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µ_s(λ) 0.016λ2.4 ₍±_6%)

for 0.4 <λ< 1.1, where λis inµm, andµ_sis in mm–1_{, when the 10% solution is diluted 1000}

7.2 g(λ) 1.1 0.58λ (±5%)

times with distilled water. Figure 7.2 shows graphs ofµs, g andµs′plotted over the range of 400 nm to 1100 nm, for 1 ml of the 10% IntralipidTMdiluted in 999 ml of water, to make 1000 ml of solution. From the bottom graph in figure 7.2, it can be seen that at 800 nm the transport scattering coefficient of the solution is approximately 0.01 mm–1_{. Tissue has a} µ

s′ of typically 1 mm–1_{. To obtain a solution with} µ

s′ = 1 mm

–1_{one needs to mix a solution comprising 1 part} of the 10% IntralipidTM_{to 9 parts distilled water. During these experiments, which had the aim} to determine if µ_s′ could be determined from the instrumentation, three different values ofµ_s′ were used - 0.3 mm–1, 1 mm–1and 3 mm–1. These required respectively 45, 150 and 450 ml of IntralipidTM_{, with the remainder of the 1500 ml being distilled water. The Intralipid}TM_{and water} were both weighed to determine the amounts to use (relative density of IntralipidTM_{is close to} 1.0), rather than measured volumetrically, as weighing was more accurate.

Van Starvansen et al136 _{state the equations 7.1 and 7.2 are valid only until the}

concentration of 10% IntralipidTM_{is above 4% (at 1100 nm) to 17% (at 400 nm), as beyond this,} the scattering events are not independent. The IntralipidTMconcentration used here is much more than this, so lies outside their stated range of validity. Work by Lovell et al137_{have shown that}

with red blood cells the concentration can be much higher than this while scattering is still proportional to concentration of red blood cells. For this reason, it was felt acceptable to use concentrations of 30% of 10% IntralipidTM_.

The background absorption of diluted IntralipidTM _{is close to that of the water it is} diluted in. Figure 7.3 shows the absorption coefficient of distilled water over the range 650-1050 nm. This data was measured in our own laboratory, and has been published by Matcher et al138_{. It can be seen that at 800 nm, the absorption coefficient of water is approximately 0.0018}

mm–1 _{- well below that of any tissue}34_{. Extra absorber must therefore be added to the}

IntralipidTM_{, to make its optical properties closer to that of tissue.}

7.1.2 Absorbing component of the optical phantom.

made by ICI (Imperial Chemical Industries Wavelength (nm) 600 700 800 900 1000 1100 0.00 0.01 0.02 0.03 0.04 0.05 µa (mm ) -1

Figure 7.3 Absorption coefficient of water.

PLC, Organics Division, Blackley, Manchester, England) was added. This is a pure absorber and so would not add any scattering, unlike India Ink, which has been used by several groups139 _{as an absorber}

(but does introduce some scatter140_{). It was}

assumed that the scattering coefficient of the phantom mixture was independent of the amount of dye added. This would only be true if the total volume of diluted dye added to the tank was small compared to the total volume of IntralipidTM _{solution in the tank, which was} originally intended to be 1300 ml. A set of pipettes were available that could measure from 10

µl to 2500µl. A step size of 200µl of dye was decided upon, as it was neither too small to make measurements inaccurate, nor so large that even with say 20 additions of dye (20 x 200µl = 4 ml), the scattering coefficient changes would only be about 100*4/1500=0.27%. A change inµa of 0.002 mm

–1

for each 0.2 ml (200µl) was chosen, so this required a µa for the dye of

where∆µais the step change in absorption coefficient required (0.002 mm –1

), Vtankis the volume

7.3 µ_a ∆µa Vtank ∆V 0.002×1300 0.2 13 mm 1

of the tank (1300 ml) and ∆V is the amount of dye added to cause the step change (200 µl = 0.2 ml).

Water had previously been added to the S109564 ICI dye, as the lid had been left off

Wavelength (nm) 650 700 750 800 850 900 950 8 10 12 14 µa (mm ) -1

Figure 7.4 Absorption coefficient of the

diluted dye, as measured on an optical spectrometer using a CCD camera detector.

and all the water had evaporated! Hence the optical properties of the dye were unknown, and could not be expected to be similar to any specifications published by ICI. The dye was far too optically dense for the intended use, so had to be diluted. The dilution required was determined retrospectively, after taking measurements of the dye at a known dilution using an infra-red spectrometer attached to a CCD camera. First the absorption spectrum of a 1 cm cuvette, filled with distilled water was

obtained. Then 1% ICI dye was mixed with 99% water (2.4 ml of dye + 237.6 ml of water = 240 ml total), as it was suggested to me by a colleague, Dr. Mark Cope, that 1% might be a sensible starting point. Next the 1% dye solution was further diluted by 50:1, before being put into the cuvette and measured in the CCD, as a 1% dilution would have been too optically dense to measure in a reasonable time. Theµaof the 1 in 5000 mixture was measured at 0.036 mm

–1 at 800 nm, indicating that the 250 ml of dye that had been mixed had a µa of 50*0.036=1.8 mm–1_{. From this it was deduced that the amount of dye needed to be increased by a factor} 13/1.8= 7.22 to increase theµ_ato 13 mm–1_{. Hence extra dye was added. The absorption spectrum} of the final dye mixture used is shown in figure 7.4, which is seen to be 13.08 mm–1at 800 nm. Although originally it was assumed the tank would be filled with 1300 ml, in fact 1500 ml of phantom solution was mixed up. This was to allow the upper fibre to be moved upwards more than the 20 mm available on the slide mechanism, while still being well below the surface. The tank was filled with 1500 ml, so the step change in µa that was caused by the addition of 200

µl of dye with aµ_a of 13.08 mm–1_{, was not 0.002 mm}–1_{, but instead 0.2*13.08/1500=0.00174} mm–1.

Although it had originally been intended to use 200µl additions of dye, it soon became apparent that making measurements with such small steps of µa would have been too time consuming. For this reason, it was decided to use additions of 500µl, which caused step changes inµaof 0.5/1500*13.08=0.00436 mm

–1_{. As the diluted Intralipid}TM_{had a baseline}µ

a of 0.0018 mm–1_{, 500}µ_{l of dye increased this to 0.0018 + 0.00436 = 0.006164 mm}–1_{. Table 7.1, on the next} page, shows the absorption coefficient of the IntralipidTM_{, for volumes of dye from 0 to 3000}

Table 7.1 Absorption coefficient of the IntralipidTM_{/dye mixture}

Amount of dye added (µl) µa (mm

–1 ) 0 0.00180 500 0.00616 1000 0.0105 1500 0.0149 2000 0.0192 2500 0.0236 3000 0.0280 3000 0.0324