 Open Access
 Total Downloads : 206
 Authors : Oindri Ray, Abhishek Adhya, Sudhin Ray, Bijay Kumar Majumdar
 Paper ID : IJERTV3IS070895
 Volume & Issue : Volume 03, Issue 07 (July 2014)
 Published (First Online): 24072014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Nano Silver Over Extracellular Matrix of Wound & Its Numerical Model
Oindri Ray
Asst.Professor,Department of Electronics & Communication Engineering, Meghnad saha Institute of Technology.
Kolkata,West Bengal,India
Abhishek Adhya
Researcher ,IPGME&R,S.S.K.M Hospital Kolkata ,West Bengal ,India
Sudhin Ray IPGME&R S.S.K.M Hospital Kolkata,West Bengal ,India
Bijay Kr.Majumdar
Professor & Head ,Department of Plastic surgery ,S.S.K.M Hospital
Kolkata ,West Bengal ,India
Abstract Wound healing is a complicated process. Infections are major constraints of mortality and morbidity in burn patient. It is seen the healing rate is much faster if nano silver particle in between 1100nm in diameter are used .The nano sized particle are very effective and reactive because of their high surface area[13].Nano silver particle in order of 20 nm is used as a wound healer to fight against microbes over wound. After application of nano silver the surface of wound is analyzed by numerical modeling using surface morphology according to its relevant chemical and biological parameters.
Keywords NanoSilver,Numerical wound model;Surfacemorphology;Numerical Solution.
I.INTRODUCTION
Wound can be categorized by the differences of its chemical and biological parameters Wound is a deformation of cells which can be designed by extracellular matrix model. This Extracellular model demonstrates the traction forces in between the cluster wise cell to cell regeneration. The Finite element analysis model is used to design and categorized those types of wound .This approach gives a numerical prominent solution over cell regeneration after burn after application of nanosilver.

NANO SILVER & ITS STANDARDIZATION
A simple chemical reduction method is used for production of nano silver .Different concentration of aqueous solution of silver nitrate; glucose and organic base are mixed to set the reactor. In this preparation controlled reaction parameters like PH, temperature, rate of reaction is closely monitored.

EXTRACELLULAR MATRIX BASED WOUND MODEL
To assess the condition of wound and rate of healing post application of nanosilver, a numerical model is introduced relation the all chemical parameters[1,2,7] .These parameters are used as observation factors[12,13]. Firstly the fibroblasts are
generally which are prone to migrate into the wound region and crating a force in between extracellular matrix zone. Secondly Fibroblasts are carried out by myofibroblasts and results into the formation of cellular adhesion .Thirdly the collagen is monitored as it behaves as one of the structural component of extracellular matrix. Collagen component is modeled using finite element model. Finally a wound generation factor is taken under observation to study the improvement of burn wound area.
Fig.1.Proposed Extracellular matrix model of Wound
All these parameters are structured by numerical equation[3,5]. Using MATLAB all those morphological surfaces are modeled to establish the effectiveness of nano particle over burn wound.
Fibroblasts Model (F):
These cells are very mobile cells, and tending to attach with the wound surface area[8]. The flux produced by these fibroblasts cells can be modeled as
JF DF.F
(1)
aF
Zn.(bF CF ) 2
x
.F.(c n) F.
t

ZF
regeneration factor.If we consider that the P is the wound regeneration factor for structural basis
x
p Dn.p Cp Zc +Zn1
t
Where JF is the volumetric flux produced by the fibroblasts tissues. DF stands for the diffusion rate relating fibroblasts tissues. F stands for partial derivative vector operator for
(5)
Dn is the diffusion rate of nanosilver within the structure of wound. p is the fibroblasts differentiation rate.Cp is the
fibroblasts tissue.aF is the initial chemo tactic sensitive
function rate .bF is the Chemo tactic sensitive response. cF is the maximum rate of fibroblasts migration over the fibroblasts density and X is the displacement vector. c is the chemical concentration of wound. n is the chemical concentration of nano silver.ZF is the Time dependent negative divergence constant and F stands for fibroblasts density in undamaged tissue.Zn is the convergence factor of nano silver.
A(r).dS
fibroblasts differentiation factor considering dermis regeneration.. Zc is the time dependent divergence constant produced by fibroblasts integrated with myofibroblasts and collagen..Zn1 is the nano silver active surface area.. x is the displacement vector which shows the tissue growth.


RESULT
The result can be categorized in two different sections[11]. First one is to categorize and establish the characteristics of
ZF= .A(r)
Lim V
(2)
nano particle and the second phase is to determine the
V 0 S
S stands for existing wound surface area having volume
V at a point r and dS points inward from the wound surface and A(r)is converging.
Myofibroblasts Model(M):
These cells are motile cells .The volumetric flux filed surface is generated by myofibroblasts can be designed by the Myofibroblasts model of the contracted wound. If Jm is the produced flux field by myofibroblasts tissue then
X
Surface of wounds parameter those are used as wound healing parameter in above section. Those above equation are simulated through matlab and the pattern of the surface is generated. Prepared nano particle is monitored using UVVis absorption spectroscopy. This absorption spectroscopy reveals silver nano particle characteristics by exhibiting typical surface Plasmon absorption maxima at 418320 nm from the UV spectrum. Mie Light scattering theory and experimental results shows that diameter of silver nano particle in order of 50 nm, Energy dispersive spectroscopy
and Transmission electron microscopy are used to
Jm = Dm . m M .
t

Zm
(3)
standardize the prepared silver nano particle.
Dm is the diffusion rate of myofibroblasts tissue. m Stands for partial derivative vector operator for myofibroblasts logistic growth rate. M stands for density of myofibroblasts for integrated damaged and undamaged tissue. X is the displacement vector. Zm is time dependent convergence constant.
Collagen Model(K):Type I collagen is primary structural component of extracellular matrix. The mesh structure is formed by using finite element structure.
X
Jk = Dk . k K.
t

Zk
(4)
Fig.2. Transmission Electron Microscopic Image Of Prepared Nano silver
Jk is the flux produced by collagen.DK is the diffusion rate of collagen. k is the partial derivative vector operator of collagen for the collagen degradation rate per unit cell. K is collagen production rate. X is the displacement vector and Zk is the time dependent divergence constant. Different types of sample wound are taken. And the above physical and biological parameters are comparatively studied by before and after application of nano silver.
Wound regeneration Factor(p):
Wound is considered as deformation[4,6]. When we observe wound first we integrate secondly differentiate the observation .This approach is similar to the finite element model if we consider wound as a deformed structure. After application od nano silver what are the feasible changes of structure is achieved is established by the Wound
Fig.3. Energy Dispersive spectoscopy of Nano silver
X
X
Y Y Z
Z
Fig.4. Differential Intensity distribution depending on diameter of nano particle
Table I
Distribution Result of prepared nano sliver, which is applied over burn wound
Distribution Result 

Peak 
Diameter(nm) 
Std.Dev 
1 
2.1 
0.4 
2 
118.4 
91.4 
3 
0.0 
0.0 
4 
0.0 
0.0 
5 
0.0 
0.0 
Average 
117.0 
91.7 
Residual 7.398e003 (0K) 
X X
(c) (d)
Fig.6. (c )3D visualization considering normalized wound factor(Y axis)
,Diffusion rate(X axis) and time (Z axis) of collagen cluster model of wound relating the parameter of Table IV & (d) . Integrated Wound regeneration factor model relating Table V.
Fig.7 Extra cellular Matrix model of wound by finite element method defining traction forces with respect to convergence and divergence along with nano silver. Stands for traction force due to converging field & stands for traction force due to divergence of extracellular matrix.
Table II
List of model Parameters related to the fibroblasts model
List of Model Parameters of proposed model 
Description 
Value 
Parameter 

DF 
Diffusion rate relating fibroblasts tissues 
2×102 cm2/day 
aF 
Initial chemo tactic sensitive function rate 
4×1010g/cm day 
Zn 
Convergence factor of nano silver 
0.345 day1 
bf 
Chemo tactic sensitive response 
3×109g/cm3 
CF 
Maximum rate of fibroblasts migration over the fibroblasts density 
108 g/cm3 
F 
Fibroblasts density in undamaged tissue 
104cells/cm3 
c 
Chemical concentration of wound 
109g/cm3 
ZF 
Time dependent negative divergence constant 
1.1×102day1 
n 
Chemical concentration of nano silver 
3×109 g/cm 
Y Z Y Z

(b)
Fig.5. (a)3D surface visualization model considering normalized wound factor(Y axis) ,Diffusion rate(X axis) and time (Z axis)visualization considering the parameter of Table II Presenting Fibroblasts structure And

Myofibroblasts Wound Model relating Table III
Table III
List of model Parameters related to the Myofibroblasts model
List of Model Parameters of proposed model 
Description 
Value 
Parameter 

Dm 
Diffusion rate of myofibroblasts tissue 
2×102 cm2 
m 
Partial derivative vector operator for myofibroblasts logistic growth rate. 
0.345 day1 
M 
Density of myofibroblasts for integrated damaged and undamaged tissue 
104 cells/cm3 
X 
Distance from the wound centre 
2cm 
Zm 
Timedependent convergence constant. 
2 
Table IV
List of model Parameters related to the Collagen model
List of Model Parameters of proposed model 
Description 
Value 
Parameter 

Dk 
Diffusion rate of collagen 
5×10 2cm2/day 
K 
Partial derivative vector operator of collagen for the collagen degradation rate per unit cell 
7.5×105 cm3/cell 
K 
Collagen production rate 
6.53×10 10g3/cm6 cell day 
ZK 
Timedependent divergence constant,considering undamaged skin poissons ratio 
0.3 
X 
Displacement from the wound centre to define displacement vector 
1.1cm 
Table V
List of model Parameters related to the Wound regeneration factor model
List of Model Parameters of proposed model 
Description 
Value 
Parameter 

Dn 
Diffusion rate of nanosilver within the structure of wound. 
3×10 2cm2/day 
p 
fibroblasts differentiation rate 
0.891 day1 
Zn1 
Nano silver active surface area 
2800cm2/g 
Cp 
Fibroblasts differentiation factor considering dermis regeneration. 
108 N/cmg 
Zc 
Time dependent divergence constant produced by fibroblasts integrated with myofibroblasts & collagen.. 
104cells/cm3 
DISCUSSION
Wound healing is a complicated process .Wound size reduction is a major issue to form the exact structure of the wound. The chemical properties along with physical properties of a burn wound can be considered as a subjective clinical study of major burn. In this work the mathematical model along with the surface of wound has been modeled, by which the convergence of wound and divergence of Extracellular matrix can be defined through the flux and density distribution. Traction forces, the itching effect at the time of cure of wound can be sensed by this structural model.
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