stem conductance

 Dendritic spines are the major target for excitatory synaptic inputs in the vertebrate brain. They are tiny evaginations of the dendritic surface consisting of a bulbous head and a tenuous stem. Spines are considered to be an important locus for plastic changes underlying memory and learning processes. The findings that synaptic morphology may be activity-dependent and that spine head membrane may be endowed with voltage-dependent (excitable) channels is the motivation for this study. We first explore the dynamics, when an excitable, yet morphologically fixed spine receives a constant current input. Two parameter Andronov–Hopf bifurcation diagrams are constructed showing stability boundaries between oscillations and steady-states. We show how these boundaries can change as a function of both the spine stem conductance and the conductance load of the attached dendrite. Building on this reference case an idealized model for an activity-dependent spine is formulated and analyzed. Specifically we examine the possibility that the spine stem resistance, the tunable “synaptic weight” parameter identified by Rall and Rinzel, is activity-dependent. In the model the spine stem conductance depends (slowly) on the local electrical interactions between the spine head and the dendritic cable; parameter regimes are found for bursting, steady states, continuous spiking, and more complex oscillatory behavior. We find that conductance load of the dendrite strongly influences the burst pattern as well as other dynamics. When the spine head membrane potential exhibits relaxation oscillations a simple model is formulated that captures the dynamical features of the full model. Received: 10 January 1997/Revised version: 25 March 1997     

The onset of oscillatory dynamics in models of multiple disease strains

 We examine a generalised SIR model for the infection dynamics of four competing disease strains. This model contains four previously-studied models as special cases. The different strains interact indirectly by the mechanism of cross-immunity; individuals in the host population may become immune to infection by a particular strain even if they have only been infected with different but closely related strains. Several different models of cross-immunity are compared in the limit where the death rate is much smaller than the rate of recovery from infection. In this limit an asymptotic analysis of the dynamics of the models is possible, and we are able to compute the location and nature of the Takens–Bogdanov bifurcation associated with the presence of oscillatory dynamics observed by previous authors. Received: 5 December 2001 / Revised version: 5 May 2002 / Published online: 17 October 2002 Keywords or phrases: Infection – Pathogen – Epidemiology – Multiple strains – Cross-immunity – Oscillations – Dynamics – Bifurcations     

Optimal allocation of building blocks between nutrient uptake systems in a microbe

 A bacterial cell must distribute its molecular building blocks among various types of nutrient uptake systems. If the microbe is to maximize its average growth rate, this allocation of building blocks must be adjusted to the environmental availabilities of the various nutrients. The adjustments can be found from growth balancing considerations. We give a full proof of optimality and uniqueness of the optimal allocation regime for a simple model of microbial growth and internal stores kinetics. This proof suggests likely candidates for optimal control regimes in the case of a more realistic model. These candidate regimes differ with respect to the information that the cells control system must have access to. We pay particular attention to one of the three candidates, a feedback regime based on a cellular control system that monitors only internal reserve densities. We show that allocation converges rapidly to balanced growth under this control regime. Received: 20 November 2000 / Revised version: 7 August 2001 / Published online: 21 February 2002     

Causal isolation robustness analysis: the combinatorial strategy of circadian clock research

This paper distinguishes between causal isolation robustness analysis and independent determination robustness analysis and suggests that the triangulation of the results of different epistemic means or activities serves different functions in them. Circadian clock research is presented as a case of causal isolation robustness analysis: in this field researchers made use of the notion of robustness to isolate the assumed mechanism behind the circadian rhythm. However, in contrast to the earlier philosophical case studies on causal isolation robustness analysis (Weisberg and Reisman in Philos Sci 75:106–131, 2008; Kuorikoski et al. in Br J Philos Sci 61:541–567, 2010), robustness analysis in the circadian clock research did not remain in the level of mathematical modeling, but it combined it with experimentation on model organisms and a new type of model, a synthetic model.