Infra-red tomography of port-wine-stain blood vessels in human skin

Specifying the distribution of laser energy within a tissue is the first step towards understanding and capitalizing on a variety of laser-tissue interactions. Whether photothermal, photochemical or photomechanical in nature, laser-tissue interactions begin with the absorption of photon energy. The spatial distribution of photon absorption specifies the required laser exposure to be delivered and the extent of subsequent therapeutic action. Using infra-red tomography (IRT), the broad, long-term objective of this research is the development of a tomographic reconstruction algorithm as a means to determine: (1) the depths and physical dimensions of discrete subsurface port-wine-stain (PWS) blood vessels in human skin; and (2) the initial space-dependent temperature increase in PWS blood vessels immediately following pulsed laser exposure. In this report, preliminary studies are described which demonstrate the potential application of IRT in the clinical management of PWS patients.


INTRODUCTION
Although the flashlamp-pumped pulsed dye laser has offered a superior approach in therapy due to its ability to destroy port-winestain (PWS) blood vessels selectively (1)(2)(3), onty a small proportion oF patients obtain 100% fading of their PWS, even after undergoing multiple laser treatments (4-7). One ~eason for poor results or treatment failure may be the lack of specificity in choosing the optimal pulse duration and light dosage to be delivered. Now that laser systems with userspecified pulse durations and light dosages are available commercially, how will the clinician select the optimal parameters for laser exposure?
Infra-red tomography (IRT)uses a fast infrared focal plane array (IR-FPA) camera to detect temperature rises in a substrate induced by pulsed radiation. The temperature rise, due to the selective optical absorption of pulsed ~aser light, creates an increase in infra-red (blackbody) emission which is measured by a 9268-8921/96/030199+06 $12.00/0 fast IR-FPA. For the purposes of IRT, chromophores in human skin can be modelled as a three-dimensional distribution of subsur~hce absorbing structures. In this model, when a pulsed laser source is used to irradiate the skin, an immediate increase in infra-red emission ~ill occur due to heating caused by optical absorption in the chromophores. The absorbing chromophore's physical dimensions are best resolved in initial infra-red emission images when thermal diffusion is limited. Infra-red emission in later images is distributed more uniformly in space due to thermal diffusion.
An IRT record of human skin in response to pulsed laser exposure is composed of a time sequence of infra-red emission images that indicate localized heating of the subsurface chromophores. Analysis of the images contained within the IRT record at each PWS site by a tomographic reconstruction algorithm provides information on: (1) the depths and physical dimensions of discrete subsurface PWS blood vessels in human skin; and (2) the initial space-dependent temperature increase in PWS blood vessels immediately following pulsed laser exposure (8). Such information can be used by the clinician to select the optimal laser pulse duration and light dosage on an individual patient basis throughout an extended treatment protocol. In this report, preliminary studies are described which demonstrate the potential application of IRT in the clinical management of PWS patients.

MATERIALS AND METHODS
The IRT integral equation, Equation l(a), can be written as a multi-dimensional convolution integral that relates the measured time sequence of infra-red emission images, AM(x,y;t) (~ where x,y;t are the tissue surface coordinates and time, respectively, to the initial space-dependent temperature increase, AT~v(~,q,~;t=0) (~ of discrete subsurface PWS blood vessels at position (~,q,0, immediately following pulsed laser exposure (pulse ends at t=0): where Kr (m -e) and KT(x-~,,y-q,~;t) (m-a) represent, respectively, the camera and thermal point spread (ie Green's) functions.
The camera point spread function (Kc) describes the inherent limitations of the IR-FPA camera which includes effects due to size of the collection aperture, lens aberrations, finite number and size of discrete detector elements.
The IRT integral Equation l(a) represents a forward problem in which a time sequence of measured infl'a-red emission images [AM(x,y;t)] may be computed from the initial space-dependent temperature increase, ATBv(~,q,~;t=0), and the known biophysical properties of human skin. Inasmuch as only hM(x,y;t) is available as input data, determination of ATBv(~,qf,;t=0) in the IRT integral Equation l(a) constitutes an ill-posed mathematical inverse problem (Equation 4): Computationally efficient one-dimensional longitudinal inversion and two-dimensional lateral deconvolution algorithms have been developed to eliminate the effects of lateral heat diffusion and limited camera spatial resolution on AM(x,y;t). Such an approach permits reconstruction of an image of individual blood vessels immediately after the laser pulse is delivered. Furthermore, whereas the spacedependent temperature increase is always positive (% ATBv_>0), a non-negative constrained conjugate gradient algorithm is used for improved solution estimates (10). A number of preliminary experiments have been conducted on PWS patients that test ~he performance of the authors' non-negative constrained conjugate gradient longitudinal inversion and lateral deconvolution algorithms. A compound infra-red lens (f/5, 50 nun diameter) imaged the surface increase in infrared emission intensity from the PWS skin on to a 128 • 128 InSb IR-FPA (Fig. 1). The camera system acquired 217 infra-red emission images per second and was triggered externally by a digital delay generator that was triggered optically by a fast silicon photo receiver, The infra-red signal collected by each detector element was digitized with a 3.5 MHz 12-bit (0-4,095) A/D converter and stored in the computer's random access memory. Immediately following exposure (%=585nm; ~p=0.45ms; spot diameter 5 ram), the IR-FPA camera system acquired a time sequence of infra-red emission images AM(x,y;t).
Temperatures as recorded in infra-red emission fl:ames AM(x,y;t) were calibrated fbr each IRT experiment. A resistor-heated aluminum surface coated with highly emissive (~>0.967) black paint was positioned in object space at the conjugate plane of the IR-FPA. A surface mount thermistor measured the temperature (sensitivity 0.01 ~ as the surface was heated slowly (1 ~ rain-J). Calibration data matched closely the curve derived from Planck's law.
Twelve subjects were recruited for this ongoing ewfiuation from an on-site population of PWS patients at the Beckman Laser Institute and Medical Clinic, University of Calitbrnia, Irvine, USA. Permission to conduct the experimental protocol was obtained from the Human Subjects Review Committee Medical (Institutional Review Board). Port-wine-stain test sites were selected on inconspicuous sectors of the PWS (eg under the arm) that were representative of the entire lesion.   (b) Depths of the epidermal melanin layer (50+_25/~m) and port-wine-stain blood vessels (275+_75 pm) determined by longitudinal inversion algorithm match the mean depths measured directly using histopathology.

RESULTS
Immediately following exposure to a 1.0J laser pulse (5.0 J cm-2), a timed sequence of 100 infra-red emission frames AM(x,y;t) was recorded over 460ms with the IR-FPA camera system. From this sequence, the onedimensional quantity AM1-D/BV(t) was determined [ Fig. 2(a)] by averaging over an area (5A=1.5 mm 2) positioned at the centre of laser exposure. Using the non-negative constrained conjugate gradient algorithm, the longitudinal inverse problem was solved [ Fig. 2(b)] for the Fig. 3. (a) Measured infra-red emission image ZXMBv(x,y;to=77 ms). (b) Infra-red emission exclusively from the deeper discrete port-wine-stain blood vessels is computed by subtracting from AMBv(X,y;to=77 ms) the infra-red emission due to epidermal melanin heating. Solution of the lateral deconvolution problem (AT2-D/BV) allows determination of the lateral physical dimensions (150-200/~m) of discrete laser-heated subsurface PWS blood vessels. The mean temperature increase (ATo=48 ~ of laser-heated discrete PWS blood vessels was computed from the fractional blood vessel area (f=0.42) in the deconvolved infra-red emission image and one-dimensional temperature increase [AT1-D/BV(z,t=0)] as determined from, respectively, the solutions of the lateral deconvolution and longitudinal inversion algorithms.
For the same PWS site, AM~v(x,y;t0=77 ms) was measured [ Fig. 3(a)]. Infra-red emission exclusively from the deeper discrete PWS blood vessels is computed by subtracting from AM~v(x,y;t0= 77 ms) the infra-red emission due to epidermal melanin heating (8). Solution of the lateral deconvolution problem (AT2-D/BV) using the subtracted image as input data allows determination of the lateral physical dimensions (150-200/1m) of discrete laserheated subsurface PWS blood vessels [ Fig.  3(b)]. The mean temperature increase (ATo= 48~ of laser-heated discrete PWS blood vessels was computed from the fractional blood vessel area (f=0.42) in the deconvolved infra-red emission image and one-dimensional temperature increase [AT1-D/BV(z,t=0)] as determined from, respectively, the solutions of the ]ateral deconvolution and longitudinal inversion algorithms.

DISCUSSION
Histopathological studies of PWS show a plexus of layers of dilated blood vessels located below the skin surface in the upper dermis. Port-wine-stain blood vessel diameters vary on an individual patient basis, and even from site to site on the same patient over a range of 10-150~1m (12). The thermal relaxation time (r,.) is defined as the time required for the core temperature, produced by the absorbed light energy within the target blood vessel, to cool to one-half of its original value immediately after the laser pulse and may be expressed: where dBv is the diameter of the targeted blood vessel and Z is the thermal diffusivity of skin (0.11 mm 2 s-l). For vessels with diameters of 10, 70 and 150/zm, r r has calculated values of 0.06, 2.8 and 12.8 ms, respectively. The pulse duration of laser exposure (t~)) governs the spatial confinement of heat and should, ideally, match the thermal relaxation time (%) for the targeted blood vessels (13). If longer pulse durations are employed (tp~z~.), heat diffuses outside the vessel during laser exposure. The target specificity is reduced resulting in non-specific thermal damage to adjacent structures. Alternatively, if too short a laser pulse is used (tp ~.zr), high-peak intravascular temperature roses can produce explosive vaporization of tissue water, or photo-acoustic transients which can result in vessel rupture. In such cases, repair mechanisms may revascularize the PWS. In conclusion, selection of the tase~ exposure crucial to successful blood vessel destruction. Only when tp ~an the criti~a! core intravas, cular temperature, necesSary ~o destroy large PWS blood vessels irreversibly, be achieved and sustained for sufficient time (14,15).
tt is important to be aware that like pulse duration, light dosage (J cm-2) is also dependent on blood vessel diameter. For larger vessels, as energy deposition is limited by the optical penetration depth in whole blood (u-~=30~m at 585 nm) higher light dosages must be administered tO reachl and sustain for sufficient time, the necessary critical core intravascular temperature (16,17). Therefore, for the clinician to select the optimal light dosage as a function of pulse duration correctly, knowledge of the initial spacedependent temperature increase in subsurface PWS blood vessels [AT~v(%,q,~;t =0)] immediately following p~Ised laser exposure is required.
For laser pulses in the millisecond domain, irreversible damage to PWS blood Vessels is assumed to occur at core temperatures higher than 80~ (16). Once ATuv(%,q,~;t=0) has been determined from the IRT record in response to a diagnostic sub-therapeutic laser pulse of duration t o and light dosage Do, the therapeutic laser light dosage (Dews) necessary to destroy the PWS blood vessels can be computed appropriately from Equation 6 knowing the critical temperature increase, ATe=50 ~ (assuming an ambient skin temperature of 30 ~ AT c tp (1-e -to/'r) Dpws=D~ to (1--e-tp '~) The rationale for using IRT in the clinical management of patients with PWS is that the technique offers a means of documenting the vascular characteristics of PWS on a site-tosite basis for each patient. Prior to the institution of laser therapy, in response to a subtherapeutic diagnostic laser pulse, analysis of the measured time sequence of emission images [AM(x,y;t)] contained within the IRT record at each PWS site by the tomographic reconstruction algorithm provides information on: (1) the depths and physical dimensions of the most superficial absorbing PWS blood vessels inside the beam spot of uniform light intensity; and (2) the initial space-dependent temperature increase [ATBv(%,~i~;t=0)] within the blood vessels immediately following pulsed 203 laser exposure:Such information can be used by the clinician to help select the optimal parameters (pulse duration and light dosage) the ~rst laser treatmentl ~nce the mean diameter of PWS blood vessels (d~v) inside the beam spot is determined from the deconvolved image, tp can be calculated (14,18). With ATBv(%,q,~;t=0) determined, the therapeutic laser light dosage (Dpws) to destroy the PWS blood vessels can be computed from Equation 6. At the next patient visit, a second IRT record is made. As the majority of the most superficial PWS blood vessels were obliterated by the first laser treatment, the diagnostic laser pulse no~ images a deeper absorbing layer of PWS blood vessels. The optimal parameters (pulse duration and light dosage) for the second laser exposure are selected based on analysis of the IRT record, and a second treatment is performed. Proceeding in this manner, the IRT record probes deeper and deeper absorbing layers of the PWS after the most superficial layers are removed by each successive treatment at the same site. In conclusion, information provided by IRT can be used by the clinician to select the optimal laser pulse duration and light dosage on an individual patient basis throughout an extended treatment protocol.