Optical Characterization of an Intra-Arterial Light and Drug Delivery System for Photodynamic Therapy of Atherosclerotic Plaque

: Although the versatility of photodynamic therapy (PDT) is well established, the technical aspects of light delivery systems vary signiﬁcantly depending on the targeted organ. This article describes the optical properties of a light and drug delivery system (catheter and light di ﬀ user) suitable for intra-arterial PDT by using a planar imaging goniometer to measure the full radiance longitudinal and angular proﬁles at the surface of the di ﬀ user at 652 nm. The results show that the system emits almost Lambertian and “top hat” proﬁles, an interesting feature to determine the light dosimetry in the many vascular applications of PDT.


Introduction
The versatility of photodynamic therapy (PDT) as a treatment method for different diseases in various organs is well established. However, apart from the general principles underpinning the method, which are unchanged from organ to organ, the technical aspects of the treatment can vary greatly (including, but not limited to, choice of photosensitizer (PS), light dose and fluence rate, drug-light interval (DLI), PS dose and administration mode, and excitation wavelength). One such aspect pertains to light delivery, which is crucially impacted by the geometry, access and sterility properties of the target location. This aspect is particularly central for vascular PDT applications.
In organs with difficult geometries, care must be taken to use or develop suitable diffusers. This is the case for arterial applications of PDT, which have recently regained attention for plaque progression prevention [1][2][3][4][5]. Some studies have reported certain drawbacks (skin photosensitivity [6][7][8]; long DLIs [9,10]; heterogenous illumination leading to irregular effects [11], plaque stabilization instead of ablation or prevention of restenosis; use of PDT for vascular treatments limited to invasive procedures; limited use for acute events; long illumination times sometimes incompatible with clinical and physiological realities [12]), but local PS delivery and homogenous intra-arterial illumination often allow for circumventing them [2]. In all instances, the goal is to achieve a controlled and as

Radiance measurements
An imaging goniometer described in detail elsewhere [11] and presented in Figure 2 was used for the radiance measurements. In brief, this set-up uses a planar goniometer (arm length: 60 cm) to measure the angular and spatial values of the radiance at the surface of cylindrical light diffusers along two axes with a filtered scientific imaging camera (EM-CCD C9100-12, Hamamatsu, Hamamatsu City, Japan) fitted with a zoom lens (TV zoom lens H6 × 2.5R-MD3; 1:1.2, Fuji Photo Optical Co., LTD, Saitama City, Japan) and a neutral density filter of T = 0.1% to avoid saturation. The detector array has 512 × 512 pixels with pixel size of 16 × 16 µm 2 . Images of the radiance were treated by image processing software developed in house to determine, at each angle θ, the longitudinal values of the radiance at the surface of the light diffuser [11]. Interestingly, this software also determines the value of the radiance for different azimuthal angles φ at the surface of the cylindrical light diffuser. Basically, the idea is to exploit the cylindrical symmetry of the diffuser to derive the radiance for different values of φ.  As small (core diameters in the several hundreds of µm) optical fibers are usually used in these applications to deliver up to several hundreds of mW of light following an endovascular route, the natural choice is to use laser sources as light emitters [19]. The main advantage of laser sources for these applications is that they deliver relatively powerful and bright light beams, which can easily be coupled into optical fibers. It should be noted, however, that the nature of this coupling as well as the laser beam specifications have an important influence on the spatial and angular distributions of the intensity emitted by light distributors that are not equipped with mode scramblers.
Generally, radial/cylindrical diffusers offer an interesting way to deliver intravascular illumination for the treatment of acute coronary syndromes and regional atherosclerosis [5,20], especially for plaque stabilization, as opposed to plaque ablation [12].
In the specific case of diffusers used for the treatment of atherosclerotic plaque, numerous groups active in the field use fiber-based diffusers passed through catheters. Caution must be exercised in that case to ensure that the illumination profile of the 10-40 mm-long light-emitting windows is not modified by the catheter's material [21,22]. Longitudinal, azimuthal or radial uncontrolled variations of the light radiance by the catheter can lead to localized irregular light distribution and hence to undesirable effects due to local under-or over-treatments. Similar caution must be exercised when the light distributor is centered within the vessel's lumen with an inflatable balloon. This approach is particularly appropriate when the fiber diameter is much smaller than the lumen diameter. Balloon catheters provide the benefit to interrupt blood flow to center the fiber in the vessel and to remove blood from the illuminated surface, features that are sometimes used intermittently [23,24]. Since it helps in minimizing blood presence in the treated areas, the absorption of the excitation light used for PDT is decreased [25]. Since the blood flow interruption is limited in duration, this feature of balloon catheters can be a disadvantage (limited total delivered light dose) or an advantage (limited risk of side effects) [26]. It should be noted that the duration of this interruption might be significantly increased using "perfusion catheters" that are designed so that the blood flow is not totally interrupted when the balloon is inflated.
Because they do not interrupt the blood flow, bare radial/cylindrical diffusers can be used for longer durations in small (<1 mm) vessels, but require that the illumination wavelength be chosen in the longer-wavelength part of the visible spectrum (>650 nm) to minimize light absorption by the blood. This also results in a comparatively deeper light penetration into tissues, and limits the possible side effects associated with intimal hyperplasia [13] or thrombosis [27]. Instances are reported [28] when the PDT effect described is too weak, a side effect that can be ascribed to the blood absorption of light [28][29][30].
In the case of a radial diffuser such as the one described in Figure 1b, it must distribute light with a longitudinal profile as close as possible to a top hat profile [31][32][33]. Consequently, the light dose (primary incidence) delivered at a given distance from the diffuser can be calculated relatively easily if the distance (d) between the diffuser surface and the vessel wall is smaller than the irradiation length (L) of the diffuser, d << L, see Figure 1b), in particular if its emission is Lambertian. It is noteworthy that, if d >> L, the parameter "d" affects not only the primary irradiance but also the shape of the illumination spot [16,33,34]. This second effect is particularly marked if the light emission (brightness) at the surface of the diffuser is not Lambertian (i.e., is backward-or forward-peaked), as described in detail and illustrated in [34]. This may result in a "translation" of the illumination spot relative to the light diffuser [11,34] with potentially dramatic consequences. Importantly, if the illumination is not Lambertian, light propagation in tissues becomes only isotropic at depths larger than 1/µ s ' (where µ s ' is the reduced scattering coefficient). Thus, if the illumination is not Lambertian, the angular distribution of the radiance at the surface of the light distributor impacts the treatment of lesions thinner than 1 mm, since µ s ' −1 in the red part of the spectrum can reach several hundreds of microns [31,33,35]. This means that, for a Lambertian source, the decrease in fluence rate in tissues starts close to the vessel surface, whereas for a collimated source, this decrease starts up to 1 mm underneath this surface, i.e., when most photons have been scattered, thus impacting any possible PDT effect [34]. It should be noted that the angular distribution of the radiance at the surface of the light distributor also significantly impacts the fluence rate in deep-seated tissues.
Unfortunately, the frequent lack of detailed description of diffusers optical properties makes it somewhat difficult to directly compare different designs and to fully master the light dosimetry associated with a given instrumental configuration [31].
This report describes a system to achieve local, intra-arterial PS delivery (catheter) and illumination (diffuser). The light diffuser's optical properties are characterized, before and after introduction into a catheter, with a dedicated goniometer-based imaging setup designed to conveniently and rapidly measure the longitudinal, polar and azimuthal distributions of the radiance. The analysis of the images of the light emitted by cylindrical diffusers enables us to minimize the moving parts of this unique device and to avoid the bias frequently generated by fully goniometer-based setups.

Catheter and Diffuser
The catheter is a stop-flow double balloon, multi-lumen nylon catheter fitted with a guide wire (based on a modified version of the typical catheter presented in Figure 1a, courtesy of Acrostak AG, Winterthur, Switzerland, and reminiscent in its design and metrics of the GENIE™ commercial catheter supplied by Acrostak AG), allowing injection, filling of an artery segment with a photosensitizing solution and subsequent aspiration thereof. The treatment zone is 30 mm long, and the balloon diameter is 3.5 mm (radial dimension). This configuration allows the positioning of the balloons covering the zone to be treated, and manometer-controlled inflation of the balloons to temporarily interrupt the blood flow during the filling of the treatment zone.
The diffuser used in this study is a commercially available product for clinical investigation (Cylindrical Light Diffuser, model RD20/250) supplied by Medlight SA (Ecublens, Switzerland). Briefly, it is a thin and very flexible (minimum bending radius: 10 mm) cylindrical light diffuser made of a plastic optical fiber with a radially emitting fiber tip producing (as per supplier documentation) a "radial light pattern, which is homogeneous all along the diffuser tip". The diffuser can be supplied with various light-emitting lengths (10,20,25,30,40, 50 and 70 mm). It was decided to use 20 mm, considering the typical size of the lesions to be treated. The core and overall diameter are 280 and 470 µm, respectively. The overall length of the diffuser, customized for our application, is 1 m from the SMA connector to the diffusing tip. The transmission is specified as 85% at 652 nm. The numerical aperture of the fiber is 0.48, and it is fitted with an SMA connecting plug. The diffuser specified maximum power density in air is 0.5 W/cm and its absolute maximum input power is 2.0 W (continuous wave in both cases).

Radiance Measurements
An imaging goniometer described in detail elsewhere [11] and presented in Figure 2 was used for the radiance measurements. In brief, this set-up uses a planar goniometer (arm length: 60 cm) to measure the angular and spatial values of the radiance at the surface of cylindrical light diffusers along two axes with a filtered scientific imaging camera (EM-CCD C9100-12, Hamamatsu, Hamamatsu City, Japan) fitted with a zoom lens (TV zoom lens H6 × 2.5R-MD3; 1:1.2, Fuji Photo Optical Co., LTD, Saitama City, Japan) and a neutral density filter of T = 0.1% to avoid saturation. The detector array has 512 × 512 pixels with pixel size of 16 × 16 µm 2 . Images of the radiance were treated by image processing software developed in house to determine, at each angle θ, the longitudinal values of the radiance at the surface of the light diffuser [11]. Interestingly, this software also determines the value of the radiance for different azimuthal angles ϕ at the surface of the cylindrical light diffuser. Basically, the idea is to exploit the cylindrical symmetry of the diffuser to derive the radiance for different values of ϕ.

Radiance measurements
An imaging goniometer described in detail elsewhere [11] and presented in Figure 2 was used for the radiance measurements. In brief, this set-up uses a planar goniometer (arm length: 60 cm) to measure the angular and spatial values of the radiance at the surface of cylindrical light diffusers along two axes with a filtered scientific imaging camera (EM-CCD C9100-12, Hamamatsu, Hamamatsu City, Japan) fitted with a zoom lens (TV zoom lens H6 × 2.5R-MD3; 1:1.2, Fuji Photo Optical Co., LTD, Saitama City, Japan) and a neutral density filter of T = 0.1% to avoid saturation. The detector array has 512 × 512 pixels with pixel size of 16 × 16 µm 2 . Images of the radiance were treated by image processing software developed in house to determine, at each angle θ, the longitudinal values of the radiance at the surface of the light diffuser [11]. Interestingly, this software also determines the value of the radiance for different azimuthal angles φ at the surface of the cylindrical light diffuser. Basically, the idea is to exploit the cylindrical symmetry of the diffuser to derive the radiance for different values of φ.  The light diffuser, which integrates a mode scrambler, was connected to a 4 watt laser diode (Ceralas ® PDT, 652 ± 4 nm/400 µm, CeramOptec GmbH, Bonn, Germany) and positioned parallel to the axis at the center of the goniometer's rotating platform, with or without the catheter external sheathing around it. Each resulting diagram shows the measurement of the radiance as a function of the longitudinal axis (Figure 3a), polar angle θ (Figure 3b,d, (x, z)-plane) or azimuthal angle ϕ (Figure 3c,e, y-axis). It is important to note that angles close to 0 • and 180 • (Figure 3b,c) were inaccessible to the line of sight of the camera due to the diffuser fixation blocking off the view. In a similar way, angles close to 90 • and 270 • (Figure 3c,e) were inaccessible to the line of sight of the camera due to emission being parallel to the diffuser surface. Further details regarding this measurement setup and procedure are beyond the purpose of this paper and are described elsewhere [11].
3c,e, y-axis). It is important to note that angles close to 0° and 180° (Figure 3b,c) were inaccessible to the line of sight of the camera due to the diffuser fixation blocking off the view. In a similar way, angles close to 90° and 270° (Figure 3c,e) were inaccessible to the line of sight of the camera due to emission being parallel to the diffuser surface. Further details regarding this measurement setup and procedure are beyond the purpose of this paper and are described elsewhere [11].

Results
Typical profiles of a radial diffuser measured at 652 nm (with and without insertion in a catheter) are given in Figure 3. The various profiles given in Figure 3 cover the measurements made to characterize the diffuser chosen for endovascular applications. Figure 3a shows the longitudinal radiance profile of a cylindrical light diffuser for endovascular illumination superimposed with the same measurement in

Results
Typical profiles of a radial diffuser measured at 652 nm (with and without insertion in a catheter) are given in Figure 3.
The various profiles given in Figure 3 cover the measurements made to characterize the diffuser chosen for endovascular applications. Figure 3a shows the longitudinal radiance profile of a cylindrical light diffuser for endovascular illumination superimposed with the same measurement in the catheter sheathing material. Figure 3b shows the polar radiance profile of the same diffuser, in air, expressed as a function of the angle θ of the camera. It is fitted (for visual support only) with a theoretical Lambertian profile (red dotted line). Figure 3d shows the same measurement for the same diffuser placed into the catheter sheathing material. Figure 3c shows the azimuthal radiance profile of the same diffuser, in air, expressed as a function of the angle ϕ with the horizontal plane (x, z) where the camera rotates. It is fitted (for visual support only) with a theoretical Lambertian profile (red dotted line). Figure 3e shows the same measurement for the same diffuser placed into the catheter sheathing material. The intra-figure comparison of the two curves in Figure 3a and the pair comparison of Figure 3b,d, as well as Figure 3c,e indicate that, in all cases, the profile is only minimally modified by the insertion of the diffuser into the catheter sheathing.

Discussion
This study aimed at exploring concepts often overlooked in the context of PDT, in particular in intravascular PDT, namely the accurate and complete description of the light delivery to the target tissue by the light distributor.
The overall objective of the exploration was to fully characterize the angular distribution of the radiance at the surface of light distributors along two directions, in order to better master the desired therapeutic results. The radiance imaging setup used for this purpose is of great interest since, in spite of the concern potentially associated with a limited control of light distribution profile compared to what is expected, few light delivery systems are optically characterized in great detail [31,35,36]. This setup is original in the sense that it enables measuring the spatial and angular distribution of the radiance, which is a directional radiometric quantity, of cylindrical light distributors with a minimal number of moving parts. Indeed, the analysis of the images provided by this setup enables us to determine the value of the radiance according to one angle, the angle ϕ in the present study, in "real time" (potentially in a fraction of second), whereas fully goniometer-based setups are much less convenient and are more subject to bias [11]. Indeed, one critical problem faced by the conventional fully goniometer-based setups is in relation with their pointing stability while measuring the angular distribution of the radiance emitted by a "small" surface element of the distributor.
It should be noted that a cheap camera, optimized in terms of sensitivity, linearity and resolution for specific cylindrical light distributors, could be used to record the image, enabling us to determine the angular distribution of the radiance along one of the angles without moving parts.
The radiance measurements show that the diffuser emits a stable, almost ideal Lambertian profile at 652 nm, a wavelength of interest in PDT. Additional comparisons with its profiles at 635 (4 watts diode laser Ceralas ® PDT, 635 ± 3 nm/400 µm, CeramOptec GmbH, Bonn, Germany) and 730 nm (Diode laser LTL730S 730 nm, TechLaser, Shanghai, China) showed that the diffusers' radiance profile was remarkably similar at these three wavelengths (data not shown). In addition, the profile is almost perfectly rectangular when measured longitudinally in air. This observation, combined with the almost perfectly Lambertian emission, is of importance to fully master the light dosimetry, and, as far as the longitudinal profile is concerned, is in good agreement with the claims of the manufacturer providing the cylindrical light distributor. This is also a positive result for possible clinical applications since it means that the diffuser can be aligned with the lesion to emit light where it is needed, with a minimal dependence on the vessel's diameter and on the chosen PS/illumination wavelength. The deviations from ideal longitudinal and Lambertian profiles probably have different origins. The longitudinal variations are likely to be due to a heterogeneous processing of the fiber core to decouple the light, whereas the deviations from a Lambertian profile are probably due to the Snell's law effect which takes place at the diffuser-air interface. Since the angular dispersion of the light exiting the diffuser is minimal for nearly orthogonal rays, this effect generates a forward-peaked emission, even if the light is isotropic in the distributor wall. It should be noted that this effect is probably significantly reduced if the distributor is surrounded by tissues or blood instead of air, since the refractive index step is reduced. The implications of these limited deviations on the treatment outcome are certainly minimal since the lengths of the longitudinal heterogeneities are smaller than the propagation length of red light in soft tissues [37]. Importantly, the deviations from ideal longitudinal profiles have a reduced effect if the distributor surface and the tissue are not in contact since the irradiance applied to the lesion results from the contribution of a large surface of the diffuser surface.
Wavelengths in the red or NIR are usually preferred to treat atherosclerotic plaque by PDT because of their deeper penetration in most soft tissues compared to shorter wavelengths [37]. In addition, their homogenous distribution in these tissues makes these wavelengths optimal for endovascular applications. Since their absorption is much smaller than their scattering in the blood vessel wall Appl. Sci. 2020, 10, 4304 7 of 11 or in the surrounding tissues, the fluence rate can be calculated using the diffusion approximation, as proposed by Ishimaru [38]. The steady-state expression to calculate the fluence rate in the tissue is: where φ(r) is the fluence rate (mW/cm 2 ), µ eff = [3µ a (µ a + µ s (1 − g)] 1/2 is the effective attenuation coefficient (mm −1 ), D = µ a /µ eff 2 is the optical diffusivity (mm), and q is the diffusive photon density (mW/cm 3 ). The absorption and scattering coefficients, µ a (mm −1 ) and µ s (mm −1 ), correspond to the inverse of the photon's mean free path before they are absorbed or scattered, respectively. g is the scattering anisotropy factor, which relates the reduced scattering µ s ' (mm −1 ) and the scattering coefficients in the expression: µ s ' = µ s (1 − g). The solution of Equation (1) for the fluence rate "far" (i.e., at several times µ s ' −1 ) from the source and interfaces produced by an infinitely long light diffuser inserted in a tissue in a cylindrically symmetric configuration is given by [39]: where P is the optical power per unit length (mW/mm) of the light diffuser with radius a (mm). K 0 and K 1 are the modified Bessel K functions of the zero and first order, respectively. The distance from the diffuser axis is expressed as r (mm).
Since the length of light diffusers used to treat atherosclerotic plaque by PDT in coronary arteries ranges between 10 and 40 mm, and since their diameter is much smaller (between several hundreds of microns and one millimeter), expression (2) can be used if the diffuser is in contact with the vessel wall.
This expression can also be used if the light diffuser is inserted at the center of a transparent balloon, provided that the radius of this balloon is much smaller than µ eff −1 and the length of the illuminated section of the artery. In that rare situation, which prevails only when NIR light is emitted by a small (diameter of 1 mm or less) balloon, the parameter a (mm) corresponds to its radius. This means that expression (2) can be used to calculate the fluence rate in the wall and around coronary arteries assuming uniform optical coefficients. The picture is different if PDT is performed in larger vessels, as is the case for peripheral atherosclerotic disease. In that case, expression (2) is no longer valid since the radius of the vessel can be in the order of the diffuser's length. An estimate of the fluence rate in the tissues at depths "z" larger than 1 mm is given by expression (3) if the balloon radius and the diffuser's length are much larger than µ eff −1 [40,41]. This situation is analogous to a "broad" (i.e., the two dimensions of the illumination spot are much larger than µ eff −1 ) uniform illumination of a "flat" (i.e., the smaller radius of curvature of the tissue surface is much larger than µ eff −1 ) air-tissue interface.
where E is the irradiance (mW/cm 2 ), z (mm) is the distance from the air-tissue interface and k is a term that describes how backscattered light increases the irradiance delivered to the surface, yielding an elevated fluence rate near the surface. Its value, which is typically in the range of 3-6 for soft tissues in the red or NIR, depends on the tissue optical properties as well as on the refractive index matching conditions [41]. Its accurate value can be determined using Monte-Carlo simulations of the propagation of light [34,42,43]. In this case, however, the angular distribution of the radiance at the surface of the light distributor must be known, a situation illustrating the interest of performing directional radiometric measurements, as reported in this paper. Using optical coefficients compiled by Roggan [44] for the aorta at 630 nm, the value of k is about 5 if the refractive indexes are mismatched [41,43]. It should be noted that expressions (2) and (3) are solutions of the diffusion approximation. Therefore, these solutions are only valid if the hypotheses that are at the origin of this approximation are fulfilled, in particular if the light flux in the tissues is isotropic. This condition is clearly satisfied at a much closer distance (less than µ s ' −1 ) from the light distributor if its emission is Lambertian rather than collimated, a fact that also illustrates the interest of multi-directional radiometric measurements. This concept is illustrated in Figure 4, which presents a comparison between the values of the normalized fluence rate determined according to Equation (3) or by Monte-Carlo simulations in the cases of broad illuminations of an air-tissue interface. This figure presents the evolution of the fluence with depth when the semi-infinite tissue, presenting the optical properties reported by Roggan [44] at 630 nm for the aorta, is subject to a collimated or a Lambertian illumination. The fluence rate is normalized in the sense that its absolute value is divided by the irradiance applied at the air-tissue interface. The Monte-Carlo simulation was based on commercially available software (Tracepro; Lambda Research Corporation, Littletown, MA, USA) and hardware described in details by Pitzschke et al. [45].
by Roggan [44] for the aorta at 630 nm, the value of k is about 5 if the refractive indexes are mismatched [41,43].
It should be noted that expressions (2) and (3) are solutions of the diffusion approximation. Therefore, these solutions are only valid if the hypotheses that are at the origin of this approximation are fulfilled, in particular if the light flux in the tissues is isotropic. This condition is clearly satisfied at a much closer distance (less than µs' −1 ) from the light distributor if its emission is Lambertian rather than collimated, a fact that also illustrates the interest of multi-directional radiometric measurements. This concept is illustrated in Figure 4, which presents a comparison between the values of the normalized fluence rate determined according to Equation (3) or by Monte-Carlo simulations in the cases of broad illuminations of an air-tissue interface. This figure presents the evolution of the fluence with depth when the semi-infinite tissue, presenting the optical properties reported by Roggan [44] at 630 nm for the aorta, is subject to a collimated or a Lambertian illumination. The fluence rate is normalized in the sense that its absolute value is divided by the irradiance applied at the air-tissue interface. The Monte-Carlo simulation was based on commercially available software (Tracepro; Lambda Research Corporation, Littletown, MA, USA) and hardware described in details by Pitzschke et al. [45]. As illustrated in Figure 4, the shape of the fluence rate is significantly different, for an identical irradiance, at the tissue "surface" (where atherosclerotic plaques potentially sit) if the illumination is collimated or Lambertian. This difference is significant down to about 0.4 mm, i.e., µs' −1 , as expected (see the red squares). Importantly, the pre-exponential factor "k", used to fit the spatial evolution of the fluence rate with a solution of the diffusion approximation (Equation (3)), decreases from about 5.15 to 3.99 (more than 25% difference in our conditions) when a Lambertian illumination is considered instead of a collimated one. As a consequence, the nature of the tissue illumination (collimated or Lambertian) affects the fluence rate significantly, even in deep-seated tissues.
If, depending on the light delivery design, the balloon or the diffuser radius is comparable to µeff −1 , as is the case when red light is used to treat plaque in the carotid, neither expression (2) nor (3) is valid. It should be noted, however, that the fluence rate can still be estimated analytically since it is confined within an interval defined by the values calculated with these two expressions, as discussed by Profio et al. [40].
When calculating the light dosimetry for the treatment of atherosclerotic plaque by PDT, it is important to consider edge effects. These effects are significant, in particular if the diffuser length is in the order of µeff −1 . They are due to the lateral spreading of light within the tissues. This spreading is balanced and canceled at the center of the illuminated area, whereas it is not the case close to the As illustrated in Figure 4, the shape of the fluence rate is significantly different, for an identical irradiance, at the tissue "surface" (where atherosclerotic plaques potentially sit) if the illumination is collimated or Lambertian. This difference is significant down to about 0.4 mm, i.e., µ s ' −1 , as expected (see the red squares). Importantly, the pre-exponential factor "k", used to fit the spatial evolution of the fluence rate with a solution of the diffusion approximation (Equation (3)), decreases from about 5.15 to 3.99 (more than 25% difference in our conditions) when a Lambertian illumination is considered instead of a collimated one. As a consequence, the nature of the tissue illumination (collimated or Lambertian) affects the fluence rate significantly, even in deep-seated tissues.
If, depending on the light delivery design, the balloon or the diffuser radius is comparable to µ eff −1 , as is the case when red light is used to treat plaque in the carotid, neither expression (2) nor (3) is valid. It should be noted, however, that the fluence rate can still be estimated analytically since it is confined within an interval defined by the values calculated with these two expressions, as discussed by Profio et al. [40]. When calculating the light dosimetry for the treatment of atherosclerotic plaque by PDT, it is important to consider edge effects. These effects are significant, in particular if the diffuser length is in the order of µ eff −1 . They are due to the lateral spreading of light within the tissues. This spreading is balanced and canceled at the center of the illuminated area, whereas it is not the case close to the edges where lateral diffusion is unbalanced. As described by Jacques [41], edge losses at the periphery of a longitudinally uniform beam extend about 3µ eff −1 from the beam edge. This corresponds to about 4 mm when using the optical coefficients reported by Roggan [37,44] at 630 nm for the aorta.
Only when the extent of the illuminated area exceeds 6µ eff −1 is the fluence rate in the central zone (where the plaque is supposed to be located) longitudinally uniform. Finally, it should be noted that the plaque itself frequently presents optical properties that are not only heterogeneous but also significantly different compared to those of the normal surrounding tissues [46]. Since these optical properties cannot realistically be determined before each treatment, one reasonable strategy is to adjust the light dosimetry on the basis of the type of plaque to be treated.
Intra-arterial applications require that the diffuser be inserted into a catheter to reach the desired position. The measurements reported here for a modified commercially available catheter designed for drug delivery demonstrated that the plastic sheathing produced by this specific catheter has virtually no impact on the light emission profile of the diffuser, making it a suitable system to illuminate optimally intra-arterial lesions and avoid absorption, with a possible resulting heating, or a patchy or irregular illumination pattern, which could possibly have negative consequences.
Overall, these results show that this system displays optimal illumination and dosimetry properties to achieve the sought-after results.