LASER DOPPLER FLOWMETERS PROTOTYPES VALIDATION

USING MONTE CARLO SIMULATIONS

Edite Figueiras

, Rita Campos

, Ricardo Oliveira

, Luís F. Requicha Ferreira

, Frits de Mul

and Anne Humeau-Heurtier

Instrumentation Center (GEI-CI), Physics Department, Faculty of Sciences and Technology of Coimbra University

Rua Larga, 3004-516, Coimbra, Portugal

University of Twente, Department of Applied Physics, Biomedical Optics Group, Enschede, Netherlands

Laboratoire d'Ingénierie des Systèmes Automatisés (LISA), Université d'Angers

62 avenue Notre Dame du Lac, 49000 Angers, France

Keywords: Laser doppler flowmetry, Monte carlo simulations, Microcirculation.

Abstract: Two new laser Doppler flowmeter prototypes are herein validated with Monte Carlo simulations. The first

prototype is a multi-wavelength laser Doppler flowmeter with different spaced detection fibres that will add

depth discrimination capabilities to LDF skin monitoring. The other prototype is a self-mixing based laser

Doppler flowmeter for brain perfusion estimation. In order to validate these two prototypes, Monte Carlo

simulations are performed. For the first prototype validation, Monte Carlo simulations in a phantom

consisting of moving fluid (pumped milk) at six different depths as well as in a skin model are proposed.

For this prototype, the results show that the first order moment of the photocurrent power spectrum (M1)

and mean depth measured both increase with the fibre distances tested. Moreover, M1 increases with the

concentration of milk, whereas the mean depth measured decreases with the milk concentration for the

phantom results. Furthermore, we show that increasing the wavelength of incoming light, in the skin model,

increases the mean depth probed. For the second prototype validation, Monte Carlo simulations are carried

out on a rat brain model. We show that the mean measurement depth in the rat brain with our probe is

0.15 mm.

1 INTRODUCTION

Laser Doppler flowmetry (LDF) is a Doppler Effect-

based technique used for microcirculation blood

flow monitoring where monochromatic light, guided

by optical fibres, is transmitted to the tissues under

study. In the tissues the laser light can be reflected,

absorbed, transmitted or scattered. The photons

scattered by moving particles, like red blood

cells (RBCs), are frequency shifted in accordance

with the Doppler Effect. These photons get red

blood cells velocity information. If they are detected,

together with static particles scattered photons, they

will produce a stochastic photocurrent in the

photodetector. This photocurrent is related with the

velocity and concentration of the RBCs (Bonner and

Nossal, 1981); (Humeau et al., 2007).

Currently, LDF does not give any absolute

measure of blood perfusion, i.e. it is not possible to

express the flux signal in absolute flow units,

because variables as the sampled volume, the

photons path-length, the direction of the blood flow,

and the amount of blood vessels and their length in

the measuring volume are unknown (Nilsson et al.,

2003); (Morales, 2005). For that reason, LDF signals

collected in different tissues cannot be directly

compared. Moreover, LDF signals recorded from

human skin lack in estimating the sampling depth.

These difficulties lead to ambiguities in the

discrimination of the fraction of light scattered from

superficial and deeper blood microcirculation skin

layers (Oliveira et al., 2011). Besides this,

commercial available flowmeters use different signal

processing algorithms and calibration procedures

making impossible the comparison of their results

(Nilsson et al., 2003); (Morales, 2005). Concerning

LDF invasive measurements, the smallest

commercial probes available (with 450 µm

diameter) are too large for research studies in small

organs of animals as rat brain, causing damage in an

Figueiras E., Campos R., Oliveira R., F. Requicha Ferreira L., de Mul F. and Humeau-Heurtier A..

LASER DOPPLER FLOWMETERS PROTOTYPES VALIDATION USING MONTE CARLO SIMULATIONS.

DOI: 10.5220/0003709100240033

In Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms (BIOINFORMATICS-2012), pages 24-33

ISBN: 978-989-8425-90-4

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

extension that may negatively impact local

measurements (Oliveira et al., 2011).

Monte Carlo methods are statistic methods used

in stochastic simulations with applications in several

areas as physics, mathematics, and biology. Monte

Carlo simulations of light transport are very helpful

in photon propagation studies in turbid media, as

skin. They have been widely used in LDF area (see

for example Figueiras et al., 2011). In Monte Carlo

methods, the light transport in turbid media is based

on the simulation of the photon trajectories, where

separate photons travel through the tissues. Several

phenomena as scattering, absorption and refraction

can be simulated based on the scattering functions,

Fresnel relations, etc.

We present herein Monte Carlo simulations

results for validation of two new laser Doppler

flowmeter prototypes. These prototypes have been

built in order to eliminate two drawbacks existing in

the LDF technique. The first prototype aims at

giving depth perfusion measurements information

(non invasive prototype) for human skin. The second

prototype aims at reducing the size of LDF invasive

probes for rat brain measurements (invasive

prototype). For the first prototype validation, Monte

Carlo simulations in a phantom consisting of moving

fluid at six different depths are herein proposed.

Simulations in a skin model are also presented. For

the second prototype validation, Monte Carlo

simulations are carried out on a rat brain model. In

what follows, we first present the two prototypes and

the three simulated models. Finally, the Monte Carlo

simulations are detailed and the computed signals

are presented.

2 MATERIALS AND METHODS

2.1 Prototypes

Skin microcirculation is present in the dermis and is

organized into two horizontal plexuses: the most

superficial is situated in the papillary dermis at 0.4 -

0.5 mm below the skin surface; the second plexus is

located at the dermal subcutaneous interface at

1.9 mm from the skin surface where arteriovenous

anastomoses can be found (Brevarman, 2000);

(Roustit et al., 2008). A new laser Doppler

flowmeter prototype with depth discrimination

capabilities is being built in order to determine the

sampling depth of the backscattered photons used to

compute the LDF signal (Oliveira et al., 2011). This

prototype is a non-invasive and multi-wavelength

prototype device, with 635, 785, and 830 nm laser

wavelengths. The probe used is from Perimed

and has a central emitting fibre and collecting fibres

located at 0.14, 0.25 and 1.2 mm from the emitting

fibre (Oliveira et al., 2011).

A self-mixing based prototype with a

miniaturized laser Doppler probe is also being built

in order to monitor blood flow changes in rat deep

brain structures without causing significant damage

to the tissue (Oliveira et al., 2011). In self-mixing

method, the monitor photodiode at the rear face of

the laser diode is used for signal detection; a single

optical fibre is therefore used for light emission and

detection. Pigtailed laser diodes, with 785 and 1308

nm laser wavelengths and with single mode optical

fibre are used. Standard single mode optical fibres

have 125 and 250 μm of cladding and jacket

diameters, respectively. The probe consists of the

stripped optical fibre inserted in a micro-needle with

an outer diameter of 260 µm (Oliveira et al., 2011).

Measurements will be made in the rat brain

hippocampus. As commercial available probes have

a 450 μm diameter, the use of only one optical fibre

allows us to reduce the size of the probe to 58%.

2.2 Phantom and Simulation Models

2.2.1 Phantom Model

The phantom model was built with the purpose to

evaluate, in vitro, the non-invasive flowmeter

prototype response to moving fluid at different

depths (as it can be found in skin) (Figueiras et al.,

2010). The phantom consists of a Teflon®

microtube rolled around an aluminium metal piece

with a total of six layers. The inner and outer

diameters of the microtube are 0.3 and 0.76 mm,

respectively. Commercial skimmed milk has been

chosen as a moving fluid because it has various

components that act as scatterers, namely

carbohydrates, fat, and protein. Moreover, it does

not sediment like microspheres, and it has similar

behaviour to intralipid solutions (Waterworth et al.,

1995). Finally, milk is easier for handling than blood

and, besides, it is cheaper. However, as milk is

unstable, we use the same milk solution for one day

only. Milk is pumped in the microtubes with a

motorized syringe with different velocities: 1.56,

3.12, 4.68, 6.25, 7.78, and 9.35 mm/s. Different milk

solutions were used: 100% milk, and aqueous

solutions with 50% and 25% of milk.

The first simulated model (presented in figure 1)

consists of three main layers. The first layer is

composed of a set of objects equivalent to the six

microtube layers and it has a total depth of 5 mm.

LASER DOPPLER FLOWMETERS PROTOTYPES VALIDATION USING MONTE CARLO SIMULATIONS

The two deeper layers mimic the aluminium plate

and have a thickness of 0.1 mm each one: one acts

as a scatterer with isotropic semi-spherical

backscattering and the other is a totally reflecting

layer. The laser light was considered as a pencil

beam shape and it was positioned at the top of the

most superficial tube. A parabolic profile was used

for the milk flow simulations where the maximum

velocity is twice the mean velocity.

Figure 1: Simulation phantom model: it consists of three

main layers: a) the upper layer, composed of microtubes

with skimmed milk as moving fluid; and the two deeper

layers, b) and c) mimic the aluminium plate. d) represents

the laser beam.

The simulations were made only for 635 nm

laser light wavelength due to the absence of

information concerning milk and Teflon optical

properties for 785 and 830 nm laser light. The milk

optical properties used were published by

Waterworth et al. (1995), where the refractive index

for milk is 1.346, absorption (µ

) and scattering

coefficients (µ

) are 0.00052 and 52 mm

-1

respectively. The Teflon optical properties used

were published by Li et al. (2008) where the

refractive index is 1.367, µ

= 0.001 mm

-1

and µ

167 mm

-1

, respectively. Henyey-Greenstein phase

function was used with g = 0.90 for both

components (Waterworth et al., 1995; Li et al.,

2008).

Simulations were made for six different

velocities for milk speed, three different milk

solutions and three different detection distances,

which gives a total of 54 simulations, with 5,000,000

photons detected in each simulation.

2.2.2 Skin Model

The skin simulations were made for three

wavelengths (635, 785 and 830 nm) and three

different emitting-receiving fibre separations (0.14.

0.25 and 1.2 mm), the ones used in the non self-

mixing prototype.

The skin model was based in the model

presented by Fredriksson et al. (2008; 2009). It

consists of 6 layers with different thicknesses and a

given blood concentration at three different flow

velocities with random direction (see table 2 from

Fredriksson et al., 2009). Oxygenated blood with

hematocrit equal to 42% was considered (normal

hematocrit values: 36-44% for females; 39-50% for

males). A parabolic distribution was considered for

the blood velocities.

The skin and blood optical properties for 635 and

785 nm were also based on Fredriksson et al. (2009),

whereas for 830 nm they were based on the results

presented by Simpson et al. (1998) and Prahl (1999).

The skin and blood optical properties are

summarized in table 1. Concerning the scattering

functions, the blood was modelled with the

Gegenbauer kernel scattering phase function, with

= 1 for all wavelengths and g

= 0.95 mm

-1

for

635 nm and g

= 0.948 mm

-1

for 785 and 830 nm.

For static tissue the Henyey-Greenstein phase

function was used with g = 0.85 mm

-1

. The

refractive index was set to 1.4 for all skin layers,

1.58 for the probe and 1 for the surrounding air.

The laser light was simulated as an external

photon beam, with pencil beam shape with a

perpendicular entrance in the tissue and the path

tracking was recorded with 1/µ’

resolution (µ’

refers to the reduced scattering coefficient). The

numerical aperture (NA) of the fibres is 0.37. A total

of 3 times 4 simulations were made where

10,000,000 photons were detected in each one.

The optical properties of deoxygenated and

oxygenated blood are equal except for the absorption

coefficient (see table 5 of Fredriksson et al., 2009).

However, this value is rather independent of the

level of oxygenation of the blood, once the chosen

wavelengths are close to the 800 nm isobestic point

of oxygenated and deoxygenated haemoglobin.

BIOINFORMATICS 2012 - International Conference on Bioinformatics Models, Methods and Algorithms

Table 1: Optical properties for the six skin layers and oxygenated blood (hematocrit=42%) used in skin simulations for 635,

785 and 830 nm.

(mm

-1

) μ’

(mm

-1

) g

Wavelength (nm) 635 785 830 635 785 830 635 785 830

Epidermis 0.15 0.1 0.0122 4.8 3.5 1.81 0.85 0.85 0.9

Papillary dermis 0.15 0.1 0.0122 3 2 1.81 0.85 0.85 0.9

Superior blood net 0.15 0.1 0.0122 3 2 1.81 0.85 0.85 0.9

Reticular dermis 0.15 0.1 0.0122 3 2 1.81 0.85 0.85 0.9

Inferior blood net 0.15 0.1 0.0122 3 2 1.81 0.85 0.85 0.9

Subcutis 0.15 0.1 0.00856 2.4 2 1.12 0.85 0.85 0.9

Blood 0.34 0.5 0.52 2.13 2 2 0.991 0.991 0.991

2.2.3 Rat Brain Model

The rat hippocampus consists of several substances

such as grey matter, white matter and blood vessels,

among others. The blood percentage is nearly 4.5%

and the white matter is up to 4% of the blood

volume. As the percentage of white matter is very

low we considered that the hippocampus has 95.5%

of grey matter and 4.5% of blood (3.6% of

oxygenated blood and 0.9% of deoxygenated blood)

(Fredriksson et al., 2009); (Hamberg et al., 1996).

The optical properties chosen in the simulations

for the 785 nm wavelength were based on

Fredriksson et al. (2009). The absorption

coefficients used were 0.2, 0.5 and 0.64 mm

-1

for

grey matter, oxygenated and deoxygenated blood,

respectively. The scattering coefficients were 0.78

-1

for the grey matter and 2 mm

-1

for oxygenated

and deoxygenated blood and the anisotropy factor

was 0.900 for grey matter and 0.991 for oxygenated

and deoxygenated blood (Fredriksson et al., 2009).

Concerning the scattering functions, the blood

(oxygenated and deoxygenated) was modeled with

the Gegenbauer kernel scattering phase function,

with α = 1 and g = 0.948 mm-1 (Fredriksson et al.,

2009). For grey matter the Henyey-Greenstein phase

function was used with g = 0.85 mm

-1

(Fredriksson

et al., 2009). For blood a hematocrit equal to 42%

was considered. The refractive index was set to 1.4

to all components and the laser light was simulated

as a pencil beam with a perpendicular entrance in the

tissue. The path tracking was recorded with 1/µ’

resolution, where µ’

is the reduced scattering

coefficient. The numerical aperture (NA) of the

optical fibres is 0.11.

The simulations were performed only for the

785 nm laser light wavelength due to the absence of

information concerning optical properties of grey

matter, oxygenated and deoxygenated blood for the

1300 nm laser light beam.

2.2.4 Monte Carlo Simulations

For the simulations, Monte Carlo software

‘MONTECARL’ from Frits de Mul was used (De

Mul et al., 1995); (De Mul, 2004).

3 RESULTS AND DISCUSSION

3.1 Phantom Simulations

The results obtained in the phantom model, namely

the mean depth of the Doppler events per photon,

the percentage of Doppler shifted photons detected

and the mean of Doppler scattering events per

photon are given in table 2 for 1.56 mm/s milk

velocity.

The emitting-receiving fibre separation

influences the measurements, in such a way that for

larger fibre separations, a larger sample volume is

probed. Therefore, increasing the fibre distance,

photons travel through deeper objects leading to an

increase in the mean depth of Doppler shifted

photons. Previous studies (Fredriksson et al., 2008;

Fredriksson et al., 2009) based on light propagation

in tissue using Monte Carlo computational

simulations are in agreement with these results. The

milk concentration also influences the mean depth,

which decreases with the increase of milk

concentration. This is due to a higher degree of

multiple Doppler shifts registered for higher milk

concentrations.

The percentage of Doppler shifted photons

detected increases with the emitting-receiving

separation for each velocity. This is expected

because when the fibre distance increases, the

measured sample volume increases, and the photons

LASER DOPPLER FLOWMETERS PROTOTYPES VALIDATION USING MONTE CARLO SIMULATIONS

will encounter a larger amount of moving scatterers.

When the concentration of milk increases the

percentage of Doppler shifts detected also increases.

The higher the milk concentration, higher scatterers

are present, consequently, more scattering events

occur.

Likewise, the mean Doppler scattering events per

photon also increase with the fibre distance for each

velocity. This is not surprising as we are considering

a homogenous model (for the scatterers velocity and

concentration). Therefore, an increase in the

sampled volume will naturally lead to more Doppler

scatters events. Increasing the milk concentration, a

higher degree of multiple Doppler scattering is

reached, because the higher the concentration, the

higher the scatterers.

Similar results were obtained for all velocities in

what concerns the mean depth of the Doppler events

per photon, the percentage of Doppler shifted

photons detected and the mean of Doppler scattering

events per photon, as this parameters are

independent of the velocity of the moving fluid.

The first order moment of the Doppler power

spectrum, M1, was also evaluated. Figure 2 shows

the effect on M1 when the fiber distance increases,

for each velocity and for a milk concentration of

25%. It can be seen that higher values of M1 come

from larger fiber separations whereas the lower

values of M1 are obtained for 0 mm fiber separation.

Another observation is that, in general, M1 increases

with the velocity and with the milk concentration.

This is not surprising since M1 is proportional to

perfusion (Perf), which in turn is proportional to the

scatterers concentration times their average velocity.

However, in some specific cases M1 does not

increase with the velocity, especially for the two

highest velocities for 1.2 mm fiber distance. This

might be due to the phantom model that saturates in

such extreme situations.

In order to better understand the path travelled by

the photons, a path tracking study was done. The

path tracking can be ‘followed’ in MC software

during the simulations. In figure 3 it can be seen the

path tracking for 25 [figure 3a)] and 13128 [figure

3b)] photons injected. In figure 3 b) it can be clearly

seen the three layers (cf. figure 1). The average

number of paths travelled by each photon and the

respective average depth were estimated.

Furthermore, the average path length for each

photon was also evaluated.

0 0.14 0.25 1.2

0.5

1.5

2.5

3.5

x 10

Emitting-receiving fibre distance (mm)

M1 (Hz)

1.56 mm/s

3.12 mm/s

4.68 mm/s

6.25 mm/s

7.78 mm/s

9.35 mm/s

Figure 2: M1 vs. emitting-receiving fibre distance, on the

phantom model with 25% milk concentration for 635 nm

laser light wavelength.

The results for 1.56 mm/s are presented in table

3. The results are similar for all simulated velocities

because these parameters are independent of the

scatterers velocity. For different milk concentrations,

there is not a clear tendency for the variation of the

number of paths with the milk concentration.

The average number of paths for each photon

increases with emitting-receiving fibre distance (cf.

table 3).

Table 2: The mean depth of the Doppler events for each photon, the percentage of Doppler shifted photons detected and the

mean of Doppler scattering events per photon for the phantom model, with milk pumped at 1.56 mm/s, for 635 nm laser

light wavelength.

Fibre distance (mm)

Mean Doppler depth (mm) Detected Doppler (%) Mean Doppler scattering

Milk concentration Milk concentration Milk concentration

25 % 50% 100% 25% 50% 100% 25 % 50% 100%

0 0.36 0.34 0.32 4.77 6.73 10.27 3.48 5.85 10.08

0.14 0.41 0.39 0.35 26 32.35 41.26 4.29 7.30 12.66

0.25 0.43 0.40 0.37 41.23 47.76 56.45 4.37 7.78 14.27

1.2 0.56 0.55 0.53 82 86 87.47 6.47 12.65 26-63

BIOINFORMATICS 2012 - International Conference on Bioinformatics Models, Methods and Algorithms

This is expected because as mentioned, a greater

fibre distance allows sampling a greater volume and

therefore, a bigger number of paths are registered.

The average path depth and the average path

length for each photon are the highest for 0 mm

emitting-receiving fibre distances, and they are the

lowest for 0.14 and 0.25 mm fibre distance. The

origin of this non-linearity is unclear for the

moment.

3.2 Skin Simulations

The mean depth of the Doppler events per photon,

the percentage of Doppler shifted photons detected

and the mean of Doppler scattering events per

photon obtained in Monte Carlo simulations, for the

skin model, are presented in table 4.

The mean depth for the Doppler events, the

percentage of Doppler shifted photons detected and

the mean Doppler scattering per photon increase

with fibre distance, as for the phantom model,

because a larger emitting-receiving separation

allows sampling a larger volume.

Furthermore, the mean measurement depth also

increases with the wavelength. This is due to both

skin absorption and scattering coefficients decrease

with the wavelength, allowing the photons to travel a

longer path. Similar results were obtained by

Figure 3: Path tracking registered during the simulations for: a) 25 and b) 13128 photons injected.

Table 3: Average mean path number, mean path depth and mean path length for photons for the phantom model, with milk

pumped at 1.56 mm/s.

Milk concentration Fibre distance (mm) <Path number> <Path depth> (mm) <Path length> (mm)

0 3.31 1.45 10.66

0.14 7.00 0.23 2.53

0.25 9.66 0.23 2.55

1.2 25.67 0.47 5.95

50%

0 3.37 1.41 10.74

0.14 7.06 0.24 2.58

0.25 9.51 0.22 2.45

1.2 25.91 0.47 6.07

100%

0 3.49 1.41 10.43

0.14 7.04 0.22 2.53

0.25 9.53 0.21 2.43

1.2 27.67 0.45 6.24

LASER DOPPLER FLOWMETERS PROTOTYPES VALIDATION USING MONTE CARLO SIMULATIONS

Fredriksson et al. (2009), with a measurement depth

slightly smaller, but with the same order of

magnitude. It can be noticed that the mean depth of

the Doppler shifted photons never reaches the

reticular dermis or the layers below this one, since

reticular dermis lies at a depth of 1.175 mm and the

mean depth predicted for the Doppler events is

always lower than this value. In addition, detected

photons reached the superior blood net dermis only

when detected with the 1.2 mm fibre distance.

The percentage of Doppler shifted detected

photons also increases with the wavelength

excluding for the 1.2 mm emitting-receiving fibre

distance. This may be related to the distribution of

the Doppler events percentage in each layer (cf.

table 5). It can be seen that the reticular dermis is the

2nd layer with the most detected Doppler photons

for 1.2 mm fibre distance (for 785 and 830 nm laser

light), whereas for the other fibre distances the 2nd

layer with the most detected Doppler photons is the

papillary dermis.

This proves that the photons detected at 1.2 mm

from the emitting fibre cross a higher volume of

blood. Besides, the Doppler events percentage in the

inferior blood net (for 1.2 mm fibre distance)

decreases going from 635 to 785 nm laser light and

increases going from 785 to 830 nm laser light. This

layer has the second higher blood concentration

when compared with the other layers. Together, with

the higher volume of blood crossed and the

increasing of the blood absorption coefficient with

the wavelength may cause this nonlinearity.

In opposition, the mean Doppler scattering event

does not follow a general trend when increasing the

wavelength of the incident light but is always

smaller than 1.5, which means that there are few

photons that suffer multiple Doppler shifts.

Simulation results also demonstrate that M1

increases with the emitting-receiving fibre distance

(see table 6). Since M1 is proportional to the

concentration of moving RBCs times its average

velocity, and both parameters increase with the fibre

distance, this was expected.

Table 4: The mean depth of the Doppler events for each photon, the percentage of Doppler events detected and the mean of

Doppler scattering events per photon for the skin model.

Fibre distance (mm)

Mean depth Doppler (mm) Detected Doppler (%) Mean Doppler scattering

Wavelength (nm) Wavelength (nm) Wavelength (nm)

635 785 830 635 785 830 635 785 830

0 0.24 0.25 0.27 1.94 1.97 3.54 1.19 1.16 1.15

0.14 0.27 0.29 0.31 9.62 10.71 14.54 1.23 1.22 1.23

0.25 0.28 0.30 0.33 15.45 16.29 20.39 1.26 1.23 1.25

1.2 0.37 0.38 0.41 47.7 41.89 43.45 1.49 1.41 1.46

Table 5: Doppler events percentage in each layer for the skin model.

Wavelength

(nm)

Fibre

Distance

(mm)

Skin layers

Epidermis

Papillary

dermis

Superior

blood net

Reticular

dermis

Inferior

blood net

Subcutis

0 0 41.07 51.19 7.24 0.5 0

635 0.14 0 35.1 53.06 10.31 1.37 0.17

0.25 0 31.98 55.23 11.1 1.49 0.21

1.2 0 19.43 56.21 19.51 4.08 0.77

0 0 41.73 48.84 8.93 0.51 0

785 0.14 0 30.85 54.86 12.97 1.33 0

0.25 0 27.69 56.42 14.38 1.51 0

1.2 0 18.81 55.44 22.24 3.51 0

0 0 38.76 49.36 10.35 1.54 0

830 0.14 0 26.66 55.91 15.09 2.33 0

0.25 0 23.09 57.05 17.27 2.59 0

1.2 0 16.57 53.06 25.15 5.21 0

BIOINFORMATICS 2012 - International Conference on Bioinformatics Models, Methods and Algorithms

In what concerns the wavelengths, M1 firstly

decreases from 635 to 785 nm and then increases for

830 nm. This can be explained if we look at the

Doppler photons percentage that exceeds the

reticular dermis. This percentage is higher for

830 nm followed by 635 nm and lower for 785 nm,

with the exception of the 0 mm fibre distance (Table

5). As the inferior blood net has the highest

concentration of the high velocity component of

RBCs (30 mm/s), it results in a higher Doppler shifts

for 635 nm than for 785 nm photons. Therefore M1

will be higher for 635 nm than for 785 nm.

Table 7 shows the results of the path tracking study

for the skin model. It can be observed that the

average path number travelled by each photon, the

mean path depth and the average path length

increase with emitting-receiving fibre distance. This

occurs, because increasing the fibre distance a

greater tissue volume is probed, and so, more

scattering events occur. The mean path number does

not follow a general trend when increasing the

wavelength of the incident light.

The path depth increases with the laser light

wavelength due to both skin absorption and

scattering coefficients decrease with the wavelength,

allowing the photons to travel a longer path. This is

in agreement with the mean depth of Doppler events

results showed in table 4. The average path length

increases with the wavelength, excluding for the 1.2

mm emitting-receiving fibre distance. This may be

related with the distribution of the Doppler events

percentage in each layer (cf. table 5) as discussed

later when the percentage of Doppler shifted

detected photons is analyzed.

3.3 Rat Brain Simulations

In the simulation made for rat brain model, it can be

seen that the photons Doppler shifted travelled a

mean depth of 0.15 mm (cf. table 8). This value is in

accordance with Frediksson et al. (2009) which

obtained 0.16 mm of measurement depth. Each

photon suffers, in average, 2.23 scatters events. In a

total of 5,000,000 photons detected 11.9% had

Table 6: First order moment of Doppler power spectrum (M1) for skin model.

Wavelength (nm)

M1 (Hz)

Fibre distance (mm)

0 0.14 0.25 1.2

635 3.57E+18 2.51E+19 3.71E+19 1.63E+20

785 3.45E+18 2.13E+19 3.23E+19 1.05E+20

830 5.30E+18 2.66E+19 3.93E+19 1.06E+20

Table 7: Mean path number, mean path depth and mean path length for photons, using the skin model.

Wavelength (nm) Fibre distance (mm) <Path number> <Path depth> (mm) <Path length> (mm)

635

0 3.16 0.02 0.23

0.14 6.1959 0.0775 0.78

0.25 7.99 0.11 1.16

1.2 19.77 0.27 4.11

785

0 3.08 0.02 0.23

0.14 5.98 0.09 0.86

0.25 7.46 0.12 1.26

1.2 14.71 0.26 3.65

830

0 3.77 0.04 0.34

0.14 6.93 0.12 1.12

0.25 8.34 0.16 1.57

1.2 14.86 0.28 4.01

LASER DOPPLER FLOWMETERS PROTOTYPES VALIDATION USING MONTE CARLO SIMULATIONS

Table 8: The percentage of Doppler events detected the mean of Doppler scattering, the mean depth of the Doppler events

for each photon and M1 for the rat model.

Mean depth Doppler (mm) Detected Doppler (%) Mean Doppler scattering M1 (Hz)

0.15 11.9 2.23 3.51E+17

suffered Doppler shift and M1 was predicted to be

3.51E+17 Hz. These results will help in the rat brain

probe positioning as it shall be 0.15 mm above the

mean measurement depth.

4 CONCLUSIONS

Monte Carlo simulations used for the two new LDF

prototypes validation showed results in accordance

with the literature. For the non invasive prototype,

the phantom model presented here to evaluate the in

vitro prototype response, has shown good agreement

with theoretical expectations. M1 increases with the

concentration and with the fibre distances. The mean

depth increases with the fibre distance and decreases

with the milk concentration. For in vivo evaluation,

the estimated parameters for the skin model

corresponded to a priori expectations. We have

shown that increasing the wavelength of incoming

light (in the range of 635-830 nm) increases the

mean depth probed. Moreover, an increase of the

source-detection fibre separations leads to a higher

mean depth and M1 value. In what concerns the rat

brain model, the mean depth that photons Doppler

shifted travel was estimated to be 0.15 mm which is

in agreement with the literature.

ACKNOWLEDGEMENTS

The authors thank the “Instituto de Investigação

Interdisciplinar (III)” of the University of Coimbra,

“Acções Universitárias Integradas Luso–Francesas”

(PAUILF) programme and “Fundação para a

Ciência e a Tecnologia (FCT), Lisbon”, for

supporting this work.

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