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Analysis of Heat Flow Produced By Specific Heating Modality on
Selected
R
egion in a Body
Jyotika Pruthi, Supriya Agrawal, Priyanka Sahu
,
Saurabh Mukherjee
Department of Computer Science,AIM&ACT Building
Banasthali
University ,Rajasthan,India
Abstract
Human body pain is an unbearable issue. Various kinds of treatments are available with
several advantages and disadvantages.
Physiotherap
y is being treated as a type of treatment in
which when a therapeutic heating
modality is used then the external stimuli plays a vital role.
The stimuli help to penetrate deep into the mussels of the region of interest and soften the
tissue extensibility. The distribution of this heat flow if analyzed can give a potential
breakthro
ugh in the field of
Physiotherap
y
. The present paper will develop a model for this
case and simulate the model to get a perception of external stimuli impact into the heat
penetrated soft tissues.
Keywords:
Physiotherap
y
,
Therapeutic
,
Diathermy,
Modalities
, Tissue, Gradient
1. Introduction
Treatment of pain related areas are common nowadays. Various biomedical instruments are
used to suit once taken case by case basis. The heat distribution is an important factor for
therapeutic heating modality. Be it the case of monopolar or bipolar, the d
iathermy treatment
is used for healing pain caused due to various factors. The region of interest in our case is the
portion where the issue of heat is critical and that is upper and lower back region. The present
paper will focus on modeling upper and low
er back heat distribution applied in the case of
therapeutic heating. The paper is divided into five sections. Section 1 gives the general
background of the paper with objective and motivation. Section 2 emphasis on the
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mathematical aspects of the heat dis
tribution. Section 3 is used to develop the mathematical
model taking non

linearity as a case. Section 3 is also used for simulation and section 4 will
discuss regarding the results and future research scope. The paper will be closed by opening a
thought t
o the research community regarding the potential to work forward in the direction of
heat distribution used in various faces of diathermy.
2.
Mathematical aspects of heat distribution:
The heat distribution used in the present paper follows the following
form.
I (z, y)
R
2
R
The heat equation is having Div (h delta of the input image), which can be written as
The above equation has been taken by the definition given by Gabor in 70’s. Using the
concepts of heat equati
ons, the present model has been devised for the heat distribution of
upper and lower back of a patient.
If we are considering the lower and upper back region as shown below, then the
equation will
be of the form,
The heat flow
that we are analysis is through gradient decent of the energy. The lower back
region as given by (
l
) has the tendency to uniform distribution. The regularity system has a
specific
heating point.
Let the flow represents a geometric polynomial shape of closed intervals. Since, in our case
the region boundaries are closed, hence the distribution has its own bounds. The specific
progressive model is as follows:
The Gaussian function is also used as the heat flows through the upper body region gradient
shown as below
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Both the lower and upper region (
u
l
) has the gradient form the rate of heat flow is


Figure 1: The diathermy treatment given to a patient suffering from upper back pain.
Figure 2: The statistical data of the upper back region with 49 degree orientation of left pad
applied to the patient.
The above figure used the existing model and given the result of the 49 degree orientation of
the pad
when heat is being applied to the upper portion of the patient. The figure demonstrates
0
20
40
60
80
100

1

0.5
0
0.5
1
Residuals
Quadratic: norm of
residuals = 2.8484e

014
Cubic: norm of residuals = 3.1389e

014
5th degree: norm of residuals = 3.0164e

014
8th degree: norm of residuals = 1
(49) degrees
y = 0.013*x
2
+ 0.99
y =
0.00012*x
3
+ 1
y = 9.8e

009*x
5
+ 1
y = 7.2e

015*x
8
data 1
quadratic
cubic
5th degree
8th degree
x min
x max
x std
y min
y max
y std
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the heat flow of the left upper portion when the cubic and 5
th
degree norms of residuals are
taken into account.
3.
Non Linearity as a special case with simulation:
T
he heat equation
∂
tp
−
p
=
0,
has been used commonly in the area of image processing
and computer vision. When using the geometric version of PDE in our case, we are assuming
the surface of our back spine as a set of surface points. We are also assuming
for simplicity
that the body under study is smooth.
Westermann et al.,
has proposed a considerable task in
PDE in the year 2000.Let the surface point be p with respect to
time t.Then
dp/dt = V (p, t)
which belongs to
R
3
. Mayer, Simonett, Escher (Escher et
al., 1998; Escher and Simonett,
1998;Simonett, 2001) and Huiskens’ (1987)
contributed a substantial research work in the
domain of Geometric Partial Differential Equations and we will use them in our study.
The system takes the temperature say between
15

55
o
C .The Geometric partial differential
equations are formed in two basic orders viz., the second order and third order of GPDE.
Assuming, the surface point p (t) is distributed normally on the surface S belongs to R
3
. Then,
dp/dt = M(p)h(b1,b2,…..bn
,k)
where M(p) is the velocity vector of the heat transfer through the surface point ,k is an
arbitrary constant, h(b1,b2,….bn) are n surface points of ROI.
.
Figure 3 The translated view of the image with diathermy treatment taking 5
th
. and
8
th
.
degree of polynomial.
X: 72.52
Y: 108.3
data 1
5th degree
8th degree
0
0.2
0.4
0.6
0.8
1
0
0.5
1
0
0.5
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
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Well, we can take the surface area and volume as two distinct parameter in our study.
Using above equation , we can computer mean heat flow as follows
dp/dt = M(p)
. H
(b1, b2…bn,
k)
1<n<m+1;
dS/dt=
∫
dVl/dt=
∫
We can study the initial effects of the above and take the integrated version of GPDE
of second and third order respectively.
The geometric differential operators like Laplace

Baltrami have been used in our
study.
Δ
s
f = div (
s
f)
Undergoing study, we found that the reduced area under optimality enhances our
result
for showing the effects of flow of heat transfer using GPDE
.
The result of the
simulation is shown in the following section. We have used the Green’s formula in our
equations as follows
dS/dt=
∫
=
∫
2
dα
dA/dt=
∫
Well, we can extend the present
representation to other variants of LB and can extend
the work to more generic mathematical modeling. The present model is a humble
attempt to study the effect of heat transfer through back pain.
While dealing with various mathematical foundations of GPDE
and subsequent usages
of Green’s function, we have developed the mathematical model for the heat flow of
the selected region as shown in the figure (1), (2) and (3). While computing the heat
flow, as stated above equations, we have used Green’s generic fu
nction as
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Heat distribution
G(s, p) =
{
}
, if s<=p;
{
}
,
if
p<=s;
The ‘uniqueness’ and ‘existence’ are two fundamentals that has been understood in a
linear operator L, which we have used in our case. The lower back portion and the
waist portion heat transfer has been modeled and simulated in particular. Since we
have us
ed PDE, the operator L for which D (L)
C ([0, 1], R) has proved an
important role in our study of simulation and modeling. The extended result is shown
below.
Bipolar Diathermy with varying magnitude
Figure 4 The
simulated view of the image with diathermy treatment taking 5
th
. and
8
th
. degree of polynomial of both left and right side.
In Figure 4, the simulation results how the distribution of the heat flows from the soft
tissue region. The following equation uses the bipolar diathermy aspect in upper
and lower back pain.
0
20
40
60
80
100
120
140
160
180
0
50
100
150
200
250
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dUS/dt=
∫
=
∫
2
dα
dUA/dt=
∫
The
heat distribution of the above equation is proportionate with t
he heating
modalities applied in upper and lower back as shown in Figure 4.
The results as shown
in figure 4 is promising shows enough potential to be applied on other living beings.
4
. Conclusions
The heat flow modeling of the upper and lower back has been taken as a case by case
basis. The simulation shows promising results. Further the research will be carried out to
other body parts as well.
Acknowledgements
We would like to acknowledge
Dr.Khushboo Singh, MPT (Orthopedics),M.D.C.P.T
Physiotherapy consultant PHYSIOFOCUS organization and Bhagwan Mahavir
Hospital,Rohini, New Delhi , Dr.Shilpi Verma, Practising phsiotheraphy ,AIIMS, New
Delhi, Dr.Judy Mayer BS CTT Auburn Thermography Institut
e, California ,USA,
Mr.Ayush Gupta,Executive

Website Operations Dept.,MakeMyTrip and many others
who helped in all the ways needed to carry out this research initiative. We hope to refine
and carry this work further.
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Mitchell SM, Trowbridge CA, Fincher AL, Cramer JT: Effect of diathermy on muscle
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1004,2008.
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Peres SE, Draper DO, Knight KL, Ricard MD: Pulsed shortwave
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