Neuro Rehabilitation Modeling – A tutorial

[The material in this tutorial is based on standard curriculum of K. N. Toosi University of Technology, Faculty of Electrical Engineering. For more information about Neuro-Rehabilitation Modeling, please write to Maryam Zangeneh: mary.zangeneh71@gmail.com]

euro-rehabilitation has received increasing attention from researchers. Unfortunately, the

topic of Neuro-Rehabilitation seems complicated and boring in first glance for the students; thus, majority of them escape from work in this context. Quite to the contrary, Neuro-Rehabilitation is neither hard to understand, nor of only theoretical interest.

This tutorial has been developed to help you understand what Neuro-Rehabilitation is, why it is important, and how to present computational modeling for it. While the mathematics are included, practical examples and analogies are used wherever possible.

What is Neuro Rehabilitation?

Rehabilitation is a process of education of the disabled person with the ultimate aim of assisting that individual to cope with family, friends, work, and leisure as independently as possible. It is a process which centrally involves the disabled person in making plans and setting goals that are important and relevant to their own particular circumstances. In other word it is a process that is not done to the disabled person but a process that is done by the

disabled person themselves, but with the guidance, support, and help of a wide range of professionals. Rehabilitation has to go beyond the rather narrow confines of physical disease and needs to deal with the psychological consequences of disability as well as the social milieu in which the disabled person has to function. Thus, a key factor that differentiates rehabilitation from much of neurology is that it is not a process that can be carried out by neurologists alone, but necessarily requires an active partnership with a whole range of health and social service professionals. The key characteristics of the rehabilitation process are summarised in box 1.

In short, neurological rehabilitation (rehab) is a doctor-supervised program designed for people with diseases, injury, or disorders of the nervous system. Neurological rehab can often improve function, reduce symptoms, and improve the well-being of the patient.

Box 1: The rehabilitation Process

An educational process Central involvement of the disabled person in program planning Key involvement of family, friends, and colleagues A process that requires clear goals to be set and measured An interdisciplinary process A process based on the concepts of disability (activity) and handicap (participation)

N

Rehabilitation techniques

Therapists use a wide variety of rehabilitation techniques in order to help the patient recover. Although many such techniques have been developed through therapists' intuition and experience, here a discussion is presented on how these techniques can be fit within the scope of this framework.

Rehabilitation techniques will be classified into a number of categories. First, those that attempt to improve the dynamics of the system. Second, those that attempt to change the personal cost function by introducing new tasks. Third, those which attempt to change the cost function by changing the dynamics of the system by introducing constraints. Box 2 summarize this paragraph. Note that first category is more common [1].

Box2: Category Purpose

Improving Dynamics

Improve the dynamics of the human motor system, affecting the optimisation performed by the patient

Changing Personal Cost via

Dynamics

Change the personal cost function through

usedependent learning through

restricting how certain tasks can be performed.

Changing Personal

Cost via Novel Tasks

Change the personal cost function through

usedependent learning through

the definition of specific exercises

What conditions can benefit from neurological rehabilitation?

The main areas that can benefit from neuro rehabilitation and cognitive stimulation which shown in figure 1 are list below:

Acquired Brain Injury

Neurodegenerative Diseases

Neurodevelopmental Disorders

Intellectual Disability

Mental Illnes

Normal Aging [2].

Figure 1: Some conditions benefit from Neuro Rehabilitation

An acquired brain injury is an injury to brain cells that occurs after birth. It can be due to various causes and depending on where the damage is located, and one or more processes will be affected. This category contains Infections, Cerebral anoxia, Brain tumors, Cerebrovascular accident (Stroke) and Traumatic brain injury (TBI). This tutorial focus on TBI patients.

What is Traumatic Brain Injury?

Clinical profile characterized by direct injury to the cranial structures, brain or meninges due to external traumatic force (contusion, penetrating injury or acceleration-deceleration forces) called TBI. Brain injuries can be classified into mild, moderate, and severe categories according to severity. Depend on the type of TBI and affected brain region, different symptoms including headache, sleeping problems, vomiting, nausea, confusion, fatigue, lack of

motor coordination, dizziness, thinking, difficulty balancing, trouble with memory and the like occur. Figure 2 and 3 represent the TBI causes and the effect of TBI in various regions of brain in patient's daily life, respectively [3].

Figure 2: TBI causes

Figure 3: The effect of TBI in various regions of brain in patient's daily life

Tutorial approach

One of the challenges in TBI patients is lower limb movement problems, so rehabilitation treatments focus on this issue. We investigate how bimanual movement affected TBI recovery by modeling the different preferred direction and modulation depths during unimanual and bimanual movement. Some necessary concepts introduce below.

Unimanual and biomanual movement

Figure 4 represent the physical difference between unimanual and bimanual movement. It is obvious that neural activity in the motor cortex differ during unimanual and bimanual movement too which is summarized in box 3. To simplify we consider the same direction for both right and left arm [4].

Box 3: Unimanual Bimanual

Maximally activating of motor cortex neurons

Not maximally activating of motor cortex neurons

Neural activity fit to cosine function Nerual activity fit to linear summation of two cosine functions

Smaller amplitude af cosine function Larger amplitude of cosine function

Figure 4: Unimanial and Bimanual

movement [4]

Encoding and decoding PDs

Another concept needed for understand our model is encoding and decoding PDs. It is briefly bring into box 4.

Box 4: Encoding and Decoding PDs

E-PDs D-PDs

Determine Determine Neural activity movement direction

Related to Related to motor planning execution

Computational model of neuro-rehabilitation

Step 1: define the relation between

encoding PDs and decoding PDs Initially, in modelling bimanual

rehabilitation, we assume that changes occur only in the PDs. Because PDs are rotated pseudo-randomly in bimanual movement, we modeled this rotation as:

E-PDs(bimanual) = E-PDs(unimanual) +

Rotation

Rotation: degree of rotating which is randomly sampled from a Gaussian distribution with a mean of 0 and variance of sigma.

Step 2: formulate E-PDs We can model encoding PDs as cosine

function of neural activity. If the angle of reaching target considered as ϴ (figure 5), the function can define for each neurons.

Ai(ϴ,Ei-PDs)cos(Ei-PDs) i: the number of neurons Ei-PDs: encoding PDs for both

unimanual and bimanual for each neuron Step 3: calculate the population vector According to Box 3, decoding PDs

determine movement direction. It shows that we should calculate population vector using both E-PDs and D-PDs.

PV(ϴ) ~(Ʃi

N Ai(ϴ,Ei-PDs).cos(Di-PDs), ƩiN

Ai(ϴ,Ei-PDs).sin(Di-PDs))T Di-PDs: decoding PDs for both

unimanual and bimanual for each neuron

Step 4: simplify formula with an assumption Given the researches decoding PDs is set

to equal the encoding PDs in the unimanual movement. During the bimanual movement, we assume that decoding PDs are not rotate.

Step 5: determine a cost function for upper limb neuro rehabilitation We model TBI rehabilitation using a cost

function two optimization terms. Supervised and unsupervised learning of Ei-PDs. Indeed, for motor cortex damaged, TBI rehabilitation induce a reorganization that can be model using an optimization framework. In this framework, the rehabilitation modifies Ei-PDs to minimizw the cost function where ϴp is the angle of the population vector and β is the regularization parameter. E=0/5[1-cos(ϴ-ϴp)+βƩi

N(Ai(ϴ, Ei-PDs))2]

The reorganization process decreases the angular error between ϴp and ϴ by

rotating PVs toward the target position. This supervised learning is modeled by the first term of equation. The process also decreases the total neural activation, or metabolic cost. This unsupervised learning is modeled by the second term of equation.

Figure 5: the position of hand and target

Step 6: Reorganization after each trial After each rehabilitation trial, the

reorganization occurs as follows(t means trial):

(Ei-PDs)t+1 = (Ei-PDs)t + sin(ϴ-ϴp)Ai(ϴ,

Ei-PDs)+sin(ϴ- Ei-PDs) The result get better trial by trial and

minimize the cost function and so the mean norm of the PV in the lesioned zone be normal. Figure 6 illistrate this fact [5].

Another model for neuro-rehabilitation!

We developed another computational neurorehabilitation model to gain insight into the interaction between strength and

coordination recovery after stroke. In this model the motor system recovers by optimizing the activity of residual corticospinal cells and reticulospinal cells to achieve a motor task. To do this, the model employs a reinforcement learning algorithm that use stochastic search based on a reward signal produced by task execution.

What is corticospinal and reticulospinal?

Corticospinal is a white matter motor pathway starting at the cerebral cortex that terminates on lower motor neurons and interneurons in the spinal cord, controlling movements of the limbs and trunk. Besides reticulospinal is an extrapyramidal motor that descends from the reticular formation in two tracts to act on the motor neurons supplying the trunk and proximal limb muscles.

Figure 6: mean norm of the PV in the lesioned zone. increasing the number of trials cause

better mean norm of the PV in lesioned zon

What is reinforcement learning algorithm?

This algorithm describe as below:

Step 1: Activate CS cells with pattern Xi=X0+Vi Vi : stochastic noise Step 2: Measure Ri produced by this pattern. Step 3: If Ri>R0, then set X0=Xi and R0=Ri Step 4: Repeat

Neuro rehabilitation in finger movement task:

We consider that middle finger and index finger are involve to do this task. Figure 7 shows force production of the left hand.

Figure 7: Model architecture for simulating force production by the index and middle

fingers of the left hand [6]

Modeling the neuro-rehabilitation:

Step1: simulate the finger force production task using a network of 400 cells with pseudorandom weighting.

F1=Ʃwi,1 gi(xi) F2=Ʃwi,2 gi(xi)

Where g represents a nonlinear

saturation function that ensures individual cells contribution to the force output is limited. On the other side the firing rate xi are multipled by their respective weighting wi.

Step 2: define F as summation of F1 and F2.

F=F1+F2 Step 3: The finger task design need moving one

finger with as much force as possible while inhibiting movement in the other finger. In other words, the model would ideally increase F1 while maximizing the individuation index and minimize F2. So a new parameter L is introduce as follow:

L = (F1-F2)/(F1+F2) Step 4: Define a reward function (R). R should

cause reward for achieving movements with greater force and better individuation. We weightened by α. The amount of α is very important, for example if α=1 or α=0 indicates that the patient only values generating force or the patient only values being able to individuate their finger movement, respectively. The reward signal is formulated below:

R = αF + (1- α)|L|

Results of model

the model predicts the nonlinear relationship between strength and coordination recovery. So there is a trade off between strength rehabilitation and coordination rehabilitation. So training with any (α>0.5) resulted in mostly strength recovery and with any (α<0.5) resulted in mostly individuation recovery which shows in figure 8.

Figure 8: the result of training with different value of α

We conclude that if there are enough focal cells to maximally activate the motor neuronal pools associated with the task, the motor system can learn to activate those cells through reinforcement learning and

achieve maximum strength and individuation. However, if there aren’t enough focal cells, after cell death, the motor system faces a tradeoff which explained before.

Neuro rehabilitation in bilateral wheelchair task

In another application of the model, we arranged the cells in bilateral hemispheres which is a bit different from the previous one. Two force were used: one for the left arm, and one for the right. we de-weighted a portion of the right hemisphere, simulating the death of these cells that control the left arm. We evaluated this model by simulating a bilateral wheelchair driving task where the arms must coordinate, working together to drive the wheelchair forward by generating as much symmetric force as possible. Ideally, the network would increase Fl and Fr while coordinating the arms, which means driving the individuation index towards zero to produce equal forces. Figure 9 illustrates the force production of this task.

Figure 9: Model architecture for simulating force by the two arms to propel a lever

drive wheelchair [6]

Modeling the neuro-rehabilitation:

Step1: simulate the peak force produced by each arm on each push of the levers of the chair.

Fl=Ʃwi,L gi(xi) FR=Ʃwi,R gi(xi) Where g represents a nonlinear

saturation function of the firing rate xi.

Step 2: define F as summation of FL and FR.

F=FL+FR Step 3: The coordination part define follow: L = (FL-FR)/(FL+FR) Step 4: Define a reward function (R). For this

reward function, R=1 still indicates that the

patient only values force (assessed by speed of

the wheelchair) but R=0 indicates that the

patient only values coordination in the sense of individuation=0.

R = αF + (1- α)(1-|L|)

Results of model

In the wheelchair task, strength and coordination recovered together. Recall that, for this task, coordination was defined as both arms working together in symmetry – exactly what the bilaterally connected cells enable. Thus, their recruitment contributes to both strength and coordination, allowing full recovery of both without a competition/tradeoff between them as is the case in the finger tapping individuation task [6].

Refrences

[1] C. Chun, J. Fong, I. Mun," Computational Models of Human Motor Movement and Learning and their Application to Neurorehabilitation", phD thesis, october, 2017. [2] https://www.neuronup.com/en/research-cognitive-stimulation-neuropsychological [3] M. Ghajari, P. J. Hellyer, D. J. Sharp," Computational modelling of traumatic brain injury predicts the location of chronic traumatic encephalopathy pathology", "Brain", vol 140, pp. 333- 343, 2017. [4] T. Hayashi, D. Nozaki," Improving a Bimanual Motor Skills Through Unimanual Training", "frontniers journal in Integrative Neuroscience", pp. 343-349, 2016. [5] K. Takiyama, M. Okada," Recovery in Stroke Rehabilitation through the Rotation of Preferred Directions Induced by Bimanual Movements", Plose One, vol 7, no 5, pp. 1-10, 2012. [6] S. L. Norman, J. L. Prat, and D. J. Reinkensmeyer," How do strength and coordination recovery interact after stroke? A computational model for informing robotic training", International Conference on Rehabilitation Robotics, 2017.