<s>
Within	O
physics	O
,	O
the	O
Hybrid	B-Application
Theory	I-Application
for	I-Application
photon	I-Application
transport	I-Application
in	I-Application
tissue	I-Application
uses	O
the	O
advantages	O
and	O
eliminates	O
the	O
deficiencies	O
of	O
both	O
the	O
Monte	B-Algorithm
Carlo	I-Algorithm
method	I-Algorithm
and	O
the	O
diffusion	B-Algorithm
theory	I-Algorithm
for	O
photon	B-Application
transport	O
to	O
model	O
photons	B-Application
traveling	O
through	O
tissue	O
both	O
accurately	O
and	O
efficiently	O
.	O
</s>
<s>
The	O
MCML	B-Algorithm
is	O
a	O
numerical	O
way	O
to	O
simulate	O
photon	B-Application
transport	O
in	O
biological	O
tissue	O
.	O
</s>
<s>
Each	O
photon	B-Application
packet	O
follows	O
a	O
random	O
walk	O
with	O
persistence	O
,	O
where	O
the	O
direction	O
of	O
each	O
step	O
dependent	O
on	O
the	O
direction	O
of	O
the	O
previous	O
step	O
.	O
</s>
<s>
By	O
averaging	O
multiple	O
independent	O
random	O
walks	O
,	O
MCML	B-Algorithm
estimates	O
the	O
ensemble-averaged	O
quantities	O
such	O
as	O
reflectance	O
,	O
transmittance	O
,	O
absorption	O
,	O
and	O
fluence	O
.	O
</s>
<s>
Briefly	O
,	O
a	O
packet	O
of	O
photon	B-Application
is	O
first	O
launched	O
into	O
the	O
biological	O
tissue	O
.	O
</s>
<s>
The	O
parameters	O
of	O
photon	B-Application
transport	O
,	O
including	O
the	O
step	O
size	O
and	O
deflection	O
angle	O
due	O
to	O
scattering	O
,	O
are	O
determined	O
by	O
random	O
sampling	O
from	O
probability	O
distributions	O
.	O
</s>
<s>
The	O
photon	B-Application
packet	O
continues	O
propagating	O
until	O
the	O
weight	O
left	O
is	O
smaller	O
than	O
a	O
certain	O
threshold	O
.	O
</s>
<s>
If	O
this	O
packet	O
of	O
photon	B-Application
hits	O
the	O
boundary	O
during	O
the	O
propagation	O
,	O
it	O
is	O
either	O
reflected	O
or	O
transmitted	O
,	O
determined	O
by	O
a	O
pseudorandom	O
number	O
.	O
</s>
<s>
Statistically	O
sufficient	O
numbers	O
of	O
photon	B-Application
packets	O
must	O
be	O
simulated	O
to	O
obtain	O
the	O
expected	O
values	O
accurately	O
.	O
</s>
<s>
This	O
Monte	B-Algorithm
Carlo	I-Algorithm
method	I-Algorithm
is	O
rigorous	O
and	O
flexible	O
.	O
</s>
<s>
However	O
,	O
because	O
of	O
its	O
statistical	O
nature	O
,	O
this	O
method	O
requires	O
tracking	O
a	O
large	O
number	O
of	O
photon	B-Application
packets	O
,	O
making	O
it	O
computationally	O
expensive	O
.	O
</s>
<s>
The	O
Diffusion	B-Algorithm
Theory	I-Algorithm
is	O
an	O
approximation	O
of	O
the	O
radiative	O
transfer	O
equation	O
(	O
RTE	O
)	O
,	O
and	O
an	O
analytical	O
way	O
to	O
simulate	O
photon	B-Application
transport	O
.	O
</s>
<s>
As	O
such	O
,	O
it	O
has	O
the	O
ability	O
to	O
model	O
photon	B-Application
propagation	O
through	O
tissue	O
quickly	O
.	O
</s>
<s>
Diffusion	B-Algorithm
Theory	I-Algorithm
is	O
more	O
computationally	O
efficient	O
than	O
MCML	B-Algorithm
.	O
</s>
<s>
However	O
,	O
it	O
is	O
also	O
less	O
accurate	O
than	O
MCML	B-Algorithm
near	O
the	O
source	O
and	O
boundaries	O
.	O
</s>
<s>
The	O
Hybrid	B-Application
Theory	I-Application
combines	O
the	O
Diffusion	B-Algorithm
Theory	I-Algorithm
and	O
the	O
Monte	B-Algorithm
Carlo	I-Algorithm
method	I-Algorithm
in	O
order	O
to	O
increase	O
accuracy	O
near	O
the	O
source	O
and	O
boundaries	O
while	O
reducing	O
computation	O
time	O
.	O
</s>
<s>
In	O
the	O
previous	O
example	O
for	O
the	O
Diffusion	B-Algorithm
Theory	I-Algorithm
,	O
a	O
semi-infinite	O
scattering	O
medium	O
with	O
only	O
one	O
boundary	O
was	O
assumed	O
.	O
</s>
<s>
A	O
Monte	O
Carlo	O
approach	O
can	O
be	O
used	O
to	O
make	O
up	O
for	O
the	O
Diffusion	B-Algorithm
Theory	I-Algorithm
's	O
inherently	O
poor	O
accuracy	O
near	O
the	O
boundaries	O
.	O
</s>
<s>
As	O
mentioned	O
before	O
,	O
the	O
Monte	B-Algorithm
Carlo	I-Algorithm
simulation	I-Algorithm
is	O
time	O
consuming	O
.	O
</s>
<s>
When	O
a	O
photon	B-Application
packet	O
is	O
within	O
a	O
critical	O
depth	O
the	O
Monte	B-Algorithm
Carlo	I-Algorithm
simulation	I-Algorithm
tracks	O
all	O
packets	O
but	O
within	O
the	O
center	O
region	O
the	O
photon	B-Application
packet	O
is	O
transformed	O
to	O
an	O
isotropic	O
source	O
and	O
subsequently	O
treated	O
with	O
Diffusion	B-Algorithm
Theory	I-Algorithm
.	O
</s>
<s>
Just	O
like	O
in	O
the	O
Monte	B-Algorithm
Carlo	I-Algorithm
simulation	I-Algorithm
,	O
any	O
photon	B-Application
packet	O
that	O
gets	O
reemitted	O
is	O
added	O
to	O
the	O
diffuse	O
reflectance	O
.	O
</s>
<s>
When	O
a	O
photon	B-Application
packet	O
is	O
scattered	O
into	O
the	O
center	O
zone	O
,	O
it	O
is	O
conditionally	O
converted	O
to	O
an	O
isotropic	O
point	O
source	O
.	O
</s>
<s>
The	O
photon	B-Application
packet	O
must	O
still	O
be	O
in	O
the	O
center	O
region	O
after	O
one	O
transport	O
mean	O
free	O
path	O
along	O
the	O
direction	O
of	O
the	O
photon	B-Application
packet	O
propagation	O
for	O
it	O
to	O
be	O
converted	O
to	O
a	O
point	O
source	O
,	O
otherwise	O
the	O
Monte	B-Algorithm
Carlo	I-Algorithm
simulation	I-Algorithm
continues	O
.	O
</s>
<s>
Before	O
the	O
conversion	O
to	O
an	O
isotropic	O
point	O
source	O
,	O
the	O
photon	B-Application
packet	O
reduces	O
its	O
weight	O
due	O
to	O
its	O
interaction	O
with	O
the	O
scattering	O
medium	O
.	O
</s>
<s>
where	O
is	O
the	O
grid	O
volume	O
and	O
is	O
the	O
number	O
of	O
photon	B-Application
packets	O
.	O
</s>
<s>
where	O
is	O
from	O
the	O
diffusion	B-Algorithm
theory	I-Algorithm
approximation	O
for	O
a	O
slab	O
and	O
is	O
the	O
azimuthal	O
angle	O
.	O
</s>
<s>
A	O
trade-off	O
between	O
simulation	O
speed	O
and	O
accuracy	O
exists	O
;	O
choosing	O
a	O
critical	O
depth	O
becomes	O
the	O
deciding	O
factor	O
for	O
simulation	O
speed	O
with	O
a	O
deeper	O
critical	O
depth	O
resulting	O
in	O
slower	O
times	O
due	O
to	O
packets	O
needing	O
to	O
be	O
tracked	O
for	O
a	O
longer	O
distance	O
before	O
the	O
transition	O
to	O
diffusion	B-Algorithm
theory	I-Algorithm
.	O
</s>
