Identification of Human MusculoSkeletal Lower Limb Dynamics

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Identification of Human MusculoSkeletal Lower Limb

Dynamics

Pedro Miguel Martins Jacinto

Thesis to obtain the Master of Science Degree in

Mechanical Engineering

Supervisors:

Prof. Jorge Manuel Mateus Martins

Eng. Vanessa Susana Gonçalves da Cunha

Examination Committee

Chairperson: Prof. Paulo Jorge Coelho Ramalho Oliveira

Supervisor: Prof. Jorge Manuel Mateus Martins

Member of the Committee: Prof. Susana Margarida da Silva Vieira

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Acknowledgments

Primeiramente, gostaria de agradecer a toda a gente que fez parte integrante do meu c´ırculo acad émico e que contribuiu, n ão s ó para a conclus ão deste trabalho, mas tamb ém para o sucesso da jornada que foram estes meus últimos anos. A todos os meus colegas de laborat ório que me receberam com enorme á vontade e afabilidade desde o primeiro dia, desejo as melhores felicidades para o futuro que certa-mente ser á risonho. Um particular agradecimento á Eng. Vanessa Cunha por todo o apoio prestado e discuss ões frut´ıferas sem as quais dificilmente teria conclu´ıdo este projeto. Um especial obrigado ao meu supervisor Prof. Jorge Martins pela orientaç ão, conselhos e transmiss ão de conhecimento que foram vitais ao longo desta tese, assim como a constante motivaç ão e confiança depositada no meu trabalho. Aproveito para agradecer tamb ém a todos os meus amigos pr óximos, que certamente recon-hecem a minha inabilidade para estas artes e por isso me desculpar ão preferir n ão referir quaisquer nomes. Eu sei quem s ão e eles tamb ém, e a v ós vos agradeço as aventuras e desventuras que jamais esquecerei. A amizade de cada um é parte do que sou.

Obrigado, aos meus pais Duarte e Conceiç ão e irm ã Sofia pelo amor incondicional, é a eles que eu tudo devo e sem os quais nada seria poss´ıvel.

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Resumo

Milh ões de pessoas sofrem de um sistema nervoso debilitado, resultando na perda de funç ões motoras que levam a altercaç ões na passada. Um dos sintomas mais comum, é a inabilidade de levantar o p é durante o swing, produzindo um movimento grosseiro e altamente prejudicial, que pode at é resultar em consequentes compensaç ões e atrofias musculares. Estimulaç ão el étrica funcional j á provou ser capaz de restaurar esta funç ão motoras, substituindo neuro-sinapses por sinais el étricos produzidos por m áquinas externas, que se aplicadas ao musculos da perna pode resultar numa rotaç ão angular correta. M últiplos estudos est ão dispon´ıveis, no entanto diversos par âmetros s ão desconhecidos ou amb´ıguos e variaç ões em constrangimentos externos aplicados ao tornozelo s ão parcas.

O trabalho aqui proposto baseia-se numa instalaç ão in-vivo, onde o torque e ângulo do tornozelo, mais o deslocamento do tend ão é medido para um grupo seleto de indiv´ıduos, á medida que se varia as condiç ões articulares para um sinal de entrada modulado em termos de amplitude e aplicado á Tibial Anterior. As din âmicas de dorsiflex ão s ão expostas e identificadas como modelos de caixa preta para maximizar a precis ão e como caixa cinzenta, construindo um modelo musculoesquel ético do membro inferior em MSMS. Os par âmetros intr´ınsecos do musculo e os detalhes antropom órficos de cada su-jeito s ão estimados e ajustados aos outputs obtidos experimentalmente. Uma metodologia baseada em conecç ões de redes neuronais é introduzida como alternativa á procura de par âmetros ótimos e m últiplas variaç ões ao modelo de caixa preta s ão testados.

Palavras-chave:

Estimulaç ão El étrica Funcional, Virtual Muscle Model, MusculoSkeletal Modelling Software, Din âmica da unidade Musculotend ão, Dorsiflex ão.

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Abstract

Millions of people worldwide have their Nervous system impaired resulting in the loss of motor capacities leading to gait altercations. One of the most common, is the inability to successfully lift the foot during the swing phase of the stride, and besides being outwardly visible and highly disruptive, it can lead to further muscular compensations and atrophies. Functional electrical stimulation has been proved to restore this motor function, where nervous synapses are substituted by electrical signals made by external machines, which if applied to the leg muscles can elicit a proper ankle rotation. Multiple researches on the topic have been done, but still many parameters are unclear or unknown and variations to the off-load configuration by constricting the ankle with defined constraints are rare.

The work proposed relies on an in-vivo setup where ankle torque and angle, plus tendon displace-ment outputs are recorded for a designated study group of four people, while changing external condi-tions to an amplitude modulated input signal applied to the Tibialis Anterior. The dorsiflexion dynamics of the muscle are exposed, and identified as a Blackbox model to maximize accuracy and as a Greybox problem by constructing an musculoskeletal lower limb model in MSMS. The muscle intrinsic parameters and each subject anthropomorphic data is estimated and fitting values compared with the experimentally recorded outputs. A connection of neural fitnet methodology is introduced as an optimization alternative to the Greybox model parameter search, and different variations between Blackbox models are tested to confirm statements.

Keywords:

Functional Electrical Stimulation, Virtual Muscle Model, MusculoSkeletal Modelling Software, MusculoTendon Unit Dynamics, Dorsiflexion.

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List of Tables

3.1 Stiffness and Damping labels and values . . . 33

3.2 Subjects Antropomorphic and Experimental data . . . 37

3.3 Trial 1 T s for IS SISO modelling . . . 38

3.4 β [N ms/rad] values for different experiments and subjects . . . 40

3.5 Parameter set dimensions(i) and HLS for each M etaN N fitnet . . . 45

3.6 MetaAlgorithm variations . . . 47

4.1 Plateau range for the full VS response set for all trials . . . 54

4.2 Time response characteristics for the S1 IS . . . 58

4.3 S1 IS Optimization Response best algorithms - k001c07 . . . 59

4.8 SISO Models Accuracy and parameters - Trial 1 IS . . . 63

4.9 WARX Identification for S2 IS and VS sets . . . 68

4.10 WARX Identification for S3 IS and VS sets . . . 72

4.11 SIMO WARX Identification for S4 IS and VS sets . . . 76

5.1 Biological parameters estimated for each subject . . . 78

2 Time response characteristics for the S1 VS . . . 101

3 Trial 1 VM parameters for the best accuracy scored algortims . . . 107

4 Mean of VM τ , ϕ and ∆T X accuracy output for all experiments and optimization algo-rithms tested. The Average column shows the mean between experiments and depicts the algorithms validity. . . 107

5 S1 SIMO LARX and WARX NRMSE accuracy scores for the VS . . . 108

6 S1 SIMO NNARX NRMSE accuracy score for the VS . . . 109

7 VM best fitted parameters and respective accuracy’s to the multiple output tracking re-quirements . . . 110

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List of Figures

2.1 a) Spinal Cord tracts and cross-section. Adapted from [4] . . . 4

2.2 Ankle joint Structure. Taken from [20]. . . 6

2.3 Ankle joint DOF . . . 7

2.4 Nervous and Muscular system link . . . 8

2.5 Skeletal muscle structure. Sarcoplasm is the fluid within a cell and sarcolema is the sheath enveloping myofibrils inner membrane. Adapted from [41]. . . 10

2.6 Nerve - Muscle Interaction . . . 12

2.7 Muscle contractile units. Adapted from [4]. . . 13

2.8 Prototypical Action Potential. From [41] . . . 14

2.9 Frequency of Stimulation relationship . The twitch expression is a second order critically damped impulse representing a standart MU [32]. . . 15

2.10 Recruitment of MU according to the Henneman‘s Size Principle. All MU are individually subjected to the Frequency of Stimulation dynamics. Taken from [62] . . . 17

2.11 Tendon Structure.Adapted from [71] . . . 18

2.12 VM mechanical structure of a single lumped unit. Taken from [118] . . . 24

2.13 VM CE Scheme. Taken from [111]. . . 25

2.14 Active elements relationships. Taken from [111, 120]. . . 28

2.15 Passive elements relationships. Taken [111, 120] . . . 29

3.1 Experimental Schema. Taken from [129] . . . 31

3.2 Input Activation U transformed form FES wave . . . 33

3.3 V-point identification, where xipoints to the pixel position on each i frame. x0corresponds to the position before activation. . . 35

3.4 Communication Scheme. Top row: Arduino Leonardo and ISTIM 2018 stimulator; MSU; surface electrodes. Middle row: Frame-grabber; Aloka Prosound 2; Case and US probe. Bottom row: Target Computer, JR3 sensor; KUKA LWR controller; KUKA LWR display and footplate . . . 36

3.5 Instrumental apparatus . . . 36

3.6 MSMS project . . . 39

3.7 Simulink environment extracted from MSMS with activation, Drivers and Plant subsystems shown . . . 39

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3.8 Drivers Subsystem containing VM properties and muscle path kinematics . . . 41

3.9 Plant Subsystem with Joint Spring & Damper block in red. The system contains a welded knee joint and a static friction block . . . 42

3.10 M eta N N structure . . . 46

3.11 NARX Model Structure. Taken from [152] . . . 49

3.12 NARX Model Structure . . . 51

4.1 τ & ϕ mean values between Trial and Experiment . . . 54

4.2 ∆T X mean values between Trial and Experiment . . . 55

4.3 Average phase duration for all trials . . . 55

4.4 IS for Trial 1 . . . 57

4.5 MSMS modelling for S1 based on Trial 1: k10c07 . . . 60

4.6 Averaged IS for Trial 2 . . . 64

4.8 Average phase duration for Trial 2,3 & 4 corresponding to S2 . . . 66

4.9 MSMS modelling for S2 based on Trial 2,3 & 4 IS . . . 67

4.10 MSMS time duration for Trial 2,3 & 4 corresponding to S2 . . . 67

4.12 Average phase duration for Trial 5 and 6 corresponding to S3 . . . 70

4.13 MSMS modelling for S3 based on Trial 5 & 6 IS . . . 71

4.14 MSMS time duration for Trial 5 & 6 corresponding to S3 . . . 71

4.16 Average phase duration for Trial 7 corresponding to S4 . . . 74

4.17 MSMS modelling for S4 based on Trial 7 IS . . . 75

4.18 MSMS time duration for Trial 7 corresponding to S4 . . . 76

1 VM most relevant relationships [111, 118] . . . 93

2 Verification Set for Trial 1 . . . 94

9 Averaged IS for Trial 3 . . . 101

10 Averaged IS for Trial 5 . . . 102

11 Linear Correlation divided between subjects by averaging each Trial‘s k10c07 experiment 103 12 MetaAlgoritm Full Diagram. . . 104

13 MSMS modelling for S1 based on Trial 1: k001c07 . . . 105

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17 S1 SIMO LARX and WARX fit percent sum between outputs . . . 108

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Chapter 1

Introduction

1.1 Motivation

Bordered interaction between little dead units hatch the cell, a microscopically visible machine which is considered the smallest thing alive, in a threshold mankind is yet to fully explain. Organization of cells arrange into organs and sequentially systems that embody an optimized energy transducer programmed with biochemical algorithms, allowing it such unique features as growth, reproduction, respiration and mortality. From the living reign, Animals, and particularly the human specie scores as the most numerous and notty cellular organization, where immense years of evolution continuously hone our components reactions so it finds an ecological niche where we could thrive over the others for an unending amount of time. To achieve this ultimate goal it is key to minimize energy expenditure, since it works as the generalized biological currency traded for system functions, and the manner in which the nervous, mus-cular and skeletal cells translate that energy into movement tends to be where most of the budget is spent, specially on the most advanced animals. Therefore, it is extremely advantageous to understand which techniques the human body uses to control limb movement and even if not every component, re-action, circuitry and structural organization of the human biological system is worth mimicking to develop robotic machinery, there is definitely some insight to be gained in how the control, actuating and sensing properties nature produces, proved by many the bio-inspired inventions currently available.

Increased medical understanding of the biochemical processes in motor contraction proves critical to develop more advanced treatments and cures, and even if constructing computational systems exactly equal to the human one is still impossible to even conceive, mathematical models around favourable working points are being increasingly studied and adjusted. Some are more general and depend solely on parametric scaling data related to individual anatomical morphometry and others are individually fitted for a specific case, but if known for a determined patient, can be used with predictive tool to accelerate recovery where multiple simulations of rehabilitation techniques can be performed in little time and different prototypes and proposed mechanisms tested on if they are or not sufficient to produce the wanted phenomenons. This may prove essential to accelerate recovery and improve human life.

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1.2 Research Objectives

Electrical stimulation was applied on the Tibialis anterior muscle (TA) to promote dorsiflexion of the ankle. The input activation was constant and varying external constraints were imposed to a focused study group. Blackbox identification is performed, recurring to a variety of methods to evaluate com-plexity, Grey box identification via Virtual Muscle Model is performed using optimization tools to better fit and describe the experimental data. Identification and validation of the gathered data and models is performed recurring to multiple sets which cross-validates the findings.

The main objectives of these thesis are to:

• Explain the underlying process and structures behind muscle activation and contraction develop-ment;

• Examine the muscle models and FES control structures available in literature and explore and revise the Virtual Muscle Model functionalities and relationships;

• Develop an experimental setup to successfully gather and synchronize valid data for the Ankle Torque, Angle and tendon displacement while imposing external constraints and skin conditions to a FES input;

• Build a musculoskeletal model that reproduces the dynamics of FES activated dorsiflexion with optimized subject-specific anthropomorphic and muscle parameters to fit the data obtained. Com-pare the grey-box model model with the real experimental recordings and Blackbox estimations; • Document output range values and biological parameter estimations;

1.3 Thesis Outline

The thesis is organized in the following structure:

• Chapter 2: Background Provides biological and physiological insights regarding the human lower leg anatomy and reactions required to move the foot, plus functional electrical stimulation and muscle model research and details are analysed.

• Chapter 3: Implementation Covers the experimental setup conducted and modelling assump-tions made for the study group. It explains the building of the neuro musculoskeletal model in detail and overviews the strategies used for parameter optimization and Blackbox identification. • Chapter 4: Results Shows and compares the curve results for all subjects experiments and

ad-joins the identification methods proposed and optimization enhancements fittings to the experi-mental values.

• Chapter 5: Conclusion Conclusion are drawn and final remarks and future enhancements estab-lished.

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Chapter 2

Background

2.1 Nervous System

Somatic Nervous System The Nervous System multiplex is divided in Central Nervous System (CNS), referring to the brain and spinal cord (SC), plus a Peripheral Nervous System (PNS), subsuming all the wiring nerves connecting CNS structures to body parts. Together, they allow for sensory, integrative, and motor control, as so, imagine looking at a cup of coffee, picking it up and having a sip. Humans can do such a task by constantly exploiting the multiple receptors in one‘s body (in the given scenario eye, nose, or even skin) and the afferent transmission of electrical stimuli to acquire information from this PNS sensory division to the CNS is made by sensory neurons (SN). Interneurons (IN), exclusively found in the CNS, continuously receive this state signals and integrate them into activation needed to inhibit and excite arm, hand and finger muscles, developing the right steadiness and smoothing it as neck, tongue and mouth ones allow us to close the lips and drink. The train of signals is sent out of the CNS to the PNS motor division by Motor Neurons (MN) and to its voluntary contraction circuitry, we call the Somatic Nervous System (SNS). The other PNS motor division is named Autonomic Nervous System (ANS) and dictates the MN activity on glands, smooth and cardiac muscles which function disregard our particular need for caffeine.

MN Descending Pathway Neurons are nerve cells. MN are nerve cells that control movement and are primarily specified by location and function in either upper or lower MN (UMN or LMN) [1]. Different biological available pathways may be taken by the maelstrom of MN axons that carry efferent instructions

down to the PNS effectors, but will rather start in the CNS, where UMN stand multipolar receivers 1_in

the motor cortex, and convey into an initial axonal tract which permits the division in pyramidal and extra-pyramidal tract. The latter is further divided into four motor paths, all belonging to the ANS and responsible for subconscious movements such as balance, palpitation or muscle tone.

Only upon a conscious thought to perform a specific action, are the UMN of the pyramidal tract activated, and this SNS pathway can be further divided into the corticonuclear and the corticospinal

1_{Neurons with a single axon and many dendrites that provide a bigger surface area for receiving and integration of information}

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tract. The term ”cortico” unveils their shared UMN origin and the suffixs points to the tracts target, either brainstem or SC LMN (crLMN or spLMN). The corticospinal descends from the brain, through the brainstem and at the end of the medulla, the fibres pile into 2 groups called the pyramids. At this point,

about 75-90% of the fibers decussate2_{and enter the SC as part of the lateral corticospinal tract while}

the rest 10-25% of non-decussated fibers enter as anterior corticospinal tract. Besides the cross-over, nerves of the dyad have slightly different specializations, with the lateral crossing the SC midline and controlling distal muscles (hand and limbs) and the anterior resuming to axial and proximal ones (truck). Efferently wired UMN have glutamatergic neurotransmitters which synapse only onto LMN (monosy-naptic) and so these stand as the ”final common path” (Nobel Prize winner Sherington,1906), or the only neurons that receive information from the neuraxis level and peripherally link the CNS to innervate PNS non-neural tissue [2]. In terms of visible movement, spLMN triggered by the lateral corticospinal UMN are the most relevant motor pathway, particularly important in complex movement entailing acti-vation and coordination of several muscles. They are the longest cell type and their extent and control stands as one of mammals most unique anatomical features [3]. The corticonuclear tract consists on few crLMN that arise in the brainstem and albeit the wide impact throughout the human body, the tract only innervates facial, eye, neck and shoulder muscles hence less relevant locomotion-wise.

(a) Corticospinal tracts with UMN/LMN division. Decussation and botle-neck in particular SC spots is shown.

(b) SC cross-section with major spLMN tract loca-tion. SC bifurcates into dorsal root to receive SN and ventral root, to send LMN

Figure 2.1: a) Spinal Cord tracts and cross-section. Adapted from [4]

2_{Decussated nerves if spawn in the left side of the brain act on the right side of the body and vice-versa. crLMN do not cross}

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MN Abnormalities Motor neuron diseases (MND) are a group of progressive neurological disorders caused by degeneration and death of MN, and thus affect the ability to control essential muscle activity such as speaking, walking, breathing and swallowing [5]. While many improvements to the patient life are possible, the disease remains incurable and the cure elusive [6], with lack of continuous muscle innervation, by and large leading to respiratory failure and eventually death within 2-4 years [6–9].

Pathogenesis of MND is not fully understood yet due to the several cellular processes that may be associated with it and which will not be explained herein, still the trademark symptom is a painless progressive muscle weakness [10] often resulting in severe motor disability [6, 7]. Defects in LMN cut direct PNS muscle activation while UMN lesion impairs the CNS reasoned stimulation of LMN, and so some symptoms are shown in both diseases, and others are essentially contrary. Different impairments can cause solely UMN disease, LMN disease or both and successfully diagnosis and treatment relies on the accurate interpretation of sings [7].

UMN lesion results mainly from head injury, stroke and SC injury; Seldom from multiple sclerosis and cerebral palsy [11, 12]. Motor pattern atrophies are associated with starting and stopping muscle contraction, where hypertonia and spasticity are common. Loss of fine movement may also be caused by hypereflexia, common in Parkinson’s disease. LMN lesion have many different aetiologies, but are usually hereditary, sporadic or immune-mediated and can be caused by ALS (also affects UMN [9]), spinal muscular atrophy, tumor compression or actual laceration to the peripheral nerve [6]. Functional disabilities from the complete lack or scarce muscle innervation results in the loss of muscle tone, week reflexes and again, spasticity dysfunction due to low co-contraction.

Lesion on either, even with distinguishable physical presentation, may affect innervation of the lateral corticospinal UMN tract or its ending spLMN arising from the the L4 to S2 SC divisions (Common Per-oneal nerve) and display weakness or inability to actively dorsiflex the ankle joint, known as Footdrop Syndrome [2, 7, 10, 12, 13].

2.2 MusculoSkeletal System

2.2.1 Lower Leg & Foot

The lower part of an human‘s lower limb is divided in three. There is the lower leg, region between the knee and the ankle, plus the ankle joint complex and distal to it, the foot. There are two bones in an human lower leg, the all weight-bearer tibia, with a medial malleolus prominence and a slender lateral bone, named fibula which also has a lower end promeminence, denominated lateral malelleolus. The bones are attached by a strong fibrous joint and the tibia‘s lower surface sits on top with the upper surface of the foot bone talus (trochlea) on the bottom, firmly locked by both malleolus on each side.

From the 26 bones of the foot, the talus has the major influence in ankle joint rotation, with support of calcaneus and the navicular bones which also provide ligament and tendons attaching sites. The joint assemble bears a force 4-7 times the persons body weight during walking, and up to 13.3 times when running [14, 15].

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2.2.2 Ankle Joint Complex Arthrokinematics

Interaction with the ground is given by a thirty-three joint bond, however is commonly constrained to the kinetic, in series linkage of only three: the talocrural joint, the subtalar and transverse-tarsal joints [16, 17]. The talocrural is a modified diartrhosis synovial hinge joint articulating the distal ends of both leg bones with the trochlea and is lossely known as the ”ankle joint”. It enables the foot primal motion, which performs in the saggital plane, known as dorsi and plantarflexion where dorsiflexion is bending of the foot upwards (dorsum direction) and plantarflexion, downwards (ground direction). In humans, both malleolus tend to prevent side to side motion, however the trochlea is often square-shaped, wider anteriorly than posteriorly, an anatomical feature which sets a non uniform radius of curvature, and con-sequent helical component to the supposed pure swing movement of an ”hinge” joint. The secondary motions occur in the frontal plane, and are named eversion-iversion, where eversion relates to the move-ment of the soles facing away from each other, and iversion is the opposite. The synovial subtalar joint stands as the main responsible for these sub-motions with the transverse-tarsal also sharing this same axis [15, 17].

Axial rotation of the leg, combines with plantarflexion and inversion to create the complex motion, called supination, where the the soles show an outward roll of the foot. In pronation, dorsiflexion and eversion act to position the sole describing an inward position [15, 17, 18]. In gait and running motions, humans tend to finish the stance phase with the foot in a supinated configuration, pronating as it touches the ground to decrease impact loads [19]. All other joints produce small foot motions contributing mostly to inversion-eversion.

(a) Ankle skeletal components (b) Sagital plane path

Figure 2.2: Ankle joint Structure. Taken from [20].

2.2.3 Muscle System

Muscles that actively move the foot and toes are located in the leg. These muscles are divided into three compartments by thick fascia into posterior, anterior and lateral groups. Generally speaking, muscles

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(a) Ankle and leg DOF axis. Taken from [17]. (b) Ankle complex motions. Taken from [4]. Figure 2.3: Ankle joint DOF

of the anterior compartment are responsible for dorsiflexion and inversion, the posterior muscles for plantarflexion and eversion, while the lateral ones comply to invert, evert, and rotate the foot. The main muscles responsible for plantarflexion are the soleus (SOL) and gastrocnemius (GA) which fuse inferiorly into the calcaneus bone through the Achilles tendon. From the anterior muscles, the TA reigns around 50% of the cross sectional area and is perched as the chief dorsiflexor of the foot [21–23].

This superficial muscle starts in the upper surface of the tibia and ends at around 2/3 of the bone‘s length fusing into the long TA tendon (TAT) that passes near the medial malleolus, inclines medially and inserts into the medial and inferior surfaces of the medial cuneiform of the foot. The muscle remains idle in a standing subject and contracts to pull and invert the segment, also promoted by the way the TAT shacks into the side of the foot [23]. Studies show at least 60 % usage of the TA during walking, sprinting and running stride, not only to dorsiflex, but also to control plantarflexion motions [24].

2.2.4 Range of Motion

Range of motion (ROM) applies to the range in degrees obtained by the movement of bones at a movable joint, and when applied to the ankle complex it usually refers to its 2 significant Degrees of Freedom (DOF) in the sagittal and frontal plane, since supination/pronation, with three-dimensional dependencies, are usually hard to define [19]. Human standardized ROM for each DOF are extensible available in literature where study groups tend to be distinguished by the most important definers, age and gender.

In 1993, [26] tabled ankle ROM of over 120 both-sex individuals and data suggested a period of maximum dorsiflexion for 20 to 39 years old females and then males, with average values of 26.0 ± 1.7 and 25.2 ± 1.9 degrees, respectively. The majority of accessible literature agrees with these statements

for the same subject-type, with peaking angles acquired of 55 ◦ _{and minimums of 13} ◦ _{[26–31]. In}

[31], thirty-five patients recorded an average decrease of 5◦ when dorsiflexing with an extended knee,

compared to a flexed one. Usually, the flexed knee configuration is chosen as it resembles walking and stepping motion, in that the opposite force to dorsiflexion is mainly produced by the stretching of SOL,

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(a) Main ankle muscle actuators on the Sagital plane. Created using Copyright c InnerBody.com .

(b) SC division on the MP that control ankle movements. Adapted from [25]

Figure 2.4: Nervous and Muscular system link

and not by the GA. For an impaired human gait cycle, the required ROM in the whole sagittal plane

is of 30 ◦_{, reaching 20} ◦ _{of plantarflexion and 10} ◦ _{for dorsiflexion [17, 32, 33] while stepping stairs}

require 35-50◦ _{and 50-60}◦ _{for ascending and descending, respectively, depending on the stair slope}

[17, 34]. On all these activities, the summit dorsiflexion angle was of 17◦, while running and sprinting,

dorsiflexion can rise up to 25◦ [35].

2.3 Skeletal Muscle Dynamics

2.3.1 Contraction Theory

Muscle Types Vertebrate muscle cells are classified as smooth, cardiac and skeletal. Smooth tissue is made of tapered mononucleated cells found in blood vessels and visceral organs walls, constricting and propelling substances as food and secretions. Cardiac ones, are named cardiomyocytes which reside solely on the heart organ, and which specialized striated cell structure enables contraction and relaxing (heartbeat) at their own intrinsic rhythms without any external stimulus. Twain muscle types are innervated by the ANS.

Unlike smooth and heart muscles, skeletal ones change their viscoelastic properties by neural im-pulses [36] and so are voluntary activated to contract and relax by human reason. These striated multinucleated cells, make up 639 muscles in the human body, and up to 40% of our body weight [4]. Besides the ability to react to signals, skeletal muscle characteristics are associated with contractility, extensibility and elasticity (ability to shorten or stretch and recoil to a resting length). They are held to bones via tendons and produce movement as the agonist (contraction muscle) pairs with a reciprocal antagonist one (relaxing muscle) and synergist to pull the segment. Additionally they may generate heat (as a contraction byproduct) helping in thermal homoeostasis.

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Skeletal Muscle Histology Skeletal muscle is arranged in a highly structured assemble of cylindrical units of decreasing size coated by connective tissue. Starting from top-level classification, and looking at the cross section of the muscle, the belly is surrounded by a dense membrane called epimysium. Un-derneath, clusters of fascicles each bundling tens to hundred fibers, are surrounded and interconnected by the perimysium. The endomysium is the connective tissue that wraps around each individual fiber and all three membranes extend beyond the muscle and fuse into the tendon cord.

The fibres are only a few-centimetres long but are the prime cellular actor in the contraction process wielding elongated myofibrils encircled by the sarcoplasmic reticulum (SR) and t-tubules. Myofibrils are specialized intercelular structures containing sarcomeres in repeated longitudinal arrays separated by z-lines, each made of thin and thick filaments aligned in a precise arrangement of exactly 6 thin radially disposed around a thick one. The centre of the sarcomere, its called the m-line and titin is an elastic protein spanning from the z to the m-line, centering the sarcomeres with the myofibrils [37]. Sarcomeres are only a few microns long, and represent the smallest functional unit of contraction, where the full lengthening and shortening of each individual array, will set the lengthen and shortening of the muscle itself. Besides myofibrils, the muscle cell comprises also mitochondrias, usually found among the myofibrils and near the z-lines, whose main porpoise is to process the energy molecule ATP [37]. The need in ATP-synthesises for large amounts of nutrients, oxygen and waste products to be eliminated are reassured by a distributed supply of capillaries and veins within the endomysium, and in close contact to each muscle fiber.

Most mammalian muscle fibres are much shorter than the muscle it encloses them. The need for the whole sarcomere arrangement to be activated nearly simultaneously, by an impulse travelling through the whole muscle cell length at a conduction speed considerably lower than a nervous one sets this physical drawback. Human evolution through a more effective mechanical action around its usual work-ing points then set the fascicles disposed in a panoply of ways which allow a common direction of force to be delivered to the muscle’s points of origin and insertion in a more feasible way. From all the schemes it can have, we will highlight the pinnated formation, in which a limited range of physiological lengths but high force is achieved due to an obliquely orientation of the fibres, directed at the muscle’s primary direc-tion of force. This pennadirec-tion angle (PA) allows more but shorter fibres to be tightly packed, decreasing the number of sarcomeres in series (and thus lengths achieved), but increasing the ones aligned par-allel to each other, developing a higher muscle force output [38, 39]. The TA is circumpennate, where

fibres are cillidrically stacked, wrapping an internal centrally lying tendon, with a PA range of 10 ◦ _to

20◦ and without significant differences between gender and contraction intensities [39]. The muscle is

vascularized by the anterior tibial artery, accompanied by the homonyous vein.

Motor Pool & Motor Unit Skeletal muscles are compounded of 2 categories of fibers: extrafusal and intrafusal. Extrafusal fibers are the ones contracting, referred before as muscle fibres or cells. Intrafusal is the new specification introduced, which denotes non-contracting fibers of sense stations, also located in the muscle but explained later. This distinction where we have one belonging to the contractile generator and other to the sensory system, leads to a distinction in somatic spLMN based

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on the fibres it innervate. spLMN controlling extrafusal fibers are called αLM N, and the dichotonic ones

synapsing onto intrafusal fibers are named γLM N . A third type, is βLM N which innervates both [40].

Regardless of type, spLMN with the same muscle target cluster together in motor pools (MP), forming an elongated column usually covering two or three SC segments and extend out to the musculature by the anterior ventral horn.

Figure 2.5: Skeletal muscle structure. Sarcoplasm is the fluid within a cell and sarcolema is the sheath enveloping myofibrils inner membrane. Adapted from [41].

Muscle and MP have a one-to-one relationship, and the MP contains all the αLM N acting on that

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poten-tial (AP) to contract multiple fibres, all at approximately the same time. To this neuron-fibers complex we name a Motor Unit (MU) [42, 43]. Observations indicate that each mammalian extrafusal fibre is

in-nervated by only one αLM N and innervation ratio (fibers per MU) is relatively proportional to the muscle

size [43–45] ranging from around 3-1750 fibres per MU, lower on muscles that need delicate and precise responses (as fingers) or higher, for the ones with a more coarse and robust force need (thigh muscles). The TA leg muscle MP recorded an averaged MU number of 445, each with an average innervation ratio of 500-700 and between 100 to 300 thousand fibres for 8 male individuals [45, 46]. Identification of the MU was dated in 1925 [47] and since it has been widely computationally modelled in both isometric and dynamics conditions [48], although still limited information is known on how their activity is so fine controlled for complex intended actions.

Neuromuscular Junction As the αLM N axon approaches a muscle, it loses the isolating myelin sheet

and branches into hundreds of terminal sites, called neuromuscular junctions (NMJ). Each represents the last point of exchange between the nerve synaptic bulb and the sarcolema ”end plate” of a muscle fibre. Eerily, the fibre and nerve terminals are not in direct contact with a gap of around 50 nm made of extracellular fluid and called synaptic cleft [49].

The axon terminal has voltage-gated calcium (Ca2+_{) and sodium (N a}+_{) channels and a bulb with}

synaptic vessels storing excitatory choline neurotransmitters called Acetylcholine (ACh). These can only be synthesized by an LMN soma‘s and its lone receptors are nicotinic ACh ones present in skeletal

muscles. Surrounding the axon, there are free-floating Ca2+_{and N a}+_{ions and upon an AP, the voltage}

difference opens the channels in the bulb conceding an entry point for these ions to diffuse inside.

Ca2+_{influx stirs and breaks the Ach pockets and the cell proceeds to release the neurotransmitters by}

exocytosis3past the presynaptic membrane, through the high N a+_{concentrated cleft and finally binding}

with a receptor in the muscle sarcolema, or postsynaptic membrane. These receptors are ligand-gated

N a+ channels and when binded with ACh, allow the extracellular N a+ _{ions into muscle sarcoplasm,}

provoking an N a+ _{influx driven AP which will travel across the sarcolema and widespread into the}

muscle fibres t-tubules while the enzyme AChE, in the cleft, destroys ACh and sets the need for more segregation, and therefore MN AP, if contraction is to be maintained.

T-tubules are inward extensions of the sarcolemma that run transverse to the sarcomeres and are

enriched with N a+_{channels that trap an abundant concentration of Ca}2+_{ions on the terminal cysternae}

pockets, in the SR. This membrane triad is where an AP is coupled to mechanical contraction as the

N a+coming from the NMJ binds with the receptors, and depolarizes the t-tubule to make it permeable,

allowing the release flow of stored Ca2+ _{from these local sites. This flooding process is called Ca}2+

induced-Ca2+ _{release and is what makes muscle contraction possible. If Ca}2+ _{fails to exist inside the}

fibre, contraction will cease.

Contraction by Sliding Theory Ca2+ _{in the fibres will excite the sarcomere arrangements,}

particu-larly, the proteinous structure of thick and thin filament headed respectively by the myosin-actin complex.

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(a) Muscle Unit projection. Adapted from [4]

(b) Single NJ detail; Sarcolema invaginates inside the sarcoplasm for a bigger surface area, and so bigger ion diffusion. Adapted from [41]

(c) spLMN projection to skeletal muscle. Adapted from [4]

Figure 2.6: Nerve - Muscle Interaction

Thin filaments are mainly composed of actin protein in an helix structure with their binding sites protected by the cilindrical wrapping of the also helix structured tropomyosin, with sparse control troponin protein

blocks laying on top. When Ca2+ _{is released, it binds to troponin morphing its shape, and since it is}

physically connected to tropomyosin, the shift will offset its axis and clear some of the actin binding sites. These will connect to myosins but may have multiple configurations and directions, hence not all actin can generate contractile force from all the myosin heads. The exact number of heads attached to actin in a fully active muscle is still an open debate. Thick filament are made of multiple pairs of myosin bodies in an helix structure stacked around a central axis, with sticking out myosin heads. The heads

rest at a cooked position after hydrolizing the ATP molecule into ADP and inorganic phosphat (P O₄3−)

and will stay so, while the muscle is relaxed and actin binding sites are closed. When they are exposed,

the myosin attaches to actin creating a crossbridge, which releases the P O₄3− and ADP, to strengthen

the connection and move the head from an upright to a bent position, provoking a power stroke where the myosin head pulls the actin closer to the m-line and the myosin itself gets closer to the z-line. In this tensed state, the whole sarcomere will become shorter, and globally the whole muscle will contract.

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The detachment of the myosin-actin bond site is accomplished with the binding of myosin with new ATP,

which will then be hidrolyzed into ADP and P O3−4 to recock the head again and sustain another cycle.

Each cross-bridge performs independently and contraction acts only in the region of overlap between actin and myosin (A band).

(a) Muscle fiber containing myofibrils and showing sarcomere arrangemenent and revolving structures.

(b) Single Sarcomere detail showing the relevant protein components Figure 2.7: Muscle contractile units. Adapted from [4].

This is the Sliding filament theory (A. Huxley and H. Huxley, 1964), where the unrelated authors stated the governing principles behind muscle contraction by aggregating the most important findings from themselves and others (H. Huxley & Hanson,1954; A. Huxley & Niedergerke,1954). Details in the biochemical changes associated with crossbridge force generation and head rotation upon stroke, titin function, structure and even name, or action of secondary enzymes and proteins have since changed, but the essential premises remained [51]. The theory utters that the sarcomere is shorten and lengthen by the relative sliding of interdigitating protein strands without changes in length for the thin and thick filaments and explains the transformation of chemical potential energy into mechanical one.

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2.3.2 Contraction Dynamics

MN Action Potential Neurons transmit discrete electrical impulses called AP. In a resting state, an

αLM N displays a negative charge, but not a static one as ions flow in and out, maintaining a fairly

consistent inside voltage average of ∼ −70 mV , ranging from −40 to −90 mV . Signals from excited neurons carry positive charged ions into the cell body, and if the temporary shift in the ionic

concen-tration surpasses a certain threshold, typically ∼ −55 mV , the αLM N is triggered and depolarizes in

response. The cell membrane becomes permeable and opens ionic gates to equalize the concentration gradient and in the process, swings past equilibrium to become positively charged [41] . The signal is spread by neurostransmiters and the cell starts to repolarize and return towards the resting state, as hyperpolarization sets the cell to a more negative state than the usual one, increasing the fire threshold to an inhibiting value. This refractory condition, is the time period in which a neuron cannot fire another AP for anatomical reasons like restablishing neurotransmitters and ions. The AP frequency is the core signal our brain uses to activate muscles and follow a general ”all-or-none” principle. This binary condi-tion states that if the stimulus is strong enough and surpasses the threshold the membrane depolarizes and the AP occurs. Stronger stimulus do not produce stronger AP, but smaller ones produce none. The neuron intensity of stimulus is therefore, not amplitude but only frequency-modulated and the operating

range of an αLM N is between 20-200 pps [41, 52].

If the MN is fired it will inevitably lead to an AP in all the fibres [53] since all the NMJ established are stable synapses, therefore each MU is usually modelled as a single unit [43].

Figure 2.8: Prototypical Action Potential. From [41]

MU Frequency of Stimulation & Recruitment The AP results is an isotonic 4 _{twitch contraction in}

the MU fibres, modelled as a myogram which traces a tension over time relation depicting the finite time gap required for contraction of the fibers. This actuator response undergoes three main phases, firstly a latent period, where stimulation is applied but contraction hasn’t started yet, denoting the brief

4_{Contractions can be isotonic, where muscle tension in produced over varying muscle lengths or isometric, where tension in}

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delay it takes for the AP to propagate and Ca2+_{ions to be released from the SR. The contraction phase}

(upward tracing) comes next, where Ca2+ ions have bound to troponin, tropomyosin has shifted away

from binding sites and so repetitive power strokes are actively shortening the sarcomeres to the point of

peak tension. Finally, the third and last phase, called relaxation (downward tracing) is where Ca2+_ions

are pumped into the SR and muscle returns to a resting state.

If a consecutive AP arrives, before the muscle fibre is able to relax, it will increment in tension in a

nonlinear summation, in which is thought that Ca2+ _{is not fully uptaked from the first release, and when}

the second AP arrives, this extra Ca2+_{will add to the normally released and together develop a greater}

force output. For a sequence of stimulus, the twitch time reduces and myogram increments, resulting in a twitch wave called unfused tetanus or, if the AP rate increases further, in a fused tetanus contraction, where the tension will plateau and its physically impossible to diminish the time gap between the MU fibres contraction phases.

Figure 2.9: Frequency of Stimulation relationship . The twitch expression is a second order critically damped impulse representing a standart MU [32].

The phases time period may differ greatly, depending on which type of extrafusal fibre predominates in the muscle and is actively being recruited. Mammalian muscles are composed of two types based on the twitch duration: slow and fast (ST and FT). Eye muscles, mainly composed by FT take around 12 ms to twitch while leg muscles, composed mainly of ST may take around 100 ms. Preferentially, a single MU innervates only one fiber type and the MP contains the MU different fibre type innervation proportions [54]. The summed up fibre twitches of activated MU in the MP develop the overall muscle force output, and these MU are coherently recruited during increasing voluntary contraction, in an hierarchical order according to its size (Henneman,1957) [55, 56]. This is the Henneman‘s Size Principle, and states that smaller MU have lower thresholds and fire at low AP frequencies until they reach a plateau. Higher rates will recruit additional MU with larger cell size and larger contraction force capability [57] until all MU are recruited and at maximum activation. Decreasing the tension follows the inverse trend, as it will set the

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deactivation of larger MU first, and the smaller precede.

MU containing ST, which have the smallest cell body diameter and therefore also threshold, respond to lower frequency stimulation. Their excess in myoglobin, gives them a dark red look and large mito-chondria inside produce ATP by aerobic cellular respiration which sets a slow activation but capacity to maintain persistent and prolonged twitch activity with a fatigue resistance greater than all other types. It is normally the most commonly present in any muscle, but proportion tends to be bigger in endurance and posture focused ones [3]. FT have the biggest cell body and so are recruited last but are also

re-sponsible for the greatest strength and and fastest contraction. αLM N innervating FT conduct signals at

100m/swhile the ones innervating mostly ST top at 85m/s [54]. Higher velocity and force production is

achieved by producing ATP by anaerobic glycolysis, which displays setbacks in terms of fatigue, energy needs and duration [3]. The high concentration of myofibrils, and low content of both myoglobin and mitochondrias gives these fibres a whitish appearance and are mainly present in muscles with fast and strong movement needs, as is necessary in ball throwing and punching.

Synchronism in MU firing rate and asynchronism in recruitment are the two crux strategies in which physiological muscle control its output to achieve a desired force profile [58]. The particular proportion of fibres type present in muscle depends on its porpoise, trainings but mostly, on genetics. The proportion between ST-FT seems to be hereditary, although the particular responsible genes are not yet understood [59] with the Olympic sprinter Brian Lewis recording 70% FT fibres for the thigh muscles, while World-record marathonist Khalid Khannouchi showed around 80% ST for the same muscle group [60]. In [61] TA distribution was of about 73% ST fibers to 27% FT fibers, and [46] showed drastic fibre type dependencies as a function of muscle depth, but the whole cross-section was averaged as 30% FT (range 19-33) and 70% ST. Both studies were made on male individuals in early adulthood.

2.3.3 Tendon Plant

Visible movement is possible since skeletal muscle contraction delivers the tension in fibres to a fixed component in the skeleton which is accomplished by a unique type of connective tissue, known as tendon [63–65]. These mediate transmission of mechanical loads between a compliant tissue (muscle) and a stiff one (bone) playing an important role in movement, propulsion, support and stability of joints [66]. Each muscle has a origin and insertion tendon, for its two skeleton attachment points and each tendon has a myotendinous juntion where the muscle thin filaments interdigitate with the tendon fibers and an osteotendinous junction, where tendon fuse to bone by collagen pairing fibres.

The collagen protein is the most abundant in our body, being present in cartilage, tendons and liga-ments. These last two are generally alike in both structure, function and dynamics [64, 65]. Preferentially, tendon attaches muscle to muscle, while ligaments connect bones to bones. The same assumption is extended to the aponeuroses , which are sheetlike tendons that attach muscle to muscle or bone.

Tendons come in various shapes and sizes, with structures that vary considerably based on func-tional uses and general body placement, yet will usually display high tensile force due to its hierarchical composite structure [67]. The extracelullar matrix of the tendon is comparable to the muscles schema

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Figure 2.10: Recruitment of MU according to the Henneman‘s Size Principle. All MU are individually subjected to the Frequency of Stimulation dynamics. Taken from [62]

since it also contains tightly packed fascicles bundling fibres embed in a proteoglycan-rich matrix. En-closing the tendon there is a layer called epitenon, which holds its structure and gives higher-order orga-nization. The matrix is loose connective tissue called endotenon which is contiguous with the epitenon and allows the bundles of fibres to glid with near-zero friction, allowing the tendon to change shape as muscle contraction undergoes and force is transmitted throughout the joint ranges. The matrix defines the viscoelastic properties and the tendon passive recoil behaviour [68].

Type I collagen fibers are the basic unit of a tendon, and inside bundles bunches of collagen fibrils which main role is to stand and resist tension. Fibril diameter define the mechanical properties where the distribution between larger vs smaller diameter sets the compromise between tensile force and ability to deform. As one ages, the tendency is for fibres to increase its diameter until the trend drops at senescence [69]. The complex three-dimensional structure and orientation of the fibrils set the whole tendon as crimped [70], and the tendon behaviour to act ”rubber band” like, storing kinetic energy to immediately pull back to a resting position when stretched from the same.

The TAT is suggested to be almost inextensible under biological working points where 2% strain making the fibrils flatten and the fibres pulled into a more parallel and linear pattern. Evidence then, suggest that if the strain remains lower than 4% the arrangement linearly recoils back to the normal resting state but if greater than 5-8% microscopic damage may occur [38, 72]. The antagonist Achilles tendon acts as an energy-saving spring with strains up to 10.3% recorded [38, 73].

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Figure 2.11: Tendon Structure.Adapted from [71]

2.3.4 Feedback System

Adaptive motor control is hierarchically distributed and uses feedback. The feedforward signal initiated in the motor cortex sets a convergent excitatory input on MN and widespread effects on SC IN, which are then coupled and adjusted as multiple SN signals are continuously processed at several levels in the CNS structures [40].

Mammals perceive the outside world by exteroception sensors and the internal state (as hunger or urine needs) by interoreception ones. We are also kitted with a kinaesthetic sense, as we all acknowl-edge one‘s limb position, the relative position of other body part and the necessary effort if intended to move it. This is achieved by proprioception receptors which form the peripheral Somatosensory sys-tem as the muscle spindles(MS) and Golgi Tendon Organs (GTO). These stand the main interaction from muscle to the SC IN, but many other smaller and less understood SN available in muscle, tendon, ligaments and even joint capsules feedback data to the SC.

SC IN are the major source of αLM N, and the main targets of upper centres and peripheral feedback,

plus they have been proved (T. Graham Brown,1911) to control the needed coordination of segment movement and phase cycle relationship between different muscles included in walking, climbing, swim-ming, breathing and swallowing etc. These is achieved by synaptically connected IN (CPG) that develop rithmic excitatory and inhibitory patterns of α, γ and β firing, setting the basic framework for repetitive ac-tivities, which is then modulated and reinforced by the peripheral circuitry commands and allow reflexes to be suppressed or enhanced at different phases [53, 74–76]. Brain involvement is rather reserved for CPG initiation or major adaptation of the muscle activation pattern [77, 78] with each stereotypical movement associated with a specific CPG, located either in the brain steam or SC [40].

Characterization of implicated neurons and reactions in CPGs are an active area of research [53] and recently, in [79] a ground breaking project enabled patients with SC injury and MN functionally dis-connected from the brain which led to complete loss of lower limb function, to stand and step obstacles recurring solely to SC epidural electrical stimulation of sub-functional peripheral connections.

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Muscle Spindles In a tipical lower limb muscle like the TA, around 200-500 muscle spindles can be found aligned with extrafusal fibres, aggregated inside the muscle belly. The spindles have a fusiform shape and encapsulate a complex of intrafusal fibers that act as dynamic gain control points innervated

by the joint action of γ and βLM N that tunes the sensor by adjusting the tension in this sub-fibres as the

muscle contracts and lengthens by the action of αLM N in extrafusal ones [74]. The CNS co-activates

the γLM N to mimic αLM N activation and so γLM N require no previous innervation but can be separately

modulated from αLM N for particular complex movements [80, 81]. γLM N activation effects in spindle

sensitivity and general dependency of α and γLM N coactivation are both well reported but the real

effects of sensitivity shifts in proprioception remains elusive [81]. βLM N seem to innervate both muscle and spindle fibers but are harder do identify and distinguish, being constantly left out of sensorimotor models. Studies suggest they exist in higher primates but is only hypothesized that they will also be present in humans [37].

There are two types of fibers inside the spindle, the nuclear bag fiber, which is sustains annular innervations by type Ia sensory fiber and the short and slender nuclear chain fiber which innervation arrives from flower spray terminations of type II sensory fiber. The spindle also has polar regions, their only contracting part which move according to the muscle. The Ia firing rate increases as the stretch rate of the polar regions increases, providing the CNS with muscle velocity information while group II report an AP dependency that informs the CNS about the absolute length of the muscle. The two sensory traducers sample this afferent signals to the SC which integrates and projects effects on IN to

control αLM N. Ia projections synapse directly onto αLM N sinnervating the same muscle at which the Ia

afferents rose [82]. This forms the monosynaptic stretch reflex, the crux of muscle activity maintenance,

where Ia /αLM N/muscle triad form a positive excitatory feedback loop. Reciprocal inhibition takes a

shadowed place denoting multiple parallel synapses of Ia branches to synergistic and antagonists IN. This connection relaxes the muscles that would tend to block the movement pretended [82].

Golgi Tendon Organ Sensory organs unevenly located in the myotendinous junction which lay in parallel and physically linked to about 3–50 muscle fibers belonging to various MUs. It possess no motor innervation and a single large type Ib axon enters into the internal capsule and pressure sensitive endings fire AP that provide the SC afferent feedback related to load or heaviness in the fibres. When the firing rate surpasses a treshold, inhibitory IN connected to the same muscle that caused the Ib afferent to fire, make the muscle weaker with a few delay seconds.

They are speculated to have a protective function (Golgi 1878) but individual models of single GTO activity proved unreliable relations between GTO afferent activity and tension. Only the mathematical model described in [83, 84] seems to accurately represent the transducer properties of the ensemble firing of GTO and provide physical meaning.

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2.4 Functional Electrical Stimulation

Research & Arquitecture Delivering electrical stimulation as a medical treatment is historical, with written documentation dating back to the Roman Empire but traced even earlier to the ancient Egyp-tians, whom were thought to use torpedo rays or the Nile electric catfish to treat headaches and joint stiffness. It is represented in few tombs carbon-dated up to 2750 BC [85–87]. The Industrial Revolution saw the rise of technology and the natural appliers were changed to man-made electrical devices [86]. Franklinism was the first stage of the 18th century boom regarding the use of electricity in a controlled way, when Benjamin Franklin used static one to generate dumbness with a frictional machine [86]. In the 1790s, Luigi Galvani introduced Galvanism as the contraction of a muscle that is stimulated by an electric current and was able to produce twitch contractions in the muscles of a frog and dog [87]. The deceased animals had their muscles stimulated by using direct current through bimetallic needles which was latter proved to be a dangerous method, since any length of time would mean necrotic destruction of cell tissues (it was actually latter investigated for the indented destruction of tumours) [87]. In 1800, Alessandro Volta, a fierce criticizer of Galvanism, invented the voltaic pile and Michael Faraday adapted it to build a source of electrical power to alternate polarity only using a relatively small current, discov-ering the values of using interrupted current by 1832 [86, 87]. Guillame Duchenne proved that Faradic stimulation with short pulse duration would no longer cause tissue degradation [86] and so the use of electricity for therapeutic ends really began. In the modern age, research on artificial electrical excitation in tissue deprived of nervous control has branched into three groups: Transcutaneous Electrical Nerve Stimulation (TENS), where electrical stimulation is used upon SN to inhibit pain signals and endorse endorphin generation [88, 89]; Neuromuscular Electrical Stimulation (NMES), where MN stimulation for muscle contraction and relaxation is made for therapeutic purposes [88, 90] and finally Functional Elec-trical Stimulation (FES) which term forges the technique of MN stimulation by bursts of elecElec-trical pulses with the goal of restoring functional movement [88, 91]. Other active approaches as functional magnetic stimulation (FMS) or passive orthoses devices will not be discussed, but may serve the same porpoises. The cardiac pacemaker, coined by the electrical engineer John Hopps, was the first clinical useful application of electrical stimulation applied to muscle when it was used to start a dog’s heart in 1949 [92, 93] but only in 1961 was FES introduced by Liberson et al, in a pioneering development of the first motor neuroprotesis to correct Footdrop. This was made recurring to a rudimentary heel-switch based open-loop circuit. When the patient was in the swing phase of the gait, the toe-off point releases the switch and enough electricity to contract the TA is sent across the electrodes. It is simple but not much reliable, since it requires continuous attention by the user, uses a constant electrical wave and erroneous detection of gait events (as heel-switch) in FES systems may be seriously problematic. In 1990, as a candid alternative to the wheel-chair, appeared Parastep 1 [94], the first FDA approved and commercially available FES device, with 6-channels wired through surface electrodes to the quadriceps and gluteal muscles to enable walking and stepping on patients with all types of SC lesion. This was an hybrid open-loop system, benefiting from a walking frame with manual switches to control stimulation parameters and avoid bad sensing issues. Ever since, the structural architecture of commercial FES

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de-vice has converged to an electronic micro-processor stimulator, a control and actuator unit [88, 91, 95] which has proved to be valid to activate dormant muscles, including upper and lower limb restoration mostly regarding hand grasping, standing or ambulating, restore bladder and bowel function, as well as providing erection, tremor, cough or even respiratory assistance [96]. Most recur to artificial sensors mounted on the body or from the body’s own physiological sensors to input information to the High-level control algorithm which identifies and switches between control states. The mechanical switches are still used but nowadays, are often provided by finite state machines(FSM) which are less sensitive to fluctuations on individual sensor values and benefited from the human gait being a patterned cycle ac-tivity which their sequential operation schema could describe. Less dogmatic strategies are established for Low-Level control, by regulating the electrical wave parameters as to ease fatigue or detect external disturbances [88]. No ”pure” closed-loop approach FES device is commercially available in the mar-ket, that completely fulfils this premises [12, 97], however state of the art projects on neural prostheses tend to use machine learning algorithms to optimize and adapt stimulation to the patient gait demands [98, 99]. This biological inspired combination has proved to mimic human control accurately and en-able anticipatory actions, but imposes a need on additional system information, often given by inertial sensors [12]. FES can also be coupled with myoelectric sensors to acquire the physiological EMG of the muscle during voluntary contraction and relate it to determine the exact electrical activation given by FES by integrating the person level of will to do so.

The boundaries of FES development is also weighted upon better actuator technologies [99]. Be-sides the more obvious increase to multiple electrodes, and thus more muscle activation and more complicated range of tasks available [11], actuator problems are almost always concerned with elec-trode placement and so, implanted simulators acting directly on the CNS are now receiving widespread endeavour [11, 100–102]. Other emerging possibility is the ”router” system, where only the electrodes are implanted and the external controller activates them wirelessly through the skin. Still, in research, less invasive ad-adhesive surface electrodes applied to the PNS pervade [103].

Considerations The whole FES compound cannot be neither bulky nor obstructive to movement and surface electrodes must be place over relevant muscles recruiting MN preferentially to SN [90, 104]. The optimal, and therefore typical FES stimulation waveform used for human ankle dorsiflexion is a biphasic rectangular pulse train with a frequency of 20 − 40 Hz, an amplitude up to 120 V , and a pulse duration of 200 − 400 µs [90, 94, 105, 106] which main objective is to change the external potential of the MN

membrane and generate an artificial AP, as the N a+_{ions near the cathode move near the anode. The}

biphasic, instead of monophasic tone is to avoid electrolytic effects and skin irritations.

Intensive studies on the best modelling parameter to achieve so have been carried, with the biological-comparable frequency proving to be less efficient compared to pulse width or even amplitude modulation. This conclusions are not completely agreed upon, and so devices and control strategies based on each or combination of parameters are available. Whatever electrical wave is used for a certain movement to be performed, FES activation adds an extra dynamic concerning how stimulation is done. Electrodes can trespass electrical flow and influence muscle contraction but not quite like our nerves do in a

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vo-litional contraction. Each αLM N is distributed in complex networks, branching into thinner and slender

ramifications to innervate the individual fibres and carry the AP. Howbeit, an electrode lies in a fixed lo-cation obligatory closer to some and distant from other nerve branches, which sets the electrical current source as unevenly distributed and rapidly decreasing as it spreads throughout the higher impedance

muscle. Other factor also constrained by the physical location of the electrodes, is the αLM N axon

branching pattern. Large ones innervate more fibres, hence the nerve divaricates more often to reach all of them and does it by successive splinting in thinner axons. The resulting diameter of some of these

branches arising from large MN become similar to the standard ones of a small αLM N and stimulation

in the vicinity tends to be equally effective in recruiting both [107]. Two modelling theories for the MU recruitment upon FES application prevail and are often grouped, the first is to assume recruitment in the inverse manner of Henneman’s size principle, the other is that FES inherently recruits MU in a re-peated non-selective tone, with no real control over the MU that are being recruited and are always the same MU to fire [90, 108]. This disorderly recruitment is normally acquainted as the reason as why FES tends to cause rapid muscle fatigue compared to the natural one and why it requires much more input frequency to produce the same motions.

Footdrop Syndrome As mentioned in Section 2.1, Footdrop syndrome is associated with MND, how-ever FES approaches to LMN and UMN conditions are utterly different. LMN lesion leads to an absence of NMJ, with the αLM N showing a complete lack or only scarce ability to excite and so, contraction can only be elicited by depolarizing the sarcolema of each single muscle fibre individually. As if this process wasn’t already almost chimerical, the sensitivity of the muscle fibre is much lower than the αLM N , and so higher and longer stimulations are required when compared to patients with intact LMN [109]. To the authors knowledge, there wasn’t been a single certified and commercially available stimulator, to treat Footdrop patients with LMN lesion even though it represents around 70% of all the impairment causes [13]. FES system prove to be most suitable when lesions act on UMN pathways since relevant periph-eral nerves between SC and muscle remain with intact MU [11, 12, 107] and even though it is a less prevalent cause, all patients with any sort of lesion on the lateral pyramidal tract UMN record an average 52% chance of developing FootDrop syndrome [13], with 2 million people/year from stroke alone [12].

Following Liberson’s first glance on the possibility of using FES to correct Footdrop , extensive re-search was dedicated to the topic in the following five decades and nowadays, many devices especially designed to this end are sealed with FDA approval and fully available in the market, as the Odstock, Ness L300 and the Walkaide [2, 12]. Normally the TA is the paretic muscle and prime focus of stimulation but other dorsiflexors and antagonist can be excited while stimulation is usually confined to pulse-width, or a merge of pulse width and amplitude modulation preset controlled by a FSM and foot or hand switches. Regular long term FES usage proved an increase in muscle strength, muscle oxidative capacity, fatigue resistance and bone density. Improvements are often retained when FES is turned off, which suggest plastic changes in the MN [89, 98].

Identification of Human MusculoSkeletal Lower Limb Dynamics