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A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects
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Available online at www.sciencedirect.com
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Original Research Article
A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects
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Mohsen Abedi a, Majid M. Moghaddam a b
a,*
, S. Mohammad P. Firoozabadi b
Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran Department of Physiology, School of Medical Sciences, Tarbiat Modares University, Tehran, Iran
article info
abstract
Article history:
Gait recovering after spinal cord injury (SCI) is a regular attempt in neurorehabilitation. For
Received 24 January 2015
this purpose, various clinical techniques have been proposed until now. However, the
Received in revised form
feasibility of these techniques has not been theoretically investigated so much. This has
23 August 2015
been mainly for difficulties of gait modeling in SCI patients. Involving these problems,
Accepted 9 December 2015
recently neuromechanical models of gait locomotion have been proposed for examining
Available online xxx
rehabilitation methods. However, these models were so simple that could not properly
Keywords:
in prior simulations. Due to this limitation, in this paper a new neuromechanical model is
express rehabilitation effects. Notably, lesion intensity is a concern that was never attended Neuromechanical modeling
proposed that classifies patients based on intensity of trauma. Explicitly, the complete,
Neurorehabilitation
severe and non-severe incomplete SCIs are imitated and effects of related clinical rehabi-
Spinal cord injury
litations are explored. Remarkably, the model indicates an incredible performance in
Gait locomotion
explaining the rehabilitation effects through presenting the compliant results with clinical
Central pattern generator
information. The suitability of this model is mainly for the applied neuromuscular plan that consists of a combined plan of central pattern generator (CPG) and neural reflexes that controls a double segment limb. The validity of this model is further proved by comparing the kinematic and kinetic results to the experimental data. # 2015 Published by Elsevier Sp. z o.o. on behalf of Nałęcz Institute of Biocybernetics and Biomedical Engineering.
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1.
Introduction
Undoubtedly, the walking is a vital human's want for movement and doing different daily jobs. The importance of this need is sensible in life of persons deprived from this gift by some means. Depression, seclusion, social problems, etc. are
routine involvement of such people. Therefore, the rehabilitation for the gait recovery after a physical impairment is a necessary effort. In addition, the spinal cord injury (SCI) is a main causative factor in most of gait disabilities in persons. Due to this concern, various rehabilitative techniques have been proposed in the literature for the gait recovery after SCI. The majority of
* Corresponding author at: Nasr Bridge, Jalal Al Ahmad Street, Tehran, Iran. E-mail address: [email protected] (M.M. Moghaddam). http://dx.doi.org/10.1016/j.bbe.2015.12.002 0208-5216/# 2015 Published by Elsevier Sp. z o.o. on behalf of Nałęcz Institute of Biocybernetics and Biomedical Engineering.
Please cite this article in press as: Abedi M, et al. A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects. Biocybern Biomed Eng (2015), http://dx.doi.org/10.1016/j.bbe.2015.12.002
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these techniques have been various clinical methods suggested in the form of statistical analysis [1–4] or different assistive robots [5–7]. Although these techniques have been helpful for the SCI patients, the researchers have believed that awareness about the physiological basis of treatment substantially enhances the effectiveness of above strategies. In this regard, in the past decades the neuroscientific studies have been largely focused on finding the biology of neural pathway restoration during clinical treatments in a damaged locomotor system [8,9]. These investigations conduct the rehabilitation process of SCI paralyzes on improved trends (for review [10]). Nevertheless, the theoretical simulation of pathological gait can notably deepen the knowledge about the neural causes of walking inabilities to be certainly functional in optimization of rehabilitation methods. Whatsoever, these models have not been so many addressed in the literature and rarely proposed for a limited number of diseases. Specifically, in a number of papers, the authors have described some pathological gaits (e.g. Parkinson and crouch gait) based on the musculoskeletal walking models [11–13]. However, these models have not possessed a cybernetic basis and thus cannot provide any details about the origin of neural disorder diseases. Due to this deficit, the idea of using neuromuscular-based models has been raised in the last decade for simulating walking locomotion of neural impairments. In these simulations, the origin of gait locomotion has been a key factor. This issue was broadly discussed for intact cases in the previous investigations. In these studies central pattern generator (CPG) and neural reflexes were recognized as the major neural policy of gait generation [14,15]. Nevertheless, use of these models for the neural disorders has been very limited so far. Specifically, Bellotti et al. [16] firstly brought up this idea for imitating the gait locomotion of SCI patients based on the CPG concept. However, this target has not been met in the paper because of the unsuitable structure of CPG. Further, Jansen et al. [17] simulated the muscle spasticity in the gait locomotion of hemiplegic persons by incorporating the neural reflexes. This effect has been modeled by modifying the gains of a-motorneurons in accordance with the clinical data. Nevertheless, a major defect in the above papers has been the absence of brain disruption influence in the pathologic gait simulations. Without this effect, most gait abnormalities associated with SCI and stroke paralysis are not justifiable. A main reason for this deficiency is the lack or inappropriate use of CPG in the above articles. Due to this limitation, Markin [18] and Spardy [19] employed a more complex CPG for simulating the gait locomotion of complete SCI cats. This CPG was a two level half-center (TLHC) model generating different patterns of locomotion by receiving the brain commands [20]. This model is really the improved form of other types of CPG like basic half-center [15,21–25] and unit burst generator [26,27]. Further, the SCI locomotor system has been imitated in these papers by cutting the mentioned brain signals on TLHC. In this way, the effect of brain disruption has been included in the model of SCI locomotion. Moreover, the above authors incorporating the afferent feedbacks into the TLHC, represented another valuable achievement by the simulation. Specifically, using this architecture the theoretical investigation of rehabilitation
methods has been explored for the first time. The rehabilita- Q2 tive technique has been dealt in these studies was the afferent feedback amplification that in the clinical treatments is achieved by the ‘‘locomotion training’’ [10,28]. Expressly, the above model theoretically illustrated how this tactic recovers the walking ability in the complete SCI patients. This outcome obtains a deeper knowledge about the effectiveness of rehabilitation methods that would be surely efficient in optimizing and accelerating the treatments. However, the above plans have still two major weaknesses in the SCI modeling and the rehabilitation issues. In the modeling of SCI, the musculoskeletal system included a low mass single segment limb as a leg of a cat that the influence of limb inertia on the TLHC performance has become ignorable. This simplicity causes that the different challenges of real gait locomotion like stability, coordination, etc. have not to be addressed in the above articles. Moreover, although the usefulness of locomotion training has been theoretically explored, proving the efficacy of this technique on complete SCIs is a noticeable conflict. Specifically, Hubli and Dietz [10] by reviewing the clinical treatments categorized SCI patients into complete, severe incomplete and non-severe incomplete SCIs. They stated that the locomotion training is only effective on non-severe incomplete SCI (iSCI) group. In comparison, for the severe iSCIs this technique should be integrated with the modulation of spinal cord excitability (MSCE) as well. Surprisingly, they demonstrated that complete SCIs are not treated by the above strategy and this method is only used for reducing many side effects. Overall, this paper mainly addressed two above weaknesses with presenting a different model for the SCI patients to better simulate the influences of the rehabilitation techniques. To do this, the biomechanical system of the model has been modified to a double segment limb and the inertial properties have been chosen from anthropometric data. In addition, for the neuromuscular system a novel combination of TLHC and reflexes are employed that coincides with the neuroscientific findings (with respect to the CPG only [27,29,30] or reflex only [31,32] plans). The validity of this model has been confirmed by the experimental data. After that, to assess the model ability to represent the rehabilitation effects, the severe and non-severe iSCIs have been modeled by adjusting TLHC drive and above programs quoted from Hubli and Dietz [10] has been examined on them. To check this program, MSCE and locomotion training were imitated by amplifying the reflexes and TLHC afferents, respectively. Noticeably, the results of this simulation have been in absolute conformity with the above program that indicates that the used modifications in the SCI model have resolved the mentioned conflict in the rehabilitation.
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Model description
In this investigation, the locomotion of SCI patients has been modeled with a neuromusculoskeletal system. In usual simulations of pathological gait, models are initially extracted for intact cases. These models are then generalized to impairment ones by inserting a malfunction into them. Form of this malfunction depends on the type of injuries discussed
Please cite this article in press as: Abedi M, et al. A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects. Biocybern Biomed Eng (2015), http://dx.doi.org/10.1016/j.bbe.2015.12.002
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Fig. 1 – The musculoskeletal model describing swing (a) and stance (b) modes. Trunk mass is considered in stance mode. Hip angle (q1) and knee angle (q2) define limb kinematic.
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in the simulation. Since in this paper a SCI model has been addressed, the mentioned fault should be such incorporated in the model that well describe the dissection of brain signals to the spinal gait generating centers. In this regards, a CPG based model has been utilized here as the locomotor of the intact case due to the dependence of its activity on the brain commands. To imitate the pathological locomotor system the brain signals would be disrupted from this model. Therefore, in the following section, the musculoskeletal and neuromuscular systems of intact model are issued and then SCI model is described in the next section.
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The musculoskeletal model used for explaining walking gait is shown in Fig. 1. Regarding this figure the leg is modeled as a double segment limb mobilized by different muscles at the hip and knee joints. Specifically, Gluteus (GLU) and Hip flexor (HFL) muscle groups antagonistically act on the thigh and rotate it about the hip joint. In addition, Hamstring muscle group (HAM) together with Vasti muscle group (VAS) turns the shank around the knee joint by a specific connection to the bones. On the other hand, Soleus (SOL) associated with the HAM has a major role in throwing the body forward in the stance phase. In order to describe the stepping motion the stance and swing phases are modeled separately with different joints and dynamic systems. In the swing mode, as shown in Fig. 1a the leg is modeled as a double pendulum hung from the hip joint. In comparison, for explaining the stance phase the inverted pendulum connected at ankle joint is used. Additionally, in order to address the trunk mass borne by a leg in the stance mode a concentrated mass is included at the top of the leg (Fig. 1b). The segments inertial and dimensional parameters are shown in Table 1. Therefore, the dynamic equation of limb is obtained via the Hamiltonian method as:
Musculoskeletal model
½Mx 22 u€
21
_ 21 þ Kx ðu;uÞ _ 21 þ Gx ðu;uÞ _ 21 þ Cx ðu;uÞ
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¼ THAM 21 þ TVAS 21 þ TGLU 21 þ THFL 21 þ TSOL 21
(1)
where u = [q1, q2] is generalized coordinate shown in Fig. 1. The subscript x denotes swing or stance phases. In addition, Mx is mass matrix, Cx is Coriolis term, Gx is gravitational term and Kx is joints stiffness term. Moreover, THAM, TVAS, TGLU, THFL and TSOL are muscles virtual works done by Hamstring, Vasti group, Gluteus, Hip flexor muscle groups and Soleus, respectively that are generally calculated from:
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T ¼ Fdl
(2)
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That F is muscular force and dl is virtual displacement of each muscle. Muscle forces are calculated based on Hill-type model from:
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F ¼ ACT Fmax Fv ðvÞFl ðlÞ þ Fp
(3)
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where Fp is passive force obtained from [18] and ACT is muscle motorneuron activation calculated individually for each muscle based on neuromuscular plan described in next section. Moreover, Fmax,x is the maximal isometric force, such that Fmax, Fmax,VAS = 150.8 N, Fmax,SOL = 251.3 N, Fmax, HAM = 56.5 N, GLU = 226.2 N and Fmax,HFL = 226.2 N. Further, in Eq. (3), Fl,i(l) is force-length dependent term that can be obtained from: ! lb 1r Fl ¼ exp (4) v
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Table 1 – Segment parameters.
Length (mm) Center of mass (mm) Mass (kg)
Thigh
Shank
Trunk
300 150 18
300 150 18
– – 60
Please cite this article in press as: Abedi M, et al. A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects. Biocybern Biomed Eng (2015), http://dx.doi.org/10.1016/j.bbe.2015.12.002
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Table 2 – Parameters of different muscles. Parameter ath,VAS ash,VAS rknee,VAS afo,SOL atr,GLU
Value (mm)
Parameter
Value (mm)
Parameter
Value (mm)
60 60 20 30 7
ash,SOL rankle,SOL ahip,HAM rthigh,HAM ath,GLU
200 30 60 300 60
rknee,HAM atr,HFL ath,HFL rhip,HFL rhip,GLU
60 7 60 840 840
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in which, b = 2.3 and v = 1.6. Moreover, l = L/Lopt so that Lopt = 325 mm, and L is muscle length obtained individually for each muscle as:
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LVAS ¼ ath;VAS þ ash;VAS þ rknee;VAS q2
(5)
LSOL ¼ afo;SOL þ ash;SOL þ rankle;SOL ðq1 q2 Þ
(6)
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1=2 2 ahip;HAM rthigh;HAM cosðq1 Þrknee;HAM cosðq1 q2 Þ 2 þ rthigh;HAM sinðq1 Þ þ rknee;HAM sinðq1 q2 Þ
LHAM ¼
i1=2 h LHFL ¼ a2tr;HFL þ a2th;HFL þ rhip;HFL cosðpq1 Þ
(7) (8)
with that, the constants of above equations are shown in Table 2. Further, in Eq. (12) Fv,i(v) is force-velocity dependent Q3 term obtained from: 8 b1 c1 vm > > < vm < 0 vm þ b1 (9) Fv ¼ b2 c2 ðlÞvm > > : vm 0 vm þ b2
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in that, b1 = 0.69, b2 = 0.18, c1 = 0.17, c2(l) = 5.34l2 + 8.41l 4.7 and vm is muscle velocity of each muscle, i.e. derivative of Eq. (5) to Eq. (8).
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Further, in Eq. (2) virtual displacement, dl, is calculated for each muscle from the following equations: 2 3 atr;HFL ath;HFL sinðq1 Þ ffi7 6 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (10) dlHFL ¼ 4 a2tr;HFL þ a2th;HFL 2atr;HFL ath;HFL cosðq1 Þ 5 0
228
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2
dlGLU
3 atr;GLU ath;GLU sinðq1 Þ q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 6 7 ¼ 4 a2tr;GLU þ a2th;GLU þ 2atr;GLU ath;GLU cosðq1 Þ 5 0
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dlVAS ¼
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TLHC structure
The TLHC structure obtained from Spardy et al. [19] is indicated in Fig. 3. Regarding this figure the model contains two separate layers for rhythm generation and pattern formation. In this system the tonic supraspinal drive, d, triggers the half-centers of rhythm generation (i.e. RG-E and RG-F) and pattern formation neurons (i.e. PF-E and PF-F). The -E and -F suffixes are standing for extension and flexion, respectively. Additionally, inhibitory interneurons, In-E and In-F keep mutual inhabitation between extensors and flexors. The CPG sides alternate the firing of motorneurons Mn-E and Mn-F to correspondingly activate a pair of antagonist muscles, i.e. GLU and HFL, respectively (Fig. 2). Additionally, afferents of each muscle are fed back into the TLHC so that Ia and II are considered for flexion, and Ia and Ib are chosen for extension sides. In order to describe this plan in a mathematical form, Hodjkin-Huxley models are used for neurons. This model expresses the dynamic of RG-, PF- and Mn- neurons with 2nd order differential equations as:
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dV ¼ Iion ISYN dt dh ðh1 ðVÞhÞ ¼ dt t h ðVÞ
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C
(15)
(11)
(12)
rknee;VAS
dlSOL ¼
0
neural controlling system comprised TLHC and reflex pathways. TLHC is responsible for stimulating GLU and HFL to rhythmically move thigh around the hip. While neural reflexes with an action on HAM, VAS and SOL muscles coordinate shank movements with thigh. In the following sections, these plans are described separately.
rankle;SOL rankle;SOL
2
dlHAM
3 ðLt ahip;HAM sinðq1 ÞLt ash;HAM sinðq1 q2 ÞÞ 6 7 LHAM 7 ¼6 4 ðahip;HAM ash;HAM sinðq2 Þ þ Lt ash;HAM sinðq1 q2 ÞÞ 5 LHAM
(13)
(14)
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4.
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The neuromuscular plan for controlling limbs during gait locomotion is shown in Fig. 2. While attending this figure, the
Neuromuscular system Fig. 2 – The neuromuscular plan for generating gait : TLHC motor commands; : neuronal locomotion. : afferent feedbacks. reflex motor command;
Please cite this article in press as: Abedi M, et al. A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects. Biocybern Biomed Eng (2015), http://dx.doi.org/10.1016/j.bbe.2015.12.002
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II ¼ kdII dnorm þ kEMGII ACT þ CII
Fig. 3 – The TLHC type CPG model used for gait generating : inhibitory signal; : excitatory signal; : [19]; : neuron; : motorneuron. inhibitory neuron;
(22)
300
In that rv = 0.6, kvIa = 6.2, kdIa = 2, kEMGIa ¼ 0:06, CIa = 0.26, kIb = 1, kdII = 1.5, kEMGII ¼ 0:06, and CII = 0. In addition, vnorm, dnorm, Fnorm and ACT are respectively, normalized lengthening speed, normalized length, normalized force and motorneuron activation of corresponding muscle. The normalized parameters are obtained from: 8 < LLth L Lth dnorm ¼ (23) : Lth 0 L < Lth
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in that, Lth = 325 mm and vnorm ¼ LÇ=Lth and: 8 < FFth F Fth Fnorm ¼ : Fth 0 F < Fth
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and describes interneurons with a 1st order differential equation:
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C
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That in above equations, V and h are neuron voltage and gate conductance, Iion is ionic current calculated according to [19] and h1 and t1 are:
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h1 ¼
1 1 þ exp Vþ51 4
(17)
283
t1 ¼
600 cosh Vþ51 8
(18)
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In addition, ISYN is a synaptic current received from supraspinal drive (d), sensory feedback ( fb) and adjacent neurons (N) can be calculated from: X X bik fbk þ cij Nj (19) ISYN ¼ ai d þ
dV ¼ Iion ISYN dt
(16)
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288
k
j
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That ai, bik and cij are constants determined according to [19]. Supraspinal drive is considered as a dc signal and can be set on different values. In addition, sensory feedback containing Ia, Ib and II are calculated from the following equations:
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v þ kdIa dnorm þ kEMGIa ACT þ CIa Ia ¼ kvIa vrnorm
(20)
Ib ¼ kIb Fnorm
(21)
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311
In that, F is muscle force obtained from Eq. (3) and Fth is threshold force set individually for each muscle. Further, for neuron output activation, N appeared in Eq. (19) is calculated from: 8
V30 < 1= 1 þ exp V Vth (25) N¼ k : 0 V < Vth
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In that, Vth = 50 mV and k is 8 for PF-, RG- and Mn- and is 3 for interneurons. It is noted that the parameter ACT in Eqs. (3), (20) and (22) is the output activation of muscle motorneuron. Accordingly, output activation of Mn-E and Mn-F is equivalent to parameter ACT in Eq. (3) for GLU and HFL, respectively.
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(24)
308
317
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Reflex pathways
The neuronal reflexes are considered as the supplementary of TLHC for coordinating the segments. The architecture of reflex pathways is shown in Fig. 2. Regarding this figure VAS, HAM and SOL motorneurons are stimulated by the reflexes. These reflexes are some sensory signals acting directly on the muscle motorneurons. This means that in dynamic equation of motorneuron (Eq. (3)) for the mentioned muscles, synaptic current, ISYN, contains the above sensory signals. These signals are chosen so that the reflexes stabilize the gait locomotion and generate walking patterns similar to the human. Thus, for the HAM reflex pathway the group II afferent feedback is selected to facilitate hip extension during the stance phase. Therefore:
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ISYN;HAM ¼ IIHAM ¼ kdII dnorm;HAM þ kEMGII ACTHAM þ CII
(26)
338
such that ACTHAM is obtained from putting ISYN,HAM in Eq. (3). Further, the ground contact force is utilized for the SOL and VAS reflex pathways for bearing the body weight at the beginning of stance phase. Hence ISYN for this muscle is calculated from: 8 < ðGRFGRFth Þ GRF GRFth (27) ISYN;x ¼ cx GRFmax : 0 GRF < GRFth
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where x denotes VAS or SOL and GRF is the ground contact force, cx is constant so that cSOL = 1.95 and cVAS = 1.0. Moreover, GRFmax = 2000 N is the maximum ground contact force and GRFth is the threshold ground contact force that is 200 N for the VAS and 100 N for the SOL.
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5.
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The locomotion of spinal cord injury is modeled by inserting a local malfunction into the neuromuscular system of the obtained intact model. The motivation for this approach has been for the local injury of central nervous system (CNS) in a spinal trauma. Therefore, the gait generator centers in a spinal cord remain undamaged in the most of SCIs. Further, the effect of spinal lesion is physiologically interpreted as the loss of supraspinal (brain, midbrain, cerebellum, etc.) signals on gait generator circuits. This signal has been imitated in the intact model by the parameter 'd' in Section 4.1. Thus, by dropping this parameter through adding a mutable gain in the neuromuscular system as shown in Fig. 4, a spinal cord lesion can be simulated. This modification by disrupting the bias of TLHC neurons stops the generation of regular gait cycles. This effect is shown in Fig. 5 such that the patient keeps the equilibrium only at the first step and stumbles at the stance phase of the second stride. Further, using this plan the classification of severe and weak iSCIs is obtainable too. Specifically, by more decreasing the supraspinal drive with the mutable gain, more serious damages are imitated. This classification is essential for checking the usefulness of rehabilitation activities. The experiments proved that for the weak iSCIs some common techniques such as 'gait training' are efficient enough. In comparison, for the severe one, extra strategies such as reflex modulation should be added as well [10]. This discrimination in the rehabilitation is investigated by the model in the next section.
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6.
Spinal cord injury gait model
Results and discussion
The simulations are performed in MATLAB Simulink (ver. R2008a). The results are presented for intact and SCI cases. The parameters for neural pathways and rehabilitations gains are
Fig. 4 – SCI model with inserting a mutable gain as a malfunction before TLHC to simulate intensity of trauma.
Fig. 5 – Gait instability in an incomplete SCI model. Variations of knee and hip angles in three steps.
obtained through a trial and error process. In this section the final values are incorporated.
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Intact model verification
As mentioned before, due to the limited effect of a spinal lesion, the locomotor basis of SCI and intact models are alike. Therefore, to check the validity of the proposed model the performance of unaffected system can be evaluated. To do this, the output of the intact model is compared to the experimental data. In this comparison different parameters of a normal gait are investigated. One of the common factors in studying the human walking is the kinematic specifications. Fig. 6 shows the variations of knee and hip angles versus the percentage of a stride. The experimental data shown in this figure are obtained from [33]. The likeness of simulation and real data proves the model correctness. These similarities could be seen in both variation trends and amplitude. Specifically, the descents and ascents of the curvatures and positions of peaks and troughs are near in simulation and experiments. This nearness confirms the validity of timing problem in the neuromuscular system of the model. The timing is primarily adjusted by the rhythm generator layer of TLHC with regular alternating of the extensor and flexor motorneurons. In addition, the good operation of reflex pathways is also effective in the timing issue with activating the muscles motorneurons in the proper times. This implies the suitability of sensory feedbacks applied in the reflex pathways architecture (Fig. 2). Moreover, due to the mass proportion of the model to the real data of an adult (Table 1), the amplitudes closeness of mentioned curvatures verifies the kinetic aspects of the simulation. Further, the pattern of muscle stimulations in gait cycles is another factor in study of locomotor functions. Specifically, the VAS, HAM and SOL activations exhibit the operation of reflex pathways. Variations of maximum value of isometric
Please cite this article in press as: Abedi M, et al. A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects. Biocybern Biomed Eng (2015), http://dx.doi.org/10.1016/j.bbe.2015.12.002
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Fig. 6 – A comparison between simulation and experiments. Hip angle variation (a) and knee angle variation (b) in a stride; right column is simulation results and left column is experimental data [33].
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contraction (MVIC) of these muscles are indicated in Fig. 7. In this figure, the results have been compared to the experimental data of reference [33]. Fig. 7a shows the activation of HAM muscle in a stride. This muscle has been stimulated by the reflex of group II afferent feedback. The similarity of simulation and experimental data shows the correctness of applied plan in firing this muscle. In addition, the SOL activity is
illustrated in Fig. 7b. A noticeable reason about this figure is that SOL has the maximum MVIC amongst all three muscles. This issue, i.e. evident in both simulations and experimental data, physiologically implies the importance of SOL in the gait cycle. The major role of this muscle is the bearing of the body weight at start of the stance phase and putting it forward. Due to this function, the peak value of SOL muscle stands on the
Fig. 7 – HAM muscle variation (a), SOL muscle variation (b) and VAS muscle variation (c) in a stride; right column is simulation results and left column is experimental data [33]. Please cite this article in press as: Abedi M, et al. A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects. Biocybern Biomed Eng (2015), http://dx.doi.org/10.1016/j.bbe.2015.12.002
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initial stages of the stance phase in the curvatures. Moreover, the activation of VAS in a stride is shown in Fig. 7c. The main operation of this muscle is to stabilize the gait locomotion by limiting the flexion of the knee. Since this function is much critical in the weight-bearing stage of the stance phase, the VAS greatest stimulation should be at the beginning of the stance mode. Thus, the VAS activation would be synchronous with the SOL as indicated in the figures. Due to this synchronicity the reflex plan of SOL and VAS muscle are taken alike in Fig. 2. Moreover, any differences between simulation and experimental data are mainly for some simplifying assumptions of the model. Specifically, the absence of foot segment in the biomechanical system interferes the results of simulations by deviating the ground contact force. In addition, withdrawing different muscles in the musculoskeletal system would make many errors in the simulations. Overall, the acceptable nearness of experimental and simulation data verifies the correctness of our proposed plan for neural controlling system of walking locomotion.
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6.2.
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As mentioned before, the main objective of this paper has been the study of rehabilitation methods with a theoretical view. Although this issue has been previously addressed by Markin [18] and Spardy et al. [19], no distinction between the classes of SCI treatment has not been drawn in these works as such. Due to this limitation, in this section, it is shown by the simulations that the applied modification in the biomechanical system well resolved this defect. To check this achievement, a rehabilitation program has been developed for the classes of SCI patients based on clinical treatment processes. Then, this program has been examined on the obtained models and the yielded results have been discussed. As noted before, the models of SCI patients are obtained by dropping the drive of the TLHC. To simulate the different classes of SCIs, this parameter is put on specific levels; that is shown in Fig. 8. Regarding this figure, the walking area has been divided into four different regions namely, intact (Region 1), weak incomplete SCI (Region 2), severe incomplete SCI (Region 3) and complete SCI (Region 4). The investigations of this section have been focused on Regions 2 and 3 that are related to the weak and severe iSCIs, respectively. Withdrawing the complete SCI (Region 4) from this investigation has
Studying the rehabilitation on the SCI model
Table 3 – Gains of afferent feedbacks of TLHC for rehabilitation of weak iSCI. Signals
Gain
Ia of HFL II of HFL Ia of GLU Ib of GLU
2 2 2 3
been for the insufficiency of mentioned rehabilitation technique for them [10].
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Rehabilitation program for weak SCI
To investigate the above conditions, at the first step a weak iSCI is modeled. To do this, the supraspinal drive is decreased to 1.5. Hubli and Dietz [10] reported that in the iSCIs, the locomotion training has a significant success in regaining the gait ability. This technique is usually performed clinically by a repeated use of treadmill. From a physiological perspective, the regular gait training leads to the amplification of spinal synapses that enhances the interaction of afferents and the spinal circuits. This means that the reinforcement of those feedbacks fed into the spinal locomotor centers facilitates the gait recovery after an iSCI. Regarding Fig. 3, in our proposed model the afferent feedbacks linking to the spinal gait generator (TLHC) contains Ia and Ib of hip extensor and Ia and II of Hip flexor. Therefore, by amplifying these signals the effect of above technique can be investigated by the model. The amplification gains of these signals are shown in Table 3. The result of these amplifications is indicated in Fig. 9 and Fig. 10. In this figures the results of simulations are compared to the experimental data of [34] that have been obtained for the clinical iSCI rehabilitation with the treadmill gait training. Attending to this figure, a regular gait pattern is produced by the above plan. This result confirms the efficacy of afferent amplification in regaining the patient walking ability. Therefore, by this model the cause of recovering the gait abilities in weak incomplete SCIs by the feedback amplification is justified.
6.2.2.
Rehabilitation program for severe iSCI
Hubli and Dietz [10] stated that for the rehabilitation of severe iSCIs, in addition to the locomotion training, the excitability modulation of spinal circuits (EMSC) is necessary as well. They denoted that this need is met in clinical treatments by different artificial methods including continuous vibration of
Fig. 8 – Classification of persons based on the supraspinal drive; the continuous cycles are generated only in the intact region (Region 1), that period is decreased with supraspinal drive increase. Level of decrease in supraspinal drive classifies SCI patients into weak iSCI (Region 2), severe iSCI (Region 3) and complete SCI (Region 4). Please cite this article in press as: Abedi M, et al. A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects. Biocybern Biomed Eng (2015), http://dx.doi.org/10.1016/j.bbe.2015.12.002
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Fig. 9 – Efficacy of afferent feedback amplification and generation of successive cycles; left column: simulation results of knee and hip joints after feedback amplification; right column: experimental data of [34] for the clinical incomplete SCIs during stepping on treadmill.
Fig. 10 – Variations of SOL, VAS and HAM muscles with respect to the MVIC; left column: simulation results after feedback amplification; right column: experimental data of [34] for the clinical incomplete SCIs during stepping on treadmill.
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the quadriceps and hamstring, continuous electrical stimulation of the peroneal or sural nerve, and magnetic stimulation of the spinal cord. To illustrate this necessity in the model, at the first step the deficiency of locomotion training for the gait recovery after severe iSCI is proved. Accordingly, the model of severe iSCI is obtained by extra decreasing of the supraspinal drive (Fig. 8). For the following simulations, this parameter is set on 1.2. Then, to check the
Table 4 – Gains of afferent feedbacks of TLHC for rehabilitation of severe iSCI. Signals
Gain
Ia of HFL II of HFL Ia of GLU Ib of GLU
2 2 2 6
Fig. 11 – Insufficiency of afferent feedback amplification in gait recovery of a severe SCI model; patient stumbles after 4 steps.
Please cite this article in press as: Abedi M, et al. A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects. Biocybern Biomed Eng (2015), http://dx.doi.org/10.1016/j.bbe.2015.12.002
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effect of locomotion training, the feedback amplification technique is again examined on the obtained model. The values used in this simulation for these gains are shown in Table 4. Regarding this table, these values are equal (Ia and II) or larger (Ib) than ones used for the weak iSCI (Table 3). Despite these variations, as shown in Fig. 11, the expected outcomes have not been achieved at all and the patient falls down finally after three steps. This means that the afferent amplification is not sufficient for the gait recovery after severe iSCI.
Table 5 – Gains of afferent feedbacks and neuronal reflexes. Signals Ia of HFL II of HFL Ia of GLU Ib of GLU Reflex of HAM Reflex of VAS Reflex of SOL
Gain 2 2 2 3 2 8 2
Fig. 12 – Efficacy of the combination of afferent feedback amplification and neuronal reflexes in rehabilitation of severe SCI model; regular cycles are generated in hip, knee, and hip motorneuron and muscle activations (black line: GLU; red line: HFL).
Fig. 13 – SOL, VAS and HAM muscle force with respect to the MVIC after combination of afferent feedback amplification and neuronal reflexes in rehabilitation of severe SCI model. Please cite this article in press as: Abedi M, et al. A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects. Biocybern Biomed Eng (2015), http://dx.doi.org/10.1016/j.bbe.2015.12.002
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Table 6 – Result of simulation for the efficacy of rehabilitation technique on different classes of SCI patients. U: successful; T: unsuccessful. Patient
Supraspinal drive (d)
Rehabilitation technique
Result
Weak iSCI
1.5
Locomotion training
U
Severe iSCI
1.2
Locomotion training Locomotion training/ EMSC
U
Complete SCI
0
Locomotion training/ EMSC
528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558
Having illustrated this deficiency, at the next step the efficacy of integrating EMSC into the locomotion training is investigated. The EMSC is imitated in the model by magnifying the reflex pathways. This idea has been obviously for the presence of reflex synapses in the spinal neuronal circuits. Therefore, similarly with the locomotion training the specific gains have been considered for the reflexes to include the EMSC effect. These gains together with the gains used for the TLHC afferents are listed in Table 5. By including these gains into the model, the rehabilitation of severe iSCI with the combination of locomotion training and EMSC is simulated. The result of this simulation is shown in Fig. 12 and Fig. 13. Fig. 12 indicates kinematic of motion in successive cycles together with hip muscles actuations and Fig. 13 illustrates activations of VAS, HAM and SOL muscles. Attending these figures, generation of these successive gait cycles implies the appropriateness of above technique for the gait recovery after severe iSCI. This outcome along with the result of the previous section indicates the conformity of the model performance to the behavior of actual SCI patients in reaction to the rehabilitation techniques. These results are summarized in Table 6 that is thoroughly in agreement with the statements of Hubli and Dietz [10]. For the complete SCI, the model is obtained by putting the supraspinal drive on zero. The rehabilitative simulations have been performed based on different values of amplifying gains. However, the acceptable results have not been obtained that implies the inefficiency of above techniques on this class of patients. For the gait recovery of complete SCI patients the adaptive gains should be included that could be examined in future works.
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In this paper, the efficacy of rehabilitation techniques for regaining the gait ability after SCI using a theoretical approach was discussed. To do this, a neuromechanical model was proposed for simulating gait locomotion of SCI patients and examining rehabilitation techniques. From this investigation following achievements are obtained:
Conclusion
- For the first time, three classes of SCI patients namely complete SCI, severe iSCI and weak iSCI are simulated with a full biological neuromechanical model. - Two well-known rehabilitation techniques namely locomotion training and EMSC are imitated. These methods are
11
examined on different classes of SCIs for the first time and their effects are theoretically explored. - Results of above simulations stated that: (1) locomotion training is successful for weak iSCI; (2) combination of locomotion training and EMSC is effective for severe iSCI; and (3) none of these strategies was advantageous for the complete SCI. - The criterion for confirming above outcomes was clinical evidences of SCI's treatment. Comparisons proved the compliancy of above statements with clinical evidences. According to this compliancy, this model represents more specifications of SCI patients than the previous works. This means, this model is a new achievement in neurorehabilitation to be incorporated for studying SCI's reactions to rehabilitation techniques. In addition, to assess the validity of the proposed model the kinematic and kinetic results of the simulation were compared to the experimental data. This comparison was made on both healthy and treated SCI models. The nearness of simulation and experiments proved the correctness of suggested system. This conformity together with the above conclusion implies that this model would be functional in describing the rehabilitation effects on the SCI patients, which is useful in optimizing the treatment process.
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Please cite this article in press as: Abedi M, et al. A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects. Biocybern Biomed Eng (2015), http://dx.doi.org/10.1016/j.bbe.2015.12.002
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/bbe 1 2 3
Original Research Article
A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects
4 5 6
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Q1
Mohsen Abedi a, Majid M. Moghaddam a b
a,*
, S. Mohammad P. Firoozabadi b
Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran Department of Physiology, School of Medical Sciences, Tarbiat Modares University, Tehran, Iran
article info
abstract
Article history:
Gait recovering after spinal cord injury (SCI) is a regular attempt in neurorehabilitation. For
Received 24 January 2015
this purpose, various clinical techniques have been proposed until now. However, the
Received in revised form
feasibility of these techniques has not been theoretically investigated so much. This has
23 August 2015
been mainly for difficulties of gait modeling in SCI patients. Involving these problems,
Accepted 9 December 2015
recently neuromechanical models of gait locomotion have been proposed for examining
Available online xxx
rehabilitation methods. However, these models were so simple that could not properly
Keywords:
in prior simulations. Due to this limitation, in this paper a new neuromechanical model is
express rehabilitation effects. Notably, lesion intensity is a concern that was never attended Neuromechanical modeling
proposed that classifies patients based on intensity of trauma. Explicitly, the complete,
Neurorehabilitation
severe and non-severe incomplete SCIs are imitated and effects of related clinical rehabi-
Spinal cord injury
litations are explored. Remarkably, the model indicates an incredible performance in
Gait locomotion
explaining the rehabilitation effects through presenting the compliant results with clinical
Central pattern generator
information. The suitability of this model is mainly for the applied neuromuscular plan that consists of a combined plan of central pattern generator (CPG) and neural reflexes that controls a double segment limb. The validity of this model is further proved by comparing the kinematic and kinetic results to the experimental data. # 2015 Published by Elsevier Sp. z o.o. on behalf of Nałęcz Institute of Biocybernetics and Biomedical Engineering.
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1.
Introduction
Undoubtedly, the walking is a vital human's want for movement and doing different daily jobs. The importance of this need is sensible in life of persons deprived from this gift by some means. Depression, seclusion, social problems, etc. are
routine involvement of such people. Therefore, the rehabilitation for the gait recovery after a physical impairment is a necessary effort. In addition, the spinal cord injury (SCI) is a main causative factor in most of gait disabilities in persons. Due to this concern, various rehabilitative techniques have been proposed in the literature for the gait recovery after SCI. The majority of
* Corresponding author at: Nasr Bridge, Jalal Al Ahmad Street, Tehran, Iran. E-mail address: [email protected] (M.M. Moghaddam). http://dx.doi.org/10.1016/j.bbe.2015.12.002 0208-5216/# 2015 Published by Elsevier Sp. z o.o. on behalf of Nałęcz Institute of Biocybernetics and Biomedical Engineering.
Please cite this article in press as: Abedi M, et al. A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects. Biocybern Biomed Eng (2015), http://dx.doi.org/10.1016/j.bbe.2015.12.002
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these techniques have been various clinical methods suggested in the form of statistical analysis [1–4] or different assistive robots [5–7]. Although these techniques have been helpful for the SCI patients, the researchers have believed that awareness about the physiological basis of treatment substantially enhances the effectiveness of above strategies. In this regard, in the past decades the neuroscientific studies have been largely focused on finding the biology of neural pathway restoration during clinical treatments in a damaged locomotor system [8,9]. These investigations conduct the rehabilitation process of SCI paralyzes on improved trends (for review [10]). Nevertheless, the theoretical simulation of pathological gait can notably deepen the knowledge about the neural causes of walking inabilities to be certainly functional in optimization of rehabilitation methods. Whatsoever, these models have not been so many addressed in the literature and rarely proposed for a limited number of diseases. Specifically, in a number of papers, the authors have described some pathological gaits (e.g. Parkinson and crouch gait) based on the musculoskeletal walking models [11–13]. However, these models have not possessed a cybernetic basis and thus cannot provide any details about the origin of neural disorder diseases. Due to this deficit, the idea of using neuromuscular-based models has been raised in the last decade for simulating walking locomotion of neural impairments. In these simulations, the origin of gait locomotion has been a key factor. This issue was broadly discussed for intact cases in the previous investigations. In these studies central pattern generator (CPG) and neural reflexes were recognized as the major neural policy of gait generation [14,15]. Nevertheless, use of these models for the neural disorders has been very limited so far. Specifically, Bellotti et al. [16] firstly brought up this idea for imitating the gait locomotion of SCI patients based on the CPG concept. However, this target has not been met in the paper because of the unsuitable structure of CPG. Further, Jansen et al. [17] simulated the muscle spasticity in the gait locomotion of hemiplegic persons by incorporating the neural reflexes. This effect has been modeled by modifying the gains of a-motorneurons in accordance with the clinical data. Nevertheless, a major defect in the above papers has been the absence of brain disruption influence in the pathologic gait simulations. Without this effect, most gait abnormalities associated with SCI and stroke paralysis are not justifiable. A main reason for this deficiency is the lack or inappropriate use of CPG in the above articles. Due to this limitation, Markin [18] and Spardy [19] employed a more complex CPG for simulating the gait locomotion of complete SCI cats. This CPG was a two level half-center (TLHC) model generating different patterns of locomotion by receiving the brain commands [20]. This model is really the improved form of other types of CPG like basic half-center [15,21–25] and unit burst generator [26,27]. Further, the SCI locomotor system has been imitated in these papers by cutting the mentioned brain signals on TLHC. In this way, the effect of brain disruption has been included in the model of SCI locomotion. Moreover, the above authors incorporating the afferent feedbacks into the TLHC, represented another valuable achievement by the simulation. Specifically, using this architecture the theoretical investigation of rehabilitation
methods has been explored for the first time. The rehabilita- Q2 tive technique has been dealt in these studies was the afferent feedback amplification that in the clinical treatments is achieved by the ‘‘locomotion training’’ [10,28]. Expressly, the above model theoretically illustrated how this tactic recovers the walking ability in the complete SCI patients. This outcome obtains a deeper knowledge about the effectiveness of rehabilitation methods that would be surely efficient in optimizing and accelerating the treatments. However, the above plans have still two major weaknesses in the SCI modeling and the rehabilitation issues. In the modeling of SCI, the musculoskeletal system included a low mass single segment limb as a leg of a cat that the influence of limb inertia on the TLHC performance has become ignorable. This simplicity causes that the different challenges of real gait locomotion like stability, coordination, etc. have not to be addressed in the above articles. Moreover, although the usefulness of locomotion training has been theoretically explored, proving the efficacy of this technique on complete SCIs is a noticeable conflict. Specifically, Hubli and Dietz [10] by reviewing the clinical treatments categorized SCI patients into complete, severe incomplete and non-severe incomplete SCIs. They stated that the locomotion training is only effective on non-severe incomplete SCI (iSCI) group. In comparison, for the severe iSCIs this technique should be integrated with the modulation of spinal cord excitability (MSCE) as well. Surprisingly, they demonstrated that complete SCIs are not treated by the above strategy and this method is only used for reducing many side effects. Overall, this paper mainly addressed two above weaknesses with presenting a different model for the SCI patients to better simulate the influences of the rehabilitation techniques. To do this, the biomechanical system of the model has been modified to a double segment limb and the inertial properties have been chosen from anthropometric data. In addition, for the neuromuscular system a novel combination of TLHC and reflexes are employed that coincides with the neuroscientific findings (with respect to the CPG only [27,29,30] or reflex only [31,32] plans). The validity of this model has been confirmed by the experimental data. After that, to assess the model ability to represent the rehabilitation effects, the severe and non-severe iSCIs have been modeled by adjusting TLHC drive and above programs quoted from Hubli and Dietz [10] has been examined on them. To check this program, MSCE and locomotion training were imitated by amplifying the reflexes and TLHC afferents, respectively. Noticeably, the results of this simulation have been in absolute conformity with the above program that indicates that the used modifications in the SCI model have resolved the mentioned conflict in the rehabilitation.
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Model description
In this investigation, the locomotion of SCI patients has been modeled with a neuromusculoskeletal system. In usual simulations of pathological gait, models are initially extracted for intact cases. These models are then generalized to impairment ones by inserting a malfunction into them. Form of this malfunction depends on the type of injuries discussed
Please cite this article in press as: Abedi M, et al. A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects. Biocybern Biomed Eng (2015), http://dx.doi.org/10.1016/j.bbe.2015.12.002
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Fig. 1 – The musculoskeletal model describing swing (a) and stance (b) modes. Trunk mass is considered in stance mode. Hip angle (q1) and knee angle (q2) define limb kinematic.
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in the simulation. Since in this paper a SCI model has been addressed, the mentioned fault should be such incorporated in the model that well describe the dissection of brain signals to the spinal gait generating centers. In this regards, a CPG based model has been utilized here as the locomotor of the intact case due to the dependence of its activity on the brain commands. To imitate the pathological locomotor system the brain signals would be disrupted from this model. Therefore, in the following section, the musculoskeletal and neuromuscular systems of intact model are issued and then SCI model is described in the next section.
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The musculoskeletal model used for explaining walking gait is shown in Fig. 1. Regarding this figure the leg is modeled as a double segment limb mobilized by different muscles at the hip and knee joints. Specifically, Gluteus (GLU) and Hip flexor (HFL) muscle groups antagonistically act on the thigh and rotate it about the hip joint. In addition, Hamstring muscle group (HAM) together with Vasti muscle group (VAS) turns the shank around the knee joint by a specific connection to the bones. On the other hand, Soleus (SOL) associated with the HAM has a major role in throwing the body forward in the stance phase. In order to describe the stepping motion the stance and swing phases are modeled separately with different joints and dynamic systems. In the swing mode, as shown in Fig. 1a the leg is modeled as a double pendulum hung from the hip joint. In comparison, for explaining the stance phase the inverted pendulum connected at ankle joint is used. Additionally, in order to address the trunk mass borne by a leg in the stance mode a concentrated mass is included at the top of the leg (Fig. 1b). The segments inertial and dimensional parameters are shown in Table 1. Therefore, the dynamic equation of limb is obtained via the Hamiltonian method as:
Musculoskeletal model
½Mx 22 u€
21
_ 21 þ Kx ðu;uÞ _ 21 þ Gx ðu;uÞ _ 21 þ Cx ðu;uÞ
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¼ THAM 21 þ TVAS 21 þ TGLU 21 þ THFL 21 þ TSOL 21
(1)
where u = [q1, q2] is generalized coordinate shown in Fig. 1. The subscript x denotes swing or stance phases. In addition, Mx is mass matrix, Cx is Coriolis term, Gx is gravitational term and Kx is joints stiffness term. Moreover, THAM, TVAS, TGLU, THFL and TSOL are muscles virtual works done by Hamstring, Vasti group, Gluteus, Hip flexor muscle groups and Soleus, respectively that are generally calculated from:
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T ¼ Fdl
(2)
187
That F is muscular force and dl is virtual displacement of each muscle. Muscle forces are calculated based on Hill-type model from:
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F ¼ ACT Fmax Fv ðvÞFl ðlÞ þ Fp
(3)
192
where Fp is passive force obtained from [18] and ACT is muscle motorneuron activation calculated individually for each muscle based on neuromuscular plan described in next section. Moreover, Fmax,x is the maximal isometric force, such that Fmax, Fmax,VAS = 150.8 N, Fmax,SOL = 251.3 N, Fmax, HAM = 56.5 N, GLU = 226.2 N and Fmax,HFL = 226.2 N. Further, in Eq. (3), Fl,i(l) is force-length dependent term that can be obtained from: ! lb 1r Fl ¼ exp (4) v
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Table 1 – Segment parameters.
Length (mm) Center of mass (mm) Mass (kg)
Thigh
Shank
Trunk
300 150 18
300 150 18
– – 60
Please cite this article in press as: Abedi M, et al. A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects. Biocybern Biomed Eng (2015), http://dx.doi.org/10.1016/j.bbe.2015.12.002
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Table 2 – Parameters of different muscles. Parameter ath,VAS ash,VAS rknee,VAS afo,SOL atr,GLU
Value (mm)
Parameter
Value (mm)
Parameter
Value (mm)
60 60 20 30 7
ash,SOL rankle,SOL ahip,HAM rthigh,HAM ath,GLU
200 30 60 300 60
rknee,HAM atr,HFL ath,HFL rhip,HFL rhip,GLU
60 7 60 840 840
202 203 204 205
in which, b = 2.3 and v = 1.6. Moreover, l = L/Lopt so that Lopt = 325 mm, and L is muscle length obtained individually for each muscle as:
206
LVAS ¼ ath;VAS þ ash;VAS þ rknee;VAS q2
(5)
LSOL ¼ afo;SOL þ ash;SOL þ rankle;SOL ðq1 q2 Þ
(6)
208 207 209 210 211 212 215 214 213 216 217 218 219 220 221
1=2 2 ahip;HAM rthigh;HAM cosðq1 Þrknee;HAM cosðq1 q2 Þ 2 þ rthigh;HAM sinðq1 Þ þ rknee;HAM sinðq1 q2 Þ
LHAM ¼
i1=2 h LHFL ¼ a2tr;HFL þ a2th;HFL þ rhip;HFL cosðpq1 Þ
(7) (8)
with that, the constants of above equations are shown in Table 2. Further, in Eq. (12) Fv,i(v) is force-velocity dependent Q3 term obtained from: 8 b1 c1 vm > > < vm < 0 vm þ b1 (9) Fv ¼ b2 c2 ðlÞvm > > : vm 0 vm þ b2
222 223 224 225
in that, b1 = 0.69, b2 = 0.18, c1 = 0.17, c2(l) = 5.34l2 + 8.41l 4.7 and vm is muscle velocity of each muscle, i.e. derivative of Eq. (5) to Eq. (8).
226 227
Further, in Eq. (2) virtual displacement, dl, is calculated for each muscle from the following equations: 2 3 atr;HFL ath;HFL sinðq1 Þ ffi7 6 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (10) dlHFL ¼ 4 a2tr;HFL þ a2th;HFL 2atr;HFL ath;HFL cosðq1 Þ 5 0
228
230 229 231
2
dlGLU
3 atr;GLU ath;GLU sinðq1 Þ q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 6 7 ¼ 4 a2tr;GLU þ a2th;GLU þ 2atr;GLU ath;GLU cosðq1 Þ 5 0
233 232 234
dlVAS ¼
236 235 237 239 238 240
246 247 248 249 250 251
4.1.
252
TLHC structure
The TLHC structure obtained from Spardy et al. [19] is indicated in Fig. 3. Regarding this figure the model contains two separate layers for rhythm generation and pattern formation. In this system the tonic supraspinal drive, d, triggers the half-centers of rhythm generation (i.e. RG-E and RG-F) and pattern formation neurons (i.e. PF-E and PF-F). The -E and -F suffixes are standing for extension and flexion, respectively. Additionally, inhibitory interneurons, In-E and In-F keep mutual inhabitation between extensors and flexors. The CPG sides alternate the firing of motorneurons Mn-E and Mn-F to correspondingly activate a pair of antagonist muscles, i.e. GLU and HFL, respectively (Fig. 2). Additionally, afferents of each muscle are fed back into the TLHC so that Ia and II are considered for flexion, and Ia and Ib are chosen for extension sides. In order to describe this plan in a mathematical form, Hodjkin-Huxley models are used for neurons. This model expresses the dynamic of RG-, PF- and Mn- neurons with 2nd order differential equations as:
253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270
dV ¼ Iion ISYN dt dh ðh1 ðVÞhÞ ¼ dt t h ðVÞ
271
C
(15)
(11)
(12)
rknee;VAS
dlSOL ¼
0
neural controlling system comprised TLHC and reflex pathways. TLHC is responsible for stimulating GLU and HFL to rhythmically move thigh around the hip. While neural reflexes with an action on HAM, VAS and SOL muscles coordinate shank movements with thigh. In the following sections, these plans are described separately.
rankle;SOL rankle;SOL
2
dlHAM
3 ðLt ahip;HAM sinðq1 ÞLt ash;HAM sinðq1 q2 ÞÞ 6 7 LHAM 7 ¼6 4 ðahip;HAM ash;HAM sinðq2 Þ þ Lt ash;HAM sinðq1 q2 ÞÞ 5 LHAM
(13)
(14)
242 241 243
4.
244 245
The neuromuscular plan for controlling limbs during gait locomotion is shown in Fig. 2. While attending this figure, the
Neuromuscular system Fig. 2 – The neuromuscular plan for generating gait : TLHC motor commands; : neuronal locomotion. : afferent feedbacks. reflex motor command;
Please cite this article in press as: Abedi M, et al. A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects. Biocybern Biomed Eng (2015), http://dx.doi.org/10.1016/j.bbe.2015.12.002
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II ¼ kdII dnorm þ kEMGII ACT þ CII
Fig. 3 – The TLHC type CPG model used for gait generating : inhibitory signal; : excitatory signal; : [19]; : neuron; : motorneuron. inhibitory neuron;
(22)
300
In that rv = 0.6, kvIa = 6.2, kdIa = 2, kEMGIa ¼ 0:06, CIa = 0.26, kIb = 1, kdII = 1.5, kEMGII ¼ 0:06, and CII = 0. In addition, vnorm, dnorm, Fnorm and ACT are respectively, normalized lengthening speed, normalized length, normalized force and motorneuron activation of corresponding muscle. The normalized parameters are obtained from: 8 < LLth L Lth dnorm ¼ (23) : Lth 0 L < Lth
301 302 303 304 305 306 307
in that, Lth = 325 mm and vnorm ¼ LÇ=Lth and: 8 < FFth F Fth Fnorm ¼ : Fth 0 F < Fth
310 309
and describes interneurons with a 1st order differential equation:
275
C
276 277 278 279
That in above equations, V and h are neuron voltage and gate conductance, Iion is ionic current calculated according to [19] and h1 and t1 are:
280
h1 ¼
1 1 þ exp Vþ51 4
(17)
283
t1 ¼
600 cosh Vþ51 8
(18)
284 285 286 287
In addition, ISYN is a synaptic current received from supraspinal drive (d), sensory feedback ( fb) and adjacent neurons (N) can be calculated from: X X bik fbk þ cij Nj (19) ISYN ¼ ai d þ
dV ¼ Iion ISYN dt
(16)
282 281
288
k
j
289 290 291 292 293
That ai, bik and cij are constants determined according to [19]. Supraspinal drive is considered as a dc signal and can be set on different values. In addition, sensory feedback containing Ia, Ib and II are calculated from the following equations:
294
v þ kdIa dnorm þ kEMGIa ACT þ CIa Ia ¼ kvIa vrnorm
(20)
Ib ¼ kIb Fnorm
(21)
296 295 297 299 298
311
In that, F is muscle force obtained from Eq. (3) and Fth is threshold force set individually for each muscle. Further, for neuron output activation, N appeared in Eq. (19) is calculated from: 8
V30 < 1= 1 þ exp V Vth (25) N¼ k : 0 V < Vth
312 313 314 315 316
In that, Vth = 50 mV and k is 8 for PF-, RG- and Mn- and is 3 for interneurons. It is noted that the parameter ACT in Eqs. (3), (20) and (22) is the output activation of muscle motorneuron. Accordingly, output activation of Mn-E and Mn-F is equivalent to parameter ACT in Eq. (3) for GLU and HFL, respectively.
318 319 320 321 322 323
4.2. 272 273 274
(24)
308
317
324
Reflex pathways
The neuronal reflexes are considered as the supplementary of TLHC for coordinating the segments. The architecture of reflex pathways is shown in Fig. 2. Regarding this figure VAS, HAM and SOL motorneurons are stimulated by the reflexes. These reflexes are some sensory signals acting directly on the muscle motorneurons. This means that in dynamic equation of motorneuron (Eq. (3)) for the mentioned muscles, synaptic current, ISYN, contains the above sensory signals. These signals are chosen so that the reflexes stabilize the gait locomotion and generate walking patterns similar to the human. Thus, for the HAM reflex pathway the group II afferent feedback is selected to facilitate hip extension during the stance phase. Therefore:
325 326 327 328 329 330 331 332 333 334 335 336 337
ISYN;HAM ¼ IIHAM ¼ kdII dnorm;HAM þ kEMGII ACTHAM þ CII
(26)
338
such that ACTHAM is obtained from putting ISYN,HAM in Eq. (3). Further, the ground contact force is utilized for the SOL and VAS reflex pathways for bearing the body weight at the beginning of stance phase. Hence ISYN for this muscle is calculated from: 8 < ðGRFGRFth Þ GRF GRFth (27) ISYN;x ¼ cx GRFmax : 0 GRF < GRFth
339 340 341 342 343 344
where x denotes VAS or SOL and GRF is the ground contact force, cx is constant so that cSOL = 1.95 and cVAS = 1.0. Moreover, GRFmax = 2000 N is the maximum ground contact force and GRFth is the threshold ground contact force that is 200 N for the VAS and 100 N for the SOL.
346 347 348 349 350 351
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5.
353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380
The locomotion of spinal cord injury is modeled by inserting a local malfunction into the neuromuscular system of the obtained intact model. The motivation for this approach has been for the local injury of central nervous system (CNS) in a spinal trauma. Therefore, the gait generator centers in a spinal cord remain undamaged in the most of SCIs. Further, the effect of spinal lesion is physiologically interpreted as the loss of supraspinal (brain, midbrain, cerebellum, etc.) signals on gait generator circuits. This signal has been imitated in the intact model by the parameter 'd' in Section 4.1. Thus, by dropping this parameter through adding a mutable gain in the neuromuscular system as shown in Fig. 4, a spinal cord lesion can be simulated. This modification by disrupting the bias of TLHC neurons stops the generation of regular gait cycles. This effect is shown in Fig. 5 such that the patient keeps the equilibrium only at the first step and stumbles at the stance phase of the second stride. Further, using this plan the classification of severe and weak iSCIs is obtainable too. Specifically, by more decreasing the supraspinal drive with the mutable gain, more serious damages are imitated. This classification is essential for checking the usefulness of rehabilitation activities. The experiments proved that for the weak iSCIs some common techniques such as 'gait training' are efficient enough. In comparison, for the severe one, extra strategies such as reflex modulation should be added as well [10]. This discrimination in the rehabilitation is investigated by the model in the next section.
381
382 383 384
6.
Spinal cord injury gait model
Results and discussion
The simulations are performed in MATLAB Simulink (ver. R2008a). The results are presented for intact and SCI cases. The parameters for neural pathways and rehabilitations gains are
Fig. 4 – SCI model with inserting a mutable gain as a malfunction before TLHC to simulate intensity of trauma.
Fig. 5 – Gait instability in an incomplete SCI model. Variations of knee and hip angles in three steps.
obtained through a trial and error process. In this section the final values are incorporated.
385 386
6.1.
387
Intact model verification
As mentioned before, due to the limited effect of a spinal lesion, the locomotor basis of SCI and intact models are alike. Therefore, to check the validity of the proposed model the performance of unaffected system can be evaluated. To do this, the output of the intact model is compared to the experimental data. In this comparison different parameters of a normal gait are investigated. One of the common factors in studying the human walking is the kinematic specifications. Fig. 6 shows the variations of knee and hip angles versus the percentage of a stride. The experimental data shown in this figure are obtained from [33]. The likeness of simulation and real data proves the model correctness. These similarities could be seen in both variation trends and amplitude. Specifically, the descents and ascents of the curvatures and positions of peaks and troughs are near in simulation and experiments. This nearness confirms the validity of timing problem in the neuromuscular system of the model. The timing is primarily adjusted by the rhythm generator layer of TLHC with regular alternating of the extensor and flexor motorneurons. In addition, the good operation of reflex pathways is also effective in the timing issue with activating the muscles motorneurons in the proper times. This implies the suitability of sensory feedbacks applied in the reflex pathways architecture (Fig. 2). Moreover, due to the mass proportion of the model to the real data of an adult (Table 1), the amplitudes closeness of mentioned curvatures verifies the kinetic aspects of the simulation. Further, the pattern of muscle stimulations in gait cycles is another factor in study of locomotor functions. Specifically, the VAS, HAM and SOL activations exhibit the operation of reflex pathways. Variations of maximum value of isometric
Please cite this article in press as: Abedi M, et al. A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects. Biocybern Biomed Eng (2015), http://dx.doi.org/10.1016/j.bbe.2015.12.002
388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419
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Fig. 6 – A comparison between simulation and experiments. Hip angle variation (a) and knee angle variation (b) in a stride; right column is simulation results and left column is experimental data [33].
420 421 422 423 424 425 426
contraction (MVIC) of these muscles are indicated in Fig. 7. In this figure, the results have been compared to the experimental data of reference [33]. Fig. 7a shows the activation of HAM muscle in a stride. This muscle has been stimulated by the reflex of group II afferent feedback. The similarity of simulation and experimental data shows the correctness of applied plan in firing this muscle. In addition, the SOL activity is
illustrated in Fig. 7b. A noticeable reason about this figure is that SOL has the maximum MVIC amongst all three muscles. This issue, i.e. evident in both simulations and experimental data, physiologically implies the importance of SOL in the gait cycle. The major role of this muscle is the bearing of the body weight at start of the stance phase and putting it forward. Due to this function, the peak value of SOL muscle stands on the
Fig. 7 – HAM muscle variation (a), SOL muscle variation (b) and VAS muscle variation (c) in a stride; right column is simulation results and left column is experimental data [33]. Please cite this article in press as: Abedi M, et al. A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects. Biocybern Biomed Eng (2015), http://dx.doi.org/10.1016/j.bbe.2015.12.002
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initial stages of the stance phase in the curvatures. Moreover, the activation of VAS in a stride is shown in Fig. 7c. The main operation of this muscle is to stabilize the gait locomotion by limiting the flexion of the knee. Since this function is much critical in the weight-bearing stage of the stance phase, the VAS greatest stimulation should be at the beginning of the stance mode. Thus, the VAS activation would be synchronous with the SOL as indicated in the figures. Due to this synchronicity the reflex plan of SOL and VAS muscle are taken alike in Fig. 2. Moreover, any differences between simulation and experimental data are mainly for some simplifying assumptions of the model. Specifically, the absence of foot segment in the biomechanical system interferes the results of simulations by deviating the ground contact force. In addition, withdrawing different muscles in the musculoskeletal system would make many errors in the simulations. Overall, the acceptable nearness of experimental and simulation data verifies the correctness of our proposed plan for neural controlling system of walking locomotion.
454
6.2.
455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476
As mentioned before, the main objective of this paper has been the study of rehabilitation methods with a theoretical view. Although this issue has been previously addressed by Markin [18] and Spardy et al. [19], no distinction between the classes of SCI treatment has not been drawn in these works as such. Due to this limitation, in this section, it is shown by the simulations that the applied modification in the biomechanical system well resolved this defect. To check this achievement, a rehabilitation program has been developed for the classes of SCI patients based on clinical treatment processes. Then, this program has been examined on the obtained models and the yielded results have been discussed. As noted before, the models of SCI patients are obtained by dropping the drive of the TLHC. To simulate the different classes of SCIs, this parameter is put on specific levels; that is shown in Fig. 8. Regarding this figure, the walking area has been divided into four different regions namely, intact (Region 1), weak incomplete SCI (Region 2), severe incomplete SCI (Region 3) and complete SCI (Region 4). The investigations of this section have been focused on Regions 2 and 3 that are related to the weak and severe iSCIs, respectively. Withdrawing the complete SCI (Region 4) from this investigation has
Studying the rehabilitation on the SCI model
Table 3 – Gains of afferent feedbacks of TLHC for rehabilitation of weak iSCI. Signals
Gain
Ia of HFL II of HFL Ia of GLU Ib of GLU
2 2 2 3
been for the insufficiency of mentioned rehabilitation technique for them [10].
477 478
6.2.1.
479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504
Rehabilitation program for weak SCI
To investigate the above conditions, at the first step a weak iSCI is modeled. To do this, the supraspinal drive is decreased to 1.5. Hubli and Dietz [10] reported that in the iSCIs, the locomotion training has a significant success in regaining the gait ability. This technique is usually performed clinically by a repeated use of treadmill. From a physiological perspective, the regular gait training leads to the amplification of spinal synapses that enhances the interaction of afferents and the spinal circuits. This means that the reinforcement of those feedbacks fed into the spinal locomotor centers facilitates the gait recovery after an iSCI. Regarding Fig. 3, in our proposed model the afferent feedbacks linking to the spinal gait generator (TLHC) contains Ia and Ib of hip extensor and Ia and II of Hip flexor. Therefore, by amplifying these signals the effect of above technique can be investigated by the model. The amplification gains of these signals are shown in Table 3. The result of these amplifications is indicated in Fig. 9 and Fig. 10. In this figures the results of simulations are compared to the experimental data of [34] that have been obtained for the clinical iSCI rehabilitation with the treadmill gait training. Attending to this figure, a regular gait pattern is produced by the above plan. This result confirms the efficacy of afferent amplification in regaining the patient walking ability. Therefore, by this model the cause of recovering the gait abilities in weak incomplete SCIs by the feedback amplification is justified.
6.2.2.
Rehabilitation program for severe iSCI
Hubli and Dietz [10] stated that for the rehabilitation of severe iSCIs, in addition to the locomotion training, the excitability modulation of spinal circuits (EMSC) is necessary as well. They denoted that this need is met in clinical treatments by different artificial methods including continuous vibration of
Fig. 8 – Classification of persons based on the supraspinal drive; the continuous cycles are generated only in the intact region (Region 1), that period is decreased with supraspinal drive increase. Level of decrease in supraspinal drive classifies SCI patients into weak iSCI (Region 2), severe iSCI (Region 3) and complete SCI (Region 4). Please cite this article in press as: Abedi M, et al. A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects. Biocybern Biomed Eng (2015), http://dx.doi.org/10.1016/j.bbe.2015.12.002
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Fig. 9 – Efficacy of afferent feedback amplification and generation of successive cycles; left column: simulation results of knee and hip joints after feedback amplification; right column: experimental data of [34] for the clinical incomplete SCIs during stepping on treadmill.
Fig. 10 – Variations of SOL, VAS and HAM muscles with respect to the MVIC; left column: simulation results after feedback amplification; right column: experimental data of [34] for the clinical incomplete SCIs during stepping on treadmill.
511 512 513 514 515 516 517 518
the quadriceps and hamstring, continuous electrical stimulation of the peroneal or sural nerve, and magnetic stimulation of the spinal cord. To illustrate this necessity in the model, at the first step the deficiency of locomotion training for the gait recovery after severe iSCI is proved. Accordingly, the model of severe iSCI is obtained by extra decreasing of the supraspinal drive (Fig. 8). For the following simulations, this parameter is set on 1.2. Then, to check the
Table 4 – Gains of afferent feedbacks of TLHC for rehabilitation of severe iSCI. Signals
Gain
Ia of HFL II of HFL Ia of GLU Ib of GLU
2 2 2 6
Fig. 11 – Insufficiency of afferent feedback amplification in gait recovery of a severe SCI model; patient stumbles after 4 steps.
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effect of locomotion training, the feedback amplification technique is again examined on the obtained model. The values used in this simulation for these gains are shown in Table 4. Regarding this table, these values are equal (Ia and II) or larger (Ib) than ones used for the weak iSCI (Table 3). Despite these variations, as shown in Fig. 11, the expected outcomes have not been achieved at all and the patient falls down finally after three steps. This means that the afferent amplification is not sufficient for the gait recovery after severe iSCI.
Table 5 – Gains of afferent feedbacks and neuronal reflexes. Signals Ia of HFL II of HFL Ia of GLU Ib of GLU Reflex of HAM Reflex of VAS Reflex of SOL
Gain 2 2 2 3 2 8 2
Fig. 12 – Efficacy of the combination of afferent feedback amplification and neuronal reflexes in rehabilitation of severe SCI model; regular cycles are generated in hip, knee, and hip motorneuron and muscle activations (black line: GLU; red line: HFL).
Fig. 13 – SOL, VAS and HAM muscle force with respect to the MVIC after combination of afferent feedback amplification and neuronal reflexes in rehabilitation of severe SCI model. Please cite this article in press as: Abedi M, et al. A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects. Biocybern Biomed Eng (2015), http://dx.doi.org/10.1016/j.bbe.2015.12.002
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Table 6 – Result of simulation for the efficacy of rehabilitation technique on different classes of SCI patients. U: successful; T: unsuccessful. Patient
Supraspinal drive (d)
Rehabilitation technique
Result
Weak iSCI
1.5
Locomotion training
U
Severe iSCI
1.2
Locomotion training Locomotion training/ EMSC
U
Complete SCI
0
Locomotion training/ EMSC
528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558
Having illustrated this deficiency, at the next step the efficacy of integrating EMSC into the locomotion training is investigated. The EMSC is imitated in the model by magnifying the reflex pathways. This idea has been obviously for the presence of reflex synapses in the spinal neuronal circuits. Therefore, similarly with the locomotion training the specific gains have been considered for the reflexes to include the EMSC effect. These gains together with the gains used for the TLHC afferents are listed in Table 5. By including these gains into the model, the rehabilitation of severe iSCI with the combination of locomotion training and EMSC is simulated. The result of this simulation is shown in Fig. 12 and Fig. 13. Fig. 12 indicates kinematic of motion in successive cycles together with hip muscles actuations and Fig. 13 illustrates activations of VAS, HAM and SOL muscles. Attending these figures, generation of these successive gait cycles implies the appropriateness of above technique for the gait recovery after severe iSCI. This outcome along with the result of the previous section indicates the conformity of the model performance to the behavior of actual SCI patients in reaction to the rehabilitation techniques. These results are summarized in Table 6 that is thoroughly in agreement with the statements of Hubli and Dietz [10]. For the complete SCI, the model is obtained by putting the supraspinal drive on zero. The rehabilitative simulations have been performed based on different values of amplifying gains. However, the acceptable results have not been obtained that implies the inefficiency of above techniques on this class of patients. For the gait recovery of complete SCI patients the adaptive gains should be included that could be examined in future works.
559
7.
560 561 562 563 564 565 566 567 568 569 570 571
In this paper, the efficacy of rehabilitation techniques for regaining the gait ability after SCI using a theoretical approach was discussed. To do this, a neuromechanical model was proposed for simulating gait locomotion of SCI patients and examining rehabilitation techniques. From this investigation following achievements are obtained:
Conclusion
- For the first time, three classes of SCI patients namely complete SCI, severe iSCI and weak iSCI are simulated with a full biological neuromechanical model. - Two well-known rehabilitation techniques namely locomotion training and EMSC are imitated. These methods are
11
examined on different classes of SCIs for the first time and their effects are theoretically explored. - Results of above simulations stated that: (1) locomotion training is successful for weak iSCI; (2) combination of locomotion training and EMSC is effective for severe iSCI; and (3) none of these strategies was advantageous for the complete SCI. - The criterion for confirming above outcomes was clinical evidences of SCI's treatment. Comparisons proved the compliancy of above statements with clinical evidences. According to this compliancy, this model represents more specifications of SCI patients than the previous works. This means, this model is a new achievement in neurorehabilitation to be incorporated for studying SCI's reactions to rehabilitation techniques. In addition, to assess the validity of the proposed model the kinematic and kinetic results of the simulation were compared to the experimental data. This comparison was made on both healthy and treated SCI models. The nearness of simulation and experiments proved the correctness of suggested system. This conformity together with the above conclusion implies that this model would be functional in describing the rehabilitation effects on the SCI patients, which is useful in optimizing the treatment process.
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references
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[12]
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Please cite this article in press as: Abedi M, et al. A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects. Biocybern Biomed Eng (2015), http://dx.doi.org/10.1016/j.bbe.2015.12.002