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Modeling and Simulation of Intrafusal Muscle Fiber Using a Multi ; Modeling AND SIMULATION OF INTRAFUSAL mus- CLE fiBER USING A multi-sarcomeric MODEL N. S. Oborin Modeling and simulation of intrafusal muscle fiber using a multi-sarcomeric model BY N. S. Oborin TO OBTAIN THE DEGREE OF Master OF Science AT THE Delft UnivERSITY OF TECHNOLOGY, TO BE DEFENDED PUBLICLY ON ThursdaY June 23, 2016 AT 9:00 AM. Student number: 1384945 Supervisor: Dr. Ir. E. DE Vlugt An ELECTRONIC VERSION OF THIS THESIS IS AVAILABLE AT http://repository.tudelft.nl/. AbstrACT Muscle SPINDLE IS AN ORGAN OF PROPRIOCEPTION THAT PLAYS AN IMPORTANT ROLE IN neuro-muscular CONTROL OF THE HUMAN joints. It IS COMPOSED OF INTRAFUSAL fibers, THE MECHANICAL PROPERTIES OF WHICH DETERMINE THE AFFERENT RESPONSE OF THE spindle. IntrAFUSAL fiBERS ARE NOT homogenous: THEY ARE COMPOSED OF MANY sarcomeres, HAVE LOCALIZED FUSIMOTOR INNERVATION AND HAVE VARYING MYOSIN COMPOSITION THROUGHOUT THEIR length. Most MODELS OF INTRAFUSAL fiBERS DO NOT TAKE THESE STRUCTURAL CONSIDERATIONS INTO ACCOUNT AND MODEL IT AS A SINGLE sarcomere, THAT WAY OMITTING POTENTIAL EMERGENT BEHAVIOR THAT ARISES FROM A POPULATION OF sarcomeres. The EFFECTS OF SARCOMERE LENGTH INHOMOGENEITY ON THE BEHAVIOR OF INTRAFUSAL fiBER IS NOT known. In THIS STUDY A multi-sarcomeric MODEL IS DEVELOPED AND SIMULATED WITH A VARYING ACTIVATION SHAPE ALONG THE INTRAFUSAL fiBER TO SEE WHETHER AN EMERGENT BEHAVIOR IN PRESENT AND HOW IT manifests. Results SHOW THAT RELATIVE ACTIVATION OF CONTRACTING SARCOMERES HAS THE LARGEST effect. The fiBER MODEL WITH VARIED ACTIVATION SHOWED HISTORY DEPENDENCE ARISING FROM non-homogenous INITIAL SARCOMERE LENGTH distribution. The MODEL ALSO DEMONSTRATED amplitude-dependent BEHAVIOR UNDER MULTISINE STRETCHES THAT DID NOT APPEAR IN A non-multi-sarcomeric model. In conclusion, IT CAN BE STATED THAT multi-sarcomeric MODELS CAN BE BENEfiCIAL IN EXPLORATORY STUDIES AS THEY CAN DEMONSTRATE BEHAVIOR THAT CANNOT BE DESCRIBED WITH SIMPLISTIC models. III Contents 1 Introduction 1 2 Building THE Spindle Model3 2.1 OvERVIEW............................................3 2.2 The Model............................................4 2.2.1 Single Half-Sarcomere.................................4 2.2.2 Multiple Sarcomeres..................................5 2.3 PARAMETER Selection AND Model VALIDATION...........................6 2.3.1 Process OF Selection OF Model PARAMETERS.......................7 2.3.2 PERTURBATION Selection.................................7 2.3.3 GenerAL Criteria FOR Selecting PARAMETERS.......................7 2.3.4 PARAMETERIZATION OF Response.............................8 2.3.5 VALIDATION OF THE Model.................................8 2.4 Introduction OF Activation Inhomogeneity...........................8 2.4.1 PERTURBATION TYPES...................................9 2.4.2 PARAMETRIZATION OF Response.............................. 10 2.4.3 Data Analysis...................................... 10 2.5 Multisine PERTURBATION..................................... 10 2.5.1 Signal Design...................................... 10 2.5.2 Data Analysis...................................... 10 3 Results 11 3.1 VALIDATION AND PARAMETER Selection Results.......................... 11 3.1.1 PARAMETER Selection OF ExtrAFUSAL Fibers........................ 11 3.1.2 VALIDATION OF Multi-SrARCOMERE Model......................... 11 3.2 Effect OF Activation Shape ON Isometric Response....................... 14 3.2.1 Effects OF abg AND aoff ................................. 14 3.2.2 Effects OF abg AND aσ ................................... 17 3.2.3 Selection OF IntrAFUSAL Response............................ 17 3.3 Multisine PERTURBATION..................................... 20 4 Discussion 23 4.1 Model Derivation........................................ 23 4.2 PARAMETER Selection...................................... 23 4.3 VALIDATION............................................ 24 4.4 Effects OF Activation Shape ON Isometric Response...................... 25 4.4.1 Effects OF Initial LENGTH Inhomogeneity........................ 25 4.5 Multisine PERTURBATION..................................... 25 4.6 Conclusion........................................... 26 A RaW Data 27 B Notes ON Derivation OF VARIOUS PARAMETERS 31 B.1 On Selection OF cext AND kext .................................. 31 BibliogrAPHY 35 V 1 Introduction A MODEL IS A TOOL TO TEST A SCIENTIfiC HYPOTHESIS OR TO PREDICT AND DESCRIBE A BEHAVIOR OF A system. The TENDENCY IN THE SCIENTIfiC COMMUNITY IS TO KEEP COMPLEXITY TO THE minimum. Adopting A MORE COMPLEX MODEL (usually WITH MORE PARameters) SHOULD BE JUSTIfiED WITH A BETTER PREDICTION OF AN outcome. HoweVER, A MODEL WHICH DESCRIBES BEHAVIOR IN TERMS OF A SET OF EASILY INTERPRETABLE PARAMETERS IS ARGUABLY LESS COMPLEx. FOR Example, A black-boX TYPE MODEL WOULD BE GOOD AT DESCRIBING BEHAVIOR OF SOME PHYSIOLOGICAL system, HOWEVER IT WOULD JUST DO that, DESCRIBE WHAT IS ALREADY known. On THE OTHER hand, A MODEL THAT MIMICS THE INTERNAL STRUCTURE OF THE SYSTEM AND ITS components, GIVES MORE INSIGHT ABOUT THE FUNCTION OF THE SYSTEM BECAUSE NOW IT IS APPARENT HOW TWEAKING ONE PARAMETER, WHICH HAS A REAL LIFE counterpart, AFFECTS OVERALL BEHAVIOR. A COMPLEX MODEL CAN POTENTIALLY SOLVE TWO problems: A BETTER PREDICTION OF PHYSICAL RESPONSE AND OFFER A BETTER INSIGHT INTO THE FUNCTION OF THE SYSTEM AND RENDER IT MORE TRACTABLE FOR STUDY AND analysis. The HUMAN NERVOUS SYSTEM IS ONE EXAMPLE OF SUCH A COMPLEX system. Consisting OF 100 BILLION NEURAL cells, IT IS STUDIED BY NUMEROUS DISCIPLINES ATTEMPTING TO SHED SOME LIGHT ON ITS FUNCTION AND organization. One CONTRIBUTOR TO THIS fiELD IS THE Neuro-Muscular Control (NMC) RESEARCH GROUP AT TU Delft, STUDYING THE NEURAL CONTROL OF MOVement, IN PARTICULAR THE ROLE OF PROPRIOCEPTIVE feedback. One OF THE MEANS OF STUDYING NEURAL CONTROL OF MOVEMENT IS THROUGH MECHANICAL PERTURBATION OF THE joint(s) FROM WHICH THE visco-elastic PROPERTIES CAN BE determined. Visco-elasticity RESULTS FROM PASSIVE tissues, MUSCLE MECHANICS AND FROM THE PROPRIOCEPTIVE feedback. This WAY, BY MEASURING JOINT visco-elasticity, INFERENCE CAN BE MADE ON THE UNDERLYING STRUCTURES SUCH AS PROPRIOCEPTIVE feed-back GAINS THAT ARE USUALLY DIFfiCULT TO MEASURE DIRECTLY. System IDENTIfiCATION AND PARAMETER ESTIMATION (SIPE) TECHNIQUES ARE EMPLOYED TO FACILITATE THIS process. It IS THEREFORE VITAL TO HAVE A GOOD MODEL OF THE SYSTEM (in THIS case, A NEUROMECHANICAL MODEL OF THE HUMAN joint(s)) IN ORDER TO STUDY THE UNDERLYING STRUCTURES AND DEDUCE THEIR functions. The ORGAN THAT IS RESPONSIBLE FOR PROPRIOCEPTION AND NEURAL FEEDBACK IS THE MUSCLE spindle. A MODEL OF A SPINDLE IS IMPORTANT FOR IDENTIfiCATION OF CONTRIBUTION OF REflEXES TO jointś visco-elastic properties. The MUSCLE SPINDLE IS A COMPLEX SENSORY ORGAN WHICH IS COMPOSED OF DIFFERENT TYPES OF INTRAFUSAL fiBERS (IFs) WHICH ARE INNERVATED BY DIFFERENT AFFERENT AND EFFERENT NERVES AT DIFFERENT locations. Its SMALL size, HIGH DEGREE OF INHOMOGENEITY AND non-linearity MAKE IT A DIFfiCULT ORGAN TO model. There HAVE BEEN A NUMBER OF ATTEMPTS OF MODELING A spindle, BUT THE QUALITY OF MODELS COULD BE IMPROVED (an OVERVIEW OF MODELS IS COVERED ELSEWHERE [14]). One OF THE PROBLEMS OF MUSCLE MODELING IS THE FACT THAT THERE IS A LOT OF EXPERIMENTAL DATA ON DIFFERENT scales: FROM MICROSCOPIC cross-bridge DYNAMICS TO GROSS MUSCLE BEHAvior; HOWEVER THERE IS NO MODEL WHICH COULD BRIDGE THE GAP BETWEEN DIFFERENT LEVELS OF Experiments. Furthermore, MOST OF THE MODELS ARE REDUCTIONIST IN nature: THE POPULATION OF SARCOMERES IS NOT modeled. This SIMPLIfiCATION CAN CONCEAL EMERGENT DYNAMICS WHICH ARISE BECAUSE OF INTERACTION OF SARCOMERES IN A population. While MODELING SKELETAL MUSCLE fiBERS AS HOMOGENOUS CAN BE ACCEPTABle, DOING SO FOR INTRAFUSAL fiBERS WHICH HAVE VARYING PROPERTIES AND LOCALIZED INNERVATION CAN BE A HINDRANCE IN DESCRIBING THEIR BEHAVIOR. Also SOME MODELS HAVE PARAMETERS WHICH ARE DIFfiCULT TO TIE TO PHYSIOLOGICAL domain, THAT WAY JEOPARDIZING THE interpretabil- ITY OF THE model. A POSSIBLE SOLUTION TO ALL OF THE AFOREMENTIONED PROBLEMS IS A PHYSIOLOGICALLY ACCURATE MODEL THAT TRIES TO MIMIC MICRO AND ULTRa-structure OF THE muscle. There EXIST A NUMBER OF MUSCLE MODELS WHICH CAN DESCRIBE MUSCULAR BEHAVIOR, HOWEVER THE HuxleY 1 2 1. Introduction MODEL TENDS TO BE MOST PHYSIOLOGICALLY ACCURate; ITS PARAMETERS CAN BE RELATED TO cross-bridge kinetics. Despite PREDICTING A GOOD RESPONSE [6] FOR EXTRAFUSAL fiBRES (the ONES THE SKELETAL MUSCLES ARE COMPOSED of), ITS EFFECTIVENESS IN DESCRIBING RESPONSE OF fiNE IF (the ONES WHICH CONSTITUTE THE SPINDLE) IS STILL unknown. The REASON IS THAT IFs DISPLAY GREAT VARIABILITY IN INNERVATION IN A VERY SMALL SPACE [1–3]. Furthermore, EACH TYPE OF IF HAS DIFFERENT MECHANICAL properties. It IS BELIEVED THAT THE RESPONSE OF THE SPINDLE IS MAINLY DETERMINED BY LOCALIZED BEHAVIOR OF THE IF [16]. A POSSIBLE REASON FOR THAT IS THAT AFFERENT INNERVATION MEASURES STRAIN OF THE IF IN THE MIDDLE OF THE fiBER, WHILE THE EFFERENT INNERVATION CREATES LOCALIZED FOCI OF CONTRaction, HENCE INDUCING LOCAL STRAIN AND stress. The MATTERS ARE COMPLICATED BY THE FACT THAT THERE ARE TWO AFFERENT RECEPTORS LOCATED IN DIFFERENT PART OF THE SAME IF, AND THE SAME IF RECEIVES MULTIPLE GAMMA innervations. This MAKES IT CRITICAL TO CONSIDER THE DISTRIBUTION OF STRAIN THROUGHOUT THE IF. The DISTRIBUTION OF STRAIN THROUGHOUT THE IF CAN BE STUDIED BY A multi-segmented MODEL (MSM), A fiBER MODEL CONSISTING OF MULTIPLE SARCOMERES CONNECTED IN series. The DAWN OF multi-segmented MODELS CAN BE TRACED TO THE WORK OF [13]. In THAT
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