Lasers in Surgery and Medicine 42:760–764 (2010)
Estimation of the Optimal Wavelengths for Laser-Induced
Wound Healing
Rinat Ankri,1,2 Rachel Lubart,1,2* and Haim Taitelbaum2
1
Department of Chemistry, Bar-Ilan University, Ramat-Gan, Israel
2
Department of Physics, Bar-Ilan University, Ramat-Gan, Israel
Background and objectives: According to earlier
in vitro low level laser therapy (LLLT) studies, wavelengths in the red and near infrared range, that are
absorbed by cytochrome oxidase, stimulate cell growth
and hence wound healing. Wavelengths in the blue region
that are absorbed by flavins were found to exert a
bactericidal effect that is very important for treating
infected wounds. However, as far as therapeutic application of light is concerned, penetration into the tissue must
be considered. For this purpose we estimated the penetration depth as a function of the relevant wavelengths,
using the formulae of the photon migration model for skin
tissue.
Methods: We use the photon diffusion model, which is an
analytical model for describing light transfer in biological
tissues. We refer to the most common chromophores in
human tissue and evaluate their volume fraction and
concentration in skin cells. These empirically estimated
mean wavelength-dependent absorption coefficients are
then substituted in the theoretical expressions for the
optical penetration depth in the tissue. The wavelengths,
for which the penetration depth is the highest, are the
optimal wavelengths to be used in wound healing treatments.
Results: Our model suggests that the optimal wavelengths
for therapeutic treatments are in the red region with a
local maximum at 730 nm. As to the blue region, a local
maximum at 480 nm was found.
Conclusion: Light at 480 nm should be used for treating
infected wounds followed by 730 nm light for enhancing
wound closure. Lasers Surg. Med. 42:760–764, 2010.
ß 2010 Wiley-Liss, Inc.
Key words: wound healing; skin tissue; photon migration model; light penetration depth
INTRODUCTION
Wavelengths in the visible and NIR light are used in the
therapeutic field, such as photo dynamic therapy (PDT),
that uses light to damage tumor cells, and low level laser
therapy (LLLT), that uses visible-NIR light to biostimulate
the cell [1–4]. In photobiostimulation, the interaction of
light with the cell is ascribed to the excitation of intracellular chromophores like endogenous porphyrins, mitochondrial and membranal cytochromes and flavoproteins.
These chromophores transfer their excited electrons to
ß 2010 Wiley-Liss, Inc.
nearby O2, thus generating low amounts of reactive oxygen
species [5], which play an important role in the activation
and control of many cellular processes, such as the release
of transcription factors, gene expression, muscle contraction, and cell growth [6,7].
Recently, it has been shown that wavelengths in the blue
region (400–500 nm), induce generation of higher amounts
of ROS than wavelengths in the red one (600–800 nm) [6].
This phenomenon is exploited for sterilization purposes,
such as bacterial eradication in contaminated wounds
[7–11].
Moreover, very recently blue light has been demonstrated to be mostly responsible for NO formation by
endothelial cells [12]. Since NO formation leads to vasodilatation and subsequent increase in microcirculatory
blood flow, the use of blue light might be of great importance
for wound healing of diabetic and venous ulcers.
However, as far as therapeutic application of light is
concerned, penetration inside the tissue must be considered. In the present work we do so by using the photon
migration model [13]. We apply this model to the dermis
layer which is the exposed layer in the wounded tissue,
neglecting the upper epidermis layer. The mean absorption
coefficients of the dermis layer are calculated and substituted in the theoretical expressions for the penetration
depth, thus getting estimation for the penetration depth as
a function of the visible wavelengths. The optimal wavelengths for clinical treatments are those that penetrate
deepest inside the tissue, within the relevant wavelength
range.
There are several methods and numerical techniques
to consider light propagation in tissues, such as Monte–
Carlo simulations, finite differences approaches, diffusion
approximation of radiative transfer equations, etc. (see,
e.g., Tuchin’s book [14]). The main advantage of the
random-walk on the lattice model, over other methods,
is the ability to derive analytical expressions for various
quantities of interest, in particular those related to the
important issue of the light penetration depth inside the
tissue [13,15,16].
*Correspondence to: Rachel Lubart, Department of Chemistry,
Bar-Ilan University, Ramat-Gan 52900, Israel.
E-mail: [email protected]
Accepted 17 June 2010
Published online 15 September 2010 in Wiley Online Library
(wileyonlinelibrary.com).
DOI 10.1002/lsm.20955
LASER-INDUCED WOUND HEALING
METHODS
Photon Migration in a One-Layer Biological Tissue
In the photon migration model, the tissue is represented
by a semi-infinite cubic lattice with two adjustable
parameters, namely its scattering and absorption factors.
The simplest version of the model refers to a one-layer
tissue and was successfully used to predict the intensity
of re-emitted flux, the mean trajectory length of detected
photons and the penetration depth of photons inside the
tissue [15]. Figure 1 shows the one-layer version of the
photon migration model: The tissue is modeled as a three
dimensioned discrete lattice with transverse coordinate,
r ¼ (x,y), and a positive z-axis pointing into the tissue.
Photons are injected at the origin, then diffuse randomly
within the tissue, eventually either reach the surface z ¼ 0,
where they can be detected, therefore disappearing from
the system, or they are being absorbed inside the tissue.
The scattering of the photon in the lattice is assumed to
be isotropic and is described by a random change in the
photon’s direction of motion on the cubic lattice. The
absorption, occurring between nodes of the lattice, is
described by Beer’s law, so that the survival probability of
a given photon is exp (m) per step on the lattice. In order to
correlate the absorption coefficient used in the model, m,
which is per step on the lattice, and the conventional
absorption coefficient used in literature, a, which has
conventional inverse length units, one should multiply m
with the lattice unit length. In the NIR region, it was found
that one lattice unit length is equivalent to a length of about
0.1–1 mm on the biological tissue. For LLLT treatments on
wounded skin tissues we have chosen a length of 0.1 mm for
one lattice step.
Among other statistical characteristics presented in the
model, the average depth reached by photons that are
eventually being absorbed inside the tissue is
1
hzia ¼ pffiffiffiffiffiffi
ð1Þ
6m
761
where m is the model parameter for the wavelengthdependent mean absorption coefficient of the tissue and
1/6 is the lattice diffusion constant, where the randomwalker has six possible directions of motion from each
lattice site. This average depth has units of lattice length,
since the diffusion constant units are (length)2 per lattice
step, and m is the absorption per step. hzia is translated to
conventional units by multiplying m with the lattice
constant length; 0.1 mm.
Model Application to the Human Skin
In order to calculate light penetration depth for wound
healing purposes, we apply the one-layer photon migration
model to the dermis layer of the skin, since it is the exposed
layer in wounded skin. Indeed, the dermis is an inhomogeneous layer since it is consisted from two main sub-layers;
the papillary dermis, which is the upper layer in the dermis,
and the reticular dermis. Still, the dermis layer can be
considered homogeneous relating to the fibroblast cells and
the blood vessels, which contains the main chromophores in
the visible region and that are homogeneously distributed
in both layers [17]. To apply the model to the dermis skin
layer, the necessary first step is to estimate the absorption
coefficients of each of the elements that constitute skin
tissue cells. Specifically, we refer to their most absorbing
chromophores in the visible region that have a significant
role in ROS formation by illuminated cells, as mentioned in
the introduction. Those chromophores are hemoglobin
(Hb), cytochrome c (Cyt c), and riboflavin (RF). Each of
these chromophores is characterized by an absorption
coefficient (i.e., wavelength dependent) and has volume
fraction (i.e., percentage in skin tissue) describing its
appearance in the dermis layer. Those chromophores are
also characterized by their concentration in a skin cell, as
explained in the Volume Fraction and Cell Concentration of
Skin Chromophores Section.
H2O molecules were also added to the mean absorption
coefficient calculation since they own a significant absorption in the NIR region (700–800 nm), therefore, in the next
paragraphs, H2O molecules will be referred as chromophores.
In order to obtain mean absorption coefficients for
the dermis we average the absorption coefficients of the
above-mentioned chromophores. The wavelength-dependent absorption coefficient values are multiplied by their
volume fraction and cell concentration in skin tissue.
In the next two paragraphs we describe the way the
absorption coefficients, volume fraction, and cell concentration data are obtained for each of those chromophores.
RESULTS
Chromophore’s Absorption Coefficients
Fig. 1. Discrete lattice representing the biological tissues in
the photon migration model and typical photon trajectories in a
one-layer tissue.
The absorption coefficients for Hb and H2O were adopted
from ‘‘Oregon Medical Laser Center’’ website [18]. The
absorption coefficients of Cyt c and RF were experimentally
calculated: solutions of Cyt c molecules, with known
concentration of 10 mM, and solutions of RF molecules,
with known concentration of 75.3 mM, were spectrally
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ANKRI ET AL.
measured using spectrophotometer (SpectrafluorPlus,
Tecan) in the visible light range (400–800 nm). The
absorption values were translated into absorption coefficients wavelength-dependent values using Beer–Lambert
linear absorption law:
A ¼ LCa
ð2Þ
where A is the absorption values (OD), L the test
tube’s length (1 cm), C the chromophore’s known concentration (M), and a the chromophore’s absorption
coefficient (1/M cm). The absorption coefficient spectra
for both chromophores, RF and Cyt c, are presented in
Figure 2a,b, respectively.
The next step was to weight those wavelength-dependent
absorption coefficients according to their volume fraction
(and cell concentration for Hb, Cyt c, and RF) as appear in
skin tissue.
Volume Fraction and Cell Concentration of Skin
Chromophores
We first referred to the hemoglobin chromophore. The
volume fraction of blood vessels in the dermis layer is 2%
[17]. A red blood cell contains 95% Hb, therefore having a
strong absorption in the visible light region. The molar
Fig. 2. Absorption coefficient spectra for (a) riboflavin (RF)
(b) cytochrome c (Cyt c).
concentration of Hb in a blood cell is 2.27E3 M, based on
its molecular weight 66,500 g/mol and its concentration in
blood, 150 g/L [17].
Other skin chromophores, as mentioned above, are Cyt c,
RF, and H2O molecules. Our assumption is that those
molecules are contained in all skin cells that are not blood
vessels in the dermis. Therefore, in the dermis layer, that
contains 2% of blood vessels, the left 98% consist of 70% H2O
molecules [19] and 30% ‘‘dry mass’’ of skin cells. Hence, one
has 68.6% of H2O molecules and 29.4% of ‘‘dry mass’’ of skin
cells in the dermis.
As mentioned above, those volume fractions of Cyt c and
RF should be multiplied by their concentration in a skin
cell. The cellular concentration of RF, 5E5 M, was taken
from literature [20], while the cellular concentration of Cyt
c was experimentally determined as follows: fibroblasts
(NIH/3T3 cells), which are cells having physical properties
similar to skin cells, were grown as described elsewhere
[21]. The cytoplasm fluid was isolated from 5.4E7 cells
using fibroblasts fractionation as followed: Aragon gas was
diffused to the cell solution in order to keep the reduced
form of Cyt c molecules. The cells were sediment using
a 1,500 rpm centrifuge. The sedimentation was deposited
in dry ice and on a hot plate, alternately, and then went
through a 20,000 rpm centrifugation for 1 hour. The
superior fluid, which is the cytoplasm, was spectrally
measured (in the visible light region) to give the absorption
spectrum, as presented in Figure 3. One can notice the
absorption peaks of the cytosol solution around wavelengths 410 and 550 nm, indicating the presence of Cyt c
molecule in fibroblast cytosol solution [22]. From those
spectral data and by using Equation (2) we obtained Cyt c
concentration in fibroblasts solution whereas:A is the Cyt
c’s absorption at 410 nm, standing for 0.048 OD, L the
test tube’s length, 1 cm, and a the Cyt c absorption
coefficient at 410 nm; a(410 nm) ¼ 5.302E4 (1/M cm).
Hence, we obtain C(l) ¼ A/(La(410 nm)) ¼ 9.2E7 M, while
C(l) is the Cyt c concentration in the entire fibroblasts
Fig. 3. Fibroblasts cytosol absorption spectra (arbitrary units)
in the visible region as measured by a spectrophotometer.
LASER-INDUCED WOUND HEALING
TABLE 1. Main Chromophores in the Dermis Layer,
Their Volume Fraction and Concentration in Cell
Chromophore
Hb
Cyt c
RF
H2O
Volume fraction
in dermis (%)
Concentration
in cell (M)
2
29.4
2.27E3
1.703E14
5E5
68.6
solution. The Cyt c concentration in a single fibroblast cell
was calculated by dividing C(l) with the number of cells
C ¼ CðlÞ=ð5:4e7 cellsÞ ¼ 1:703e 14 M=cell
The results from previous paragraphs are summarized
and presented in Table 1. One can see that the skin cellular
concentration of Cyt c is very small compared to Hb and RF
skin cell concentrations, thus it can be neglected in the
entire calculation. In addition, our results indicate that RF
absorption coefficients are very small, so they can also be
ignored. The absorption coefficients of H2O are not high
in the visible region, but in the NIR region they become
significant. Moreover, their volume fraction is very high, so
they must be taken into account in the general calculation.
In conclusion, our results indicate that the absorption
coefficients of Hb were the most dominant factors in the
calculation.
763
DISCUSSION AND SUMMARY
In the present study, we characterize the top layer in the
wounded skin tissue (dermis) by referring to its chromophores’ absorption coefficients. We obtain the wavelengthdependent absorption coefficients, m(l), of the dermis and
use the relevant expressions in the statistical photon
migration model to calculate the penetration depth of the
visible-NIR light in homogeneous skin tissue. The penetration depth graph consists of two different local maxima;
one around 480 nm and the other around 730 nm. As
mentioned in the Introduction Section, low level red and
NIR light, when irradiated on biological cells, stimulate low
ROS fluxes which play an important role in the activation
and control of many cellular processes, such as the
release of transcription factors, gene expression, cell
growth [23–25], recovery of damaged nerve cells [26], and
more. As the clinical use of LLLT is mostly for wound
healing [27] it turns out that 730 nm is the optimal
wavelength since it penetrates best the wound. Blue light,
which was found to be more effective than red light for ROS
Mean Absorption Coefficient and Light Penetration
Depth in the Dermal Layer
We now apply the above results to the simplest version of
the photon migration model. Following Table 1, the mean
absorption coefficient of the dermis layer is assumed to
follow the weighted form:
mðlÞ ¼ aHb ðlÞ2%ð2:27e 3Þ þ aH2 O ðlÞ68:6%
þ less absorbing elements
ð3Þ
where aHb (l) and aH2 O ðlÞ are taken from the OMLC
website [18] and the less absorbing elements refer to Cyt c
and RF molecules, which were argued above not to
contribute to the skin tissue total absorption.
From Equation (3) an absorption coefficient wavelengthdependent graph is obtained and is presented in Figure 4a.
The graph is very similar to that of hemoglobin’s absorption
coefficient graph [18] indicating that the main absorbing
chromophore in the dermis layer is the hemoglobin.
Assuming that the dermis layer is a homogeneous
tissue, we next use Equation (1) to calculate the averaged
penetration depth of the irradiated light as a function
of wavelength in the visible-NIR region. Following the
above mentioned relation between a and m (see the
Photon Migration in a One-Layer Biological Tissue Section)
we multiply the empirical absorption coefficients (a) by
0.1 mm and thus define the modelistic absorption coefficients (m). Figure 4b presents two local maxima at 480 and
730 nm.
Fig. 4. Homogeneous dermis tissue. a: The mean absorption
coefficient, calculated using Equation (3). b: Penetration depth
of irradiated light, calculated using Equation (1).
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ANKRI ET AL.
formation [28] and hence for bacteria killing [29], has not
yet been clinically used because of its low penetration depth
in the tissue. The present results, estimating a depth of
0.5 mm for 480 nm, may encourage clinicians to use this
wavelength for sterilizing infected wounds. It is therefore
recommended to illuminate infected wounds with 480 nm
for killing the pathogens prior to 730 nm light for stimulating skin cells growth and wound closure. The potential of
480 nm to enhance NO formation for increasing blood
circulation in wounds should also be considered.
In conclusion, the photon migration model substantiates
theoretically the clinical routines of wound healing using
lasers and light emitting diodes (LEDs) in the red-NIR
region [30,31] and suggests the 730 nm to be the optimal
wavelength for enhancing wound closure. Moreover, our
theoretical approach presents another local maximum in
the penetration depth, at 480 nm, suggesting its use for
sterilizing infected wounds.
12.
13.
14.
15.
16.
17.
18.
19.
20.
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