Some mathematical models of reflex-metameric therapy

Some mathematical models of reflex-metameric therapy

$631 Track 18. Trends in Cranial and Spinal Biomechanics requiring differentiation and integration. The redundancy of multiple sensors can be used t...

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$631

Track 18. Trends in Cranial and Spinal Biomechanics

requiring differentiation and integration. The redundancy of multiple sensors can be used to improve calculation accuracy. The method was applied to horses and elephants, using two miniature MT9 (Xsens, Netherlands) sensors (combining both 3D accelerometers and gyroscopes) firmly mounted on the dorsal peak of the fore and hindquarters. Sensor data during horse trotting (speed: 2.10-4.10m/s) with simultaneous force plate data were recorded in our gait laboratory. Elephant data during slow and fast walking (speed: 1.35-4.03 m/s)were recorded outdoors (Woburn Safari Park, UK) using bodymounted data loggers. The horse results show good agreement with the force plate records in vertical and horizontal directions, but overestimate the lateral force. This is probably due to errors in centre of mass location estimation, and the large lateral skin movements on the spine with respect to the underneath bones. The shapes of the estimated GRF vs % gait cycle curves for the elephant compare well with preliminary GRF data for elephants and GRF data from other walking quadrupeds. This multi-sensor method has the advantage that it does not require a gait laboratory environment and can be used for field studies with an untethered, completely body-mounted recording system. As the orientation data are also recorded by gyroscopes, this provides the possibility of real-time inverse dynamics analysis in a global coordinate system. 4593 Mo-Tu, no. 15 (P67) A comparison between tendon and muscle fibre strain and strain rate in two ankle extensor muscles in the rat during treadmill locomotion E.R Tole, J.M. Wakeling. The Structure and Motion Laboratory, The Royal Veterinary College, Hatfield, UK The mechanical roles of muscles and tendons are often studied independently, despite the highly inter-dependent nature of their functioning. Researchers have shown that the contractile properties of muscles are well matched to the cycles of length changes that occur during normal locomotion. It is equally well known that elastic energy storage and release, facilitated by tendons, can be an important energy-conserving mechanism during some forms of locomotion. It is therefore of interest to consider the interaction between these two tissues. Work in running turkeys [1] and hopping wallabies [2], has shown that during steady, level locomotion the ankle extensor muscles produce high levels of force, while undergoing very low strain rates. In contrast, during incline running in turkeys the ankle extensor muscles are shown to actively shorten. Such a pattern has not been shown to hold true in wallabies, a fact attributed to their specialised limb design. It is of interest to determine how wide spread such a phenomenon is within terrestrial animals. Furthermore, tendon-muscle interactions may be influenced by the intrinsic properties of the muscle and represents an area that warrants further investigation. We present sonomicrometry and fluoroscopy data quantifying strains and strain rates in the tendon and muscle fibres of the soleus and plantaris muscles of the rat, thus comparing predominantly slow and fast fibre muscles respectively. Manipulating locomotor velocity (20-50cm s -1) and incline (0-25 °) led to variations in strain patterns, associated with the intrinsic properties of the muscles and their interaction with the associated tendons. References [1] Roberts T.J., et al. Muscular force in running turkeys: the economy of minimizing work. Science 1997; 275(5303): p. 1113-1115. [2] Biewener A.A., et al. Dynamics of leg muscle function in tammar wallabies (M. eugenil) during level versus incline hopping. J Exp Biol. 2004; 207(2): p. 211-223.

6426 Mo-Tu, no. 16 (P67) The relation between running economy and kinematical variables: influence of body mass in competitive runners L.A. Peyr6-Tartaruga, M.H. de Medeiros, M. Coertjens, M. Peikriszwili Tartaruga, L.R Martins Kruel. Exercise Research Laboratory, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil The movement mechanics together with the limiting physiological factors of human performance may influence the results of running economy (i.e., oxygen uptake during submaximal running). For example, a successful endurance runner is characterized by less vertical oscillation and longer strides. Despite these observations, the interaction between the biomechanical and physiological factors is not well known. One cause seems be due to scaling relative to body mass. The aim of this study was to analize the influence of body mass through of the allometric expressions on relation between running economy with kinematical variables in competitive runners. Nine female endurance runners ran at 12 km.h -1 . Respiratory gases were collected. Kinematic records were obtained by a high-speed video camera (120 Hz). A Principal component factor analysis with varimax rotation was used. A Pearson Correlation Coefficient were also used for analize the linear association between biomechanical variables and running economy at differents allometric expressions (b=0, -0.67, -0.73, -0.75, -1). The scaling exerted a decrease on explanation power of kinematical descriptors about the economy running ( b = - l : 75.8%; b=-0.75: 74.9%, b=-0.73: 74.6%; b=-0,67: 73,7%) and

the correlation coefficients (r 2, * p < 0.05) between stride length with running economy were: b = - l : r 2 =0.687*; b =-0.75: r 2 =0.518"; b =-0.73: r2 = 0.488*; b=-0.67: r2=0.413), between stride time with running economy ( b = - l : r2=0.687"; b=-0.75: r2=0.515"; b=-0.73: r2=0.488"; b=-0.67: r2=0.409) and between stride rate with running economy (b =-1: r2 =0.624*; b =-0.75: r2 =0.499*; b=-0.73: r2 =0.471"; b=-0.67: r2 =0.404*). The relation between swing time and running economy presented a r2 greater when b = -0.75 (b = -1: r2 =0.485", b =-0.75: r2 =0.662*; b =-0.73: r2 =0.644*; b =-0.67: r2 =0.603*). Furthermore, the variables relative stride length, stride rate and swing time were the most predictives of running economy. These data yield novel insights into relations between the running economy and the biomechanical variables in competitive runners. 6219 The microstructure and L. Farran 1, S. Eichhorn 1, Manchester, Manchester, Manchester, Manchester,

Mo-Tu, no. 17 (P67) mechanical properties of human fingernails R. Ennos 2. 1School of Materials, University of UK, 2Faculty of Life Sciences, University of UK

This study uses an interdisciplinary approach to investigate the properties of human fingernails. Techniques from the fields of biology and materials science are used in conjunction to give an introductory analysis of the mechanical properties and microstructure of human fingernails, and to explore the influence of humidity on nail properties. The techniques employed include cutting tests, indentation, mechanical thermal analysis, Raman spectroscopy and scanning electron microscopy. Cutting tests have shown that nails have a high work of fracture in the region 11-22 kJm -2 and, like many biological materials, are anisotropic. This property is shown to be influenced by relative humidity, with the highest anisotropy occurring at 55%. Scanning electron microscopy has revealed qualitative information on the microstructure of nails, and this has been compared with feline claws. Nails have been observed to have a highly complex hierarchical arrangement comprising three distinct histological layers, whereas feline claws possess a much simpler homogeneous microstructure. It is thought that fibres within the intermediate nail layer are responsible for deflecting cracks away from the delicate nail bed, and that this mechanism gives rise to the observed anisotropy. This study provides an insight into the relationship between microstructure and mechanical properties, and the effect of humidity on nails. This could provide useful information for evolutionary biologists wishing to investigate the functional morphology of the nail, and may ultimately aid the cosmetic industry by providing information on the relationship between nail hydration and toughness.

Track 18

Trends in Cranial and Spinal B i o m e c h a n i c s 6383 Mo-Tu, no. 1 (P67) Some mathematical models of reflex-metameric therapy I. Selezov 1, V. Bersenev 2. 1Department of Wave Processes, Institute of Hydromechanics, Nat. Acad. Sci., Ukraine, Kiev, 2Institute of Pain Problems, Kiev, Ukraine An extended mathematical model of propagating medicine injected into a tissue.is presented. Earlier this problem has been considered on the basis of the simplest model without taking into account the dependence on spatial coordinates (Bellman, 1983). Analytical solutions of the initial boundary value (IBV)-problem are obtained and analyzed numerically. Characteristic features and estimations of decreasing medicine concentration during spreading are presented. Another problem deals with a response of the active nerve fiber to an extracellurar excitation. Our aim is to evaluate the effect of the exciting pulse deviation from a step-function on changing the transmembrane potential in time and space. Earlier the solution for a step-function excitation was obtained (Hodgkin & Rushton, 1946). Analytical solutions of IBV-problem are obtained and analyzeda allowing to establish and evaluate a delay in potential rise. The medicine injection is accompanied with many phenomena such as spreading of injected substance in a tissue, excitation of membranes and transport processes in cells (Hodgkin & Huxley, 1952; Selezov 1994), excitation of receptor fields and, as a consequence, nerve fibers and its tissue-targets skeleton muscles, propagation of deformation waves in neurons. The problems above presented are directly connected with the reflexmetameric therapy dealing with the metameric nerve excitation and medicine delivery (Bersenev, 2000). Metamery is a subdivision of the spinal column of human body onto a set of repeated each other parts (metamers), each of

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Journal of Biomechanics 2006, Vol. 39 (Suppl 1)

them is responsible for innervation of its part of the body and controls this part. Such a therapy allows to excite a nerve structure directly connected with a treatment zone and to deliver the medicine to a nearest vicinity of this zone. As a result, it opens the possibilities of triggering the renewal processes in disordered regions. 4335 Mo-Tu, no. 2 (P67) Simulating intra-ventricular drug delivery: an experimental investigation using a geometrically accurate, physical model of the human ventricular system L. Howden 1, D. Giddings 1, A. Aroussi 1, H. Power 1, M. Vloeberghs 2, D. Walker 2, M. Garnett 3. 1School of Mechanical, Materials and Manufacturing

Engineering, University of Nottingham, UK, 2School of Human Development, Faculty of Medicine and Health Sciences, University of Nottingham, UK, 3School of Pharmacy, University of Nottingham, UK The Human Ventricular System (HVS) can be described as four chambers that contain Cerebrospinal fluid (CSF), a water-like substance that prevents the brain from impact against the skull. The flow dynamics of CSF are not entirely understood, however CSF is known to flow from the HVS to the outer surface of the brain. A test rig and model have been constructed to investigate CSF flow patterns, optically, within the HVS [1]. The model of the CSF space was constructed from MRI data and reproduced using vacuum formed acrylic sheet at 2:1 scale. CSF is in communication with the Central Nervous System (CNS) and provides an ideal mechanism for delivering cancer treating drugs to areas of the body [2]. Understanding how a drug moves through the CSF is essential to developing any drug delivery techniques. This paper describes attempts to visualise the movement of drugs injected into the HVS, using dye to illustrate drug movement through a transparent physical model of the entire CSF volume. The investigation aims to examine the effect that initial drug injection Reynolds number will have on the movement and concentration of a drug as it travels through the HVS. No real or experimental data currently exists and so this paper provides the first experimental demonstration of Intraventricular drug delivery. The results show that the injection tube Reynolds number is important in determining how a drug injected into the CSF will move and its concentration at various regions of the CNS. The results show that laminar and turbulent injections produce significantly different flow patterns, each with their advantages to drug delivery. References [1] Aroussi A, Vloeberghs M, Etchell S, Gransden J, Latimer R, Giddings D. Simulation of Human Cerebrospinal fluid Flow. 11th International Symposium on Flow Visualization. Notre Dame, Indiana, 2004. [2] Ghersi-Egea JF, Strazielle N. Brain drug delivery, drug metabolism, and multidrug resistance at the choroid plexus. Microscopy Research & Technique 2001 ; 52(1): 83-8. 7165 Mo-Tu, no. 3 (P67) The importance of sensomotorical systems in biomechanics and orthopaedics W. Plitz, G. Pfaff. Labor fEtr Biomechanik und Experimentelle Orthop~die der

Ludwig-Maximilians Universit~t MfJnchen, Klinikum Grol3hadem, Munich, Germany Sensomotorical systems are the neurological basic information for posture and movement patterns of our orthopaedic patients. Coordination of muscle tension is the result of integration of different steering systems. Little alterations in these neurological steering systems cause reaction, adaptation and compensation in muscles and skeleton. The coordination of nerves, muscles and bones can be compared to a computer system: False software information can cause a chain reaction that can lead to hardware problems. Muscular dysbalance, myotendinosis, myofascial or pseudoradicular painsyndroms, only to mention some examples are very often the result of sensomotoric faults of coordination between afferent and efferent impulses. For fundamental treatment of functional disorders of the muscle and skeleton system afferent modulating therapies based on proprio- and exteroception should be preferred. Especially the treatment with sensomotoric orthopaedic orthotics should consider these aspects. The outcome of functional therapies on posture and movement patterns can be shown by an optical 3D-spinemeasuring system (formetric ®) and mobile monitoring of movement patterns (sonoSens ®) based on ultrasonic technique.

Poster Presentations

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Biotransport 5274 We-Th, no. 1 (P67) Mechanical analysis on the role of the endothelial surface glycocalyx in microvessel permeability M. Sugihara-Seki, T. Akinaga, T. Itano. Kansai University, Osaka, Japan The luminal surface of vascular endothelial cells is covered by a layer of macromolecules referred to as the glycocalyx, and its role as a molecular filter and diffusive barrier has been pointed out to be crucial for microvessel walls to maintain low permeability to macromolecules. The present study is aimed to examine theoretically the role of the glycocalyx in micorvessel permeability. A mathematical model for the solute and water transport across the glycocalyx was developed, based on the quasi-periodic ultrastructure of the endothelial surface glycocalyx obtained from a detailed structual analysis [1]. Assuming a hexagonal arrangement of core proteins with 12 nm diameter and characteristic spacings of 20 nm [2], we made fluid mechanical computations on the motion of spherical solutes of 2-4 nm diameter and suspending fluid flowing between core proteins due to a pressure difference and concentration difference of solutes across the glycocalyx. The predicted values of the diffusive permeability to solutes decline with solute size, known as "restricted diffusion", and show a reasonable agreement with experimental observations. The reflection coefficient to solutes corresponding to serum albumin is predicted to be as high as 0.8, accounting satisfactorily for the observed molecular filtering. These results conform to the hypothesis that the glycocalyx forms the primary size selective structure to solutes in microvessel permeability. The water flow through the glycocalyx converging into the entrance of the interendothelial cleft was also computed together with the flow through the cleft in the presence of tight junction strands and their gaps [3], to estimate the the hydraulic conductivity. The results predict that the glycocalyx contributes to the hydraulic resistance of the microvessel wall less than the interendothelial clefts, if the cleft width is 18nm, the gap length is 315nm [3], the cleft spacing is 10urn and the glycocalyx thickness is 150 nm. References [1] Squire et al. J. Struct. Biol. 2991; 136: 239. [2] Sugihara-Seki. J. Fluid Mech. In press. [3] Adamson et al. J. Physiol. 2994; 557.3: 889. 6653 We-Th, no. 2 (P67) An electrostatic model for osmotic flow through charged pores M. Sugihara-Seki, T. Akinaga, T. Itano. Kansai University, Osaka, Japan The endothelial cells of microvessels form the critical barrier controlling the material exchange between the circulating blood and the body tissues. Experimental studies have shown that the luminal endothelial membrane and the endothelial surface glycocalyx are negatively charged, and thus, the microvascular permeability to anionic macromolecules is lower than neutral or cationic ones. As a basis to understand the contribution of electrical charges to the transport property of the microvessel wall, we have developed an electrostatic model for osmotic flow through pores with surface charges in the presence of charged solutes, based on the so-called "pore theory" of capillary permeability. The classical analysis for the osmotic flow across membranes with long circular cylindrical pores [1] was extended to include the electrical interaction between surface charges of solutes and pores, and the osmotic reflection coefficient was evaluated from mechanical and thermodynamic considerations when the concentration difference of the solutes are present across the pore. For simplicity, we have assumed that the solute is a rigid sphere with uniformly distributed surface charges, and the solutes are suspended in an electrolyte which is an incompressible Newtonian fluid. The electrical potential was solved for a solute placed in a circular cylindrical pore, by a finite element-spectral method applied to the Poisson-Boltzmann equation together with the condition of the electrical neutrality, and the interaction energy between surface charges was used to express the osmotic reflection coefficient as a function of the surface charges, the ion concentration of the fluid, and the radius ratio of the solute and the pore. Our model predicts that even for small Debye length compared to the pore radius, the surface charges could significantly increase the osmotic reflection coefficient, when the charges of the solute and the pore have the same sign. If the reciprocity relation applies, this result suggests a substantial electrical effect on the solute transport across the microvessel wall. References [1] Anderson and Malone. Biophys. J. 1974; 14: 957.