Int. J., Vol. x, No. x, 200x
1
Biometry of electromechanical and artificial neural network models of
arm gait in Huntington’s disease patient
O.O.E. Ajibola, V.O.S. Olunloyo and O. Ibidapo-Obe
Department of Systems Engineering,
University of Lagos
Akoka, Yaba, Lagos, 234(01) Nigeria.
ABSTRACT
In 1837, George Huntington described Huntington’s disease (HD) as an heirloom which had unleashed untold
suffering on people in the dim past. Huntington’s disease is a neurodegenerative disease which has been traced to
mutant alleles in the short arm of chromosome 4. Since the etiology of the disease is not clearly understood, the
question of cure is not addressable at the moment but management of HD presentations is addressable. To this end,
this paper is directed towards management of chorea, a major presentation of HD. Earlier attempts made by our study
group have given birth to two distinct models designed to facilitate an electroconvulsive therapy for the ailment. In
this work however, we have done a comparative analysis of both models in order to promote a better understanding
of HD, and concluded that even though the electromechanical model may not completely capture the gait disorder,
both models have the capability of forming a strong basis for the design of a management model for the
phenomenon.
Keywords: chorea, Huntington’s disease, electromechanical model, artificial neural network model, arm gait,
graphical analysis
1.
INTRODUCTION
A major presentation of Huntington’s disease (HD) is the
choreiform movements called chorea that forms a major
symptom of the disease. Although there are other symptoms
of HD, existing literature pointed in the direction of chorea
whenever a common denominator symptom is being
considered. Unlike other presentations of the disease which
may be detected only on close observation, a glance at HD
patient reveals chorea, a devastating presentation that
constitute a debacle to happiness in the life of the patient.
To this end, we have directed our effort in this paper
towards the promotion of a better understanding of these
unwanted movements that have constituted great barrier to
day to day activities of HD sufferer.
In the past, several works have been done in the area of
modeling of the dynamics of human linkages. For instance,
in the works of Amirabdollahian, F. et al (2002), Flash, T. et
al (2001), Flash, T. and Hogan, N. (1985), Rai, J.K. et al
(2009), and Zhang, Y. (2009), motion related analyses were
cleverly done with different sets of authors choosing a
unique path of the body of the study of biomechanics with
special emphasis on human linkages. Although these
authors considered motions without recur to their causes,
they have made no small contributions to the study of
motion-related diseases especially the neurodegenerative
diseases such as the Parkinson’s disease and the
Huntington’s disease.
Banaie, M. et al (2008), described the gait in Huntington’s
disease by a schematic model which did a chronological
analysis of post-synaptic potentiation that culminates in
choreiform movements, the form of gait in Huntington’s
disease. In Yashar, S. et al (2007), both the inhibitory and
excitatory potentiation were captured in Hill functions using
varying level of GABAergic precipitations in their analyses.
In this paper, we have only considered the two models
namely: electromechanical model by Ibidapo-Obe, O. et al
(2010) and artificial neural network simulation model by
Ajibola, O.O.E. et al (2010) and the comparison of the two
models were done using statistical tool.
2.
ELECTROMECHANICAL MODEL
ANN SIMULATION MODEL
VERSUS
In Ibidapo-Obe, O. et al (2010), the electromechanical
model for the arm gait in HD was proposed. The model was
based on the interactions between both the inhibitory and
the excitatory postsynaptic potentials in the postsynaptic
membrane of HD sufferer. According to the paper, the
process which leads to the precipitation of jerk in HD began
with the release of acetylcholine (Ach) into the synaptic
cleft as a result of a nerve action potential that invades the
presynaptic terminal. The Ach diffuses across the synaptic
cleft and combines with receptors on the postjunctional
membrane. The resultant increase in Na + and K+
permeabilities depolarizes the postsynaptic membrane
triggering an action potential in the muscle cell which
produces an impulse in the form of muscular contraction in
the muscle cell. Invariably, the jerk produced depends on
the electromotive force (emf) produced by the EPSP. The
rate of change in emf is a function of the magnitude of jerk
produced among other factors, Ibidapo-Obe, O. et al (2010).
And the governing equation for the gait (i.e. jerk) is defined
by:
2 
2


 d3y   
 1  d 3 x 
RT  C o 


 exp   
E   ln

dt
2  3 
 dt 3   
nF  C i 
 C  dt 

  

 

(1)
yt    t xt 
(2)
Subject to:
heat sources and pulses in the theory of heat conduction, to
mention but a few.
At this juncture, we introduce the point action. Let us
imagine that a sudden excitation is administered to a system.
Suppose the excitation is denoted by d x which has a
a
nonzero
value
over
the
infinitesimal
interval
I *  a   , a    , but is zero otherwise. The total impulse
impact to the system is thus defined by:
Where Ci and Co are the concentration of ions both inside
and outside the neuron; T is the absolute temperature; n is
the charge on the ion; the Faraday constant, F is the
magnitude of the charge per mole of electrons; R is the
universal gas constant.
The graph of the electromechanical equation (1) is a
parabolic smooth curve which is a derivation of the
experimental evidential model of jerk as presented by Flash
and Hogan in their paper entitled “The coordinate of arm
movements: an experimentally confirmed mathematical
model”, Flash and Hogan, (2005), and corroborated by
Chuanasa, J. et al, (2010). Figure 1 is the graphical analyses
of equation (1) as contained in O. Ibidapo-Obe et al for
three distinct patients with slightly different thresholds.
I  aa   x  a dx  1  x  x  a,  ,   0,   1
(3)
The value of I is a measure of the strength of the sudden
excitation. Defining the integral of any continuous and
bounded function f in terms of the unit impulse function and
applying the mean value theorem of the integral calculus,
then;

   x    f xdx  f  
(4)
defines the excitation graphed by f for every point
  a   , a    , Ajibola, O.O.E. (2008).
Figure 2: The graph of Dirac delta function I    t  .
Figure 1: The graphical analysis of arm gait in HD
patient
Curled from: http://en.wikipedia.org/wiki/File:
Dirac_function_approximation.gif
In physics and in engineering, mathematical consideration
of such a staccato motion as jerk inevitably deal with the
notion of "point actions", that is, actions which are highly
localized in space and/or time. These include point forces
and couples in solid mechanics, impulsive forces in rigid
body dynamics, point masses in gravitational field theory,
point charges and multi-poles in electrostatics, and point
However, jerk is the total impulse impart produced by the
cumulative excitatory post-synaptic potentiation, and
potentiated by the failure of the inhibitory post-synaptic
potentiation track in the body system thus exacerbating a
point action that is described by the Dirac delta function and
by extension, by equation (4). The implication of equation
(4) is that the function f is an enhancement of the Dirac delta
function
in
equation
(3)
over
the
domain
D  t 0  t , t 0  t of its definition. It suffices to claim


therefore that the jerk takes the shape of the points traced by
Artificial Neural Networks (ANN) is an information
processing paradigm that is inspired by the way biological
nervous systems, such as the brain, process information. An
ANN is composed of a large number of highly
interconnected parallel processing elements called neurons.
The neurons work in unison to solve specific class of
problems through repetitive learning process, modifying the
inference rules following arrival of new information thereby
adjusting to the synaptic connections that exist between the
neurons much like the biological systems. Hypothetically, a
neural network is made up of very simple computational
units (or neurodes). An artificial neuron is an eclectic
simulation of biological neuron, and it consists of its own
dendrites, synapses, cell body and axon terminals. It
receives stimulation from nearby cells, or from its
environment, and generates a modified nerve signal,
Ajibola, O.O.E. et al (2010). The architectural system
underlying human cognitive performance is functionally
modular, Long, D.L. et al (1998). An ANN system is
composed of a number of dedicated processing components
each of which contains knowledge that is specific to the
operations it performs and this knowledge is available only
to the component responsible for these operations. In
addition, the partial results of operations that are specific to
one component are unavailable to other components.
An ANN has remarkable ability to derive meaning from
complicated or imprecise data used to extract patterns, and
detect trends that are too complicated to be noticed by either
human or known computer techniques. In the words of
Long, D.L. et al (1998), a trained ANN can be thought of as
an “expert” that can provide projections when given new
situations of interest using the outcomes from primary
information to provide adequate answer to “if what”
questions that may arise from the new situations in the
category of information it has been given to analyse. Other
advantages of ANN include the ability to learn how to do
tasks based on the data given for training or initial
experience. An ANN can create its own representation of
the information it receives during learning time, organise
same and carry out computations in parallel, using special
hardware devices designed and manufactured to take
advantage of this capability. Even though partial destruction
of a network may lead to the corresponding degradation of
performance, some network capabilities may be retained
even with major network damage.
As a result of the aforementioned advantages of ANN, the
arm gait in Huntington’s disease patient was captured in an
Artificial Neural Network (ANN) simulation model,
Ajibola, O.O.E. et al (2010). In the paper titled: Artificial
neural network simulation model of arm gait in
Huntington’s disease patient, the jerk was simulated based
on the primary data used for the electromagnetic model for
the same presentation so as to establish leverage between
the two models. The learning rate of 0.0004 was used to
train the ANN with an error tolerance of 0.0002. The
number of cycles used for its training is 500 while the ANN
architecture of 17 18 1 was used. The artificial neural
network analysis was done in computer C++ programming
language environment. To ascertain high efficiency, the
C++ program from which the results for the ANN training
procedure were obtained was based both on the source and
derived data from where epoch values of Table 1 were
obtained. However, Figure 3 represents the graph of the
deprocessed data for the ANN simulation model, Ajibola,
O.O.E, (2010).
Figure 4: The graph of ANN Analysis of Arm gait of HD
Patient
GRAPH OF CRISP MODEL VS ANN MODEL
4
3.5
EXCITATORY POST-SYNAPTIC
POTENTIAL BUILD-UP
the Dirac delta function  t  as described by Figure 2 as
t  0 . But a jerk requires a build-up of excitatory postsynaptic potentiation (EPSP) to a threshold level after which
excessive EPSP produced results in the staccato nature of
the gait (i.e. jerk) much like orgasm is attained during
sexual intercourse, after which the process terminates
abruptly. To that extent, the Dirac delta function of Figure
(2) and by extension Figure (1), and consequently equation
(1) failed to capture the jerk in the arm of HD patient. The
Dirac function may only approximate the jerk as a  0 . It
is the recognition of this fact that exacerbated our exploit of
the Artificial Neural Network paradigm.
3
2.5
2
CRISP
ANN
1.5
1
0.5
0
1
4
7
10
13
16
19
22
25
28
31
34
-0.5
TIME IN MSEC
3.
STOCHASTIC ANALYSIS OF BOTH MODELS
Of important in this work is the comparative analysis of the
mathematical models we have developed for the arm gait in
HD patient in our earlier papers namely: the
electromechanical model from “On equation of arm gait of
Huntington’s disease patient”, Ibidapo-Obe, O. et al (2010)
and ANN model from “artificial neural network simulation
of arm gait of Huntington’s disease patient”, Ajibola,
O.O.E. et al (2010). A veritable tool for measuring the
degree of agreement between two set of data arising from
scientific experiments reside entirely in a body of
knowledge called statistics. In analyzing our models, we
have adopted statistical tools to establish the relationship
between the two models in order that we may make an
enduring assertion as regards their relationship with the
choreiform movements that characterizes HD.
In this paper, we have applied regression analysis, using a
measure of correlation of the graph of the two models in our
attempt to summarize the relationship between the two
mathematical models. And where applicable, Microsoft
excel statistical tool was applied for numerical computations
to facilitate our argument. The summary of data which serve
as the basis for our analysis as contained in the paper by
Ajibola, O.O.E et al (2010) and augmented with the data for
our regression line (in red) is presented in Table 1.
Figure 5: The Scatter diagram/Regression line for the
data from both models
Table 1: Data from Electromechanical and ANN models
with the Regression Line
EPOCH
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
CRISP
0
0.154582
0.308486
0.461202
0.612217
0.761006
0.907089
1.049966
1.189172
1.324243
1.45474
1.580243
1.700331
1.814628
1.922773
2.024421
2.119241
2.206961
2.287297
2.360008
2.424899
2.481789
2.530528
2.571012
2.603179
2.626985
2.64243
2.649559
2.648462
2.639275
2.622163
2.597351
2.565126
2.525803
ANN
0
-0.06304
-0.05758
0.021569
0.136378
0.275615
0.435387
0.584056
0.735779
0.891097
1.047544
1.204307
1.357654
1.508385
1.654963
1.795944
1.930563
2.058157
2.177237
2.287022
2.386293
2.473638
2.548048
2.607585
2.650445
2.67428
2.67565
2.649545
2.590686
2.709225
3.239446
3.34505
3.363036
3.223094
Y
0
0.154581
0.308484
0.461200
0.612214
0.761002
0.907084
1.049960
1.189166
1.324236
1.454732
1.580235
1.700322
1.814618
1.922763
2.024410
2.119230
2.206949
2.287285
2.359995
2.424886
2.481776
2.530515
2.570998
2.603165
2.626971
2.642416
2.649545
2.654629
2.697206
2.776512
2.891504
3.040851
3.223094
And the graphical analysis is as presented in Figure 5:
In Figure 5, both the scatter diagram and the regression line
have been presented as line diagrams to facilitate easy
comparison. The freehand method was used for the
regression line since it is adequate for the purpose of this
analysis. The regression line is completely described by its
slope and the intercept on the y-axis. For ease of analysis
the line has been partitioned into two segments labelled AB
and BC. The segment AB with positive slope is an
indication that there is an agreement between the two
models while the segment BC has negative slope
representing a dispersal of the two graphs from each other.
The determination of the level of agreement or otherwise
between two sets of data is a statistical measure of their
correlation coefficient defined by:
Corr  X , Y  
where
Cov X , Y  
Cov X , Y 
s X sY

(5)

 iN 1 X i  X Yi  Y
N 1

(6)
Using the Microsoft Excel Statistical tool, the correlation
coefficient of the two graphs along segment AB of Figure 5
is CorrAB  X , Y   0.989329 this is a confirmation of a
strong agreement between the two models. Relating this to
the post-synaptic potentiation that produces the arm gait,
this part of the graphs, Figure 6, represents the excitatory
precipitation of jerk at the level of threshold and our
statistical analysis shows that the two models both represent
this phenomenon adequately within the interval under
consideration (i.e. to the point of threshold). This is evident
from Figure 6 where the behavior of the two models is
graphed from the point of initiation of the excitatory process
to the threshold of the jerk.
Figure 6: The excitatory precipitation at the level
threshold of jerk
of
Any point above the threshold line, especially after point B,
will contribute to the gait in one way or the other whereas
every point below the threshold line will not. It is therefore
clear from the figure that one of the models (i.e. the ANN
model) completely captured the phenomenon as it reflects
the jerk.
4.
However,
a
correlation
coefficient
CorrBC  X , Y   0.75494 indicates that there is a strong
disagreement between the two graphs from point B. This
may mean one of the following:


None of the two graphs captured the arm gait
phenomenon
One of the two graphs captured the arm gait
phenomenon
The instrument used in this analysis can be found in Figure
7. The blue curve (series 1) is the graph of the
electromechanical model, the red (series 2) of ANN
simulation model while the green straight line (series 3)
stands for the threshold.
Figure 7: Relating Both Models with Arm Gait
Phenomenon
DISCUSSION
A survey of opinions from patients of Huntington’s disease
is revealing. The presence of depression in the list of the
symptoms of HD is more of a product of the discovery by
patients that they belong to HD family. And one of the
causes of the patients’ withdrawal from the public is the
presence of the choreiform movements which distinguishes
the patients among their friends and colleagues. In this work
we have forged ahead to do a statistical analysis of both
methods we proposed earlier namely, the electromechanical
model and the artificial neural network simulation model all
in our attempt to promote a better understanding of chorea,
a major presentation of this devastating ailment. Clinical
consideration of biomechanics of HD patients opined that
the GABAergic pathway in the affected patients might have
been malfunctioning causing inadequacy in the supply of
inhibitory neurotransmitters that is required to support the
inhibitory post-synaptic potentiation (IPSP) needed to match
the excitatory post synaptic potentiation (EPSP) which
pathway is assume to perform at optimum level. It is
believed that it is not impossible that the GABAergic
pathways in HD patients might have been constricted much
like a near rupture rusted narrow water iron pipe at
advanced stage of the disease causing the dopaminergic
pathways to produce excessive EPSP thus precipitating jerk
at will.
However, the graphical analysis in Figure 7 revealed that
although the electromechanical model did not capture the
jerk phenomenon completely, the strong agreement between
the two graphs shows that both graphs provide adequate
representation of the process of chemical build-up that
precipitates the staccato movement (the jerk) to the point of
threshold and therefore both models are adequate to propose
a model for the management of the phenomenon since what
we seek to eliminate is the jerk. It is therefore enough to
introduce a damper that neutralizes the excitatory
neurotransmitter produce in excess of IPSP at the threshold
of the jerk. It is believed that this work has contributed to a
better understanding of chorea and as such can serve as a
basis which is strong enough to attempt to propose a
management model for the phenomenon with any of the two
models as pedestal.
5.
CONCLUSION AND FUTURE WORK
The paper is a major leap from our preliminary exploration
in the modeling of chorea that constitutes major impediment
to day-to-day activities of HD patient. In this paper we have
attempted to provide a strong pedestal for proposing a
dependable model for the management of the physiological
presentation of HD that has debased the personality of the
patient by carrying out a comparative analysis of the
electromechanical model and the artificial neural network
model using statistical tool. The essence of this paper is to
determine the strength of each of the models when used as a
basis for proposing a model for the electroconvulsive
therapy for the arm gait phenomenon in HD. In the near
future we hope to design a model for the management of the
physiological presentation called chorea based on the
electromechanical model and subsequently, the artificial
neural network model.
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