Solution of the infrared tomography inverse problem

Infrared tomography is a non contact method to determine the size and position of port wine stain blood vessels from analysis of recorded infrared emission images immediately following pulsed laser irradiation. To develop a diagnostic tool for clinical use, infrared emission images from laser irradiated tissue have been simulated on a computer. Analysis of the simulated infrared emission images shows that size and position of the laser heated vessels can be predicted.


INTRODUCTION
Port wine stains (PWS) are congenital hypervascular cutaneous malformations that appear as a light red to purple discoloration of human skin.' Irradiation with a flashlamp pumped pulsed dye laser (A = 585 nm, pulse duration 'i = 450ps) has become the treatment of choice, however, some patients experience a poor clinical result with sub-optimal fading. Several reasons for the poor response have been proposed. Tan et al.2 suggest that laser wavelength should be adjusted to maximize the depth of damaged vessels. Alternatively, theoretical3'4 and clinical studies5 suggest the ideal pulse duration is between 0.5 and 10 ms, and depends on vessel diameter. Knowledge of vessel size and position prior to laser therapy can guide the clinician to select the appropriate pulse duration and wavelength for optimal treatment results.
The traditional method to determine PWS vessel diameter is analysis of a biopsy specimen using light microscopy. This technique is invasive and invariably leaves a scar. Furthermore, results are of questionable practical value as artifacts may be introduced during processing of the tissue specimen.
Infrared tomography (IRT)6'7 uses a fast infrared focal plane array (IR-FPA) camera system to measure increases in infrared emission at the skin surface following pulsed laser irradiation. From the recorded time sequence of infrared emission images, size and position of subsurface chromophores can be deduced.
A mathematical relationship between the time sequence of infrared emission images and the temperature distribution within the skin immediately following pulsed laser irradiation is defined. Using this relationship, the size and position of three vessels in our model of skin is correctly estimated from a simulated time sequence of infrared emission images.

THEORY
The measured change in infrared emission at the the tissue surface (A.M(x, y, t)) following pulsed laser irradiation is given by,7 = JfJ KT(X -, y -, (,t)T3'(, i,(;t0)ddidC (1) where LiT3D is the three-dimensional temperature increase in skin at the end of the laser pulse (t = t0). The three-dimenensional thermal point spread function, KT,6'7 is an analytical expression derived from solution of the bioheat equation. 8 Lateral dimensions x and y refer to position on a plane parallel with the surface, while is distance into the tissue from the surface (z = 0).
The three-dimensional thermal point spread function is dependent on tissue parameters in Table 1

METHODS
A program employing a non-negative constrained conjugate-gradient algorithm to solve Eq. 1 has been implemented on a DEC Alpha 3000 computer. In this technique, the initial estimate for LT3D is taken to be zero, and adjusted at successive iterations to minimize the difference between the simulated time sequence of infrared emission images and that computed from Eq. 1 . The algorithm is constrained so that negative values of are not permitted.
Three simulated rectangular parallelpiped blood vessels (60 x 60 x 600 jim3), lateral separation 300 m, depth 250 pm, were positioned in a 1 x 1 x 0.75 mm3 volume of skin. The three-dimensional temperature increase in skin immediately following pulsed laser irradiation, ZT3D, was stored in a 64x64x64 element array in the computer, where each element represents a voxel of the simulated skin volume (Fig. 1). Light absorption in the epidermis was neglected. Infrared emission images of the skin surface at 64 uniformly spaced time points in the interval (0,0.42] 5 was used as input to the conjugate-gradient algorithm. The algorithm does not require any particular geometry, but this model was selected to simplify our analysis. y-axis (mm) Figure 1: The position of vessels in skin model and coordinate system used.
The computed image simulates results from an IR-FPA camera operating in "snapshot mode" , where all pixels are active at the same time. For this technique to be used with cameras that operate in "rolling readout" mode, additional processing is required to assign a varying time offset to the data from each pixel in the IR-FPA.

RESULTS
Initial result after 50 iterations of the constrained conjugate-gradient program are shown in Fig. 2, which required one hour of CPU time on a DEC Alpha 3000 computer. From Fig. 2a and 2b

CONCLUSIONS
Our simulation shows that the depth and lateral position of PWS vessels can be predicted from the time sequence of recorded infrared emission images. For this simulation, the vessel diameter is overestimated but underestimates the peak temperature.