In-vivo light dosimetry for HPPH-mediated pleural PDT

Abstract

This study examines the light fluence (rate) delivered to patients undergoing pleural PDT as a function of treatment time, treatment volume and surface area. The accuracy of treatment delivery is analyzed as a function of the calibration accuracies of each isotropic detector and the calibration integrating sphere. The patients studied here are enrolled in a Phase I clinical trial of HPPH-mediated PDT for the treatment of non-small cell lung cancer with pleural effusion. Patients are administered 4mg per kg body weight HPPH 24-48 hours before the surgery. Patients undergoing photodynamic therapy (PDT) are treated with light therapy with a fluence of 15-60 J/cm² at 661nm. Fluence rate (mW/cm²) and cumulative fluence (J/cm²) is monitored at 7 different sites during the entire light treatment delivery. Isotropic detectors are used for in-vivo light dosimetry. The anisotropy of each isotropic detector was found to be within 15%. The mean fluence rate delivery and treatment time are recorded. A correlation between the treatment time and the treatment volume is established. The result can be used as a clinical guideline for future pleural PDT treatment.

1. Introduction

This study examines the light fluence (rate) delivered to patients undergoing pleural PDT as a function of treatment time, treatment volume and surface area. The accuracy of treatment delivery is analyzed as a function of the calibration accuracies of each isotropic detector and the calibration integrating sphere.

Using measured optical properties performed in-vivo, theoretical calculations can be performed to determine the relationship between the treatment time and the treatment area and compared to the measured results. Long term accuracy of in-vivo light dosimetry was studies by examining individual calibration accuracies of the integrating sphere used for detector calibration, the detector anisotropy, and the overall calibration factor uncertainties over a long period of time.

2. Methods

2.1 Patient treatment

The patients studied here are enrolled in a Phase I clinical trial of HPPH-mediated PDT for the treatment of non-small cell lung cancer with pleural effusion [1]. Patients are administered 4mg per kg body weight HPPH 24-48 hours before the surgery. Patients undergoing photodynamic therapy (PDT) are treated with light therapy with a fluence of 15-22.5 J/cm² at 661nm. Fluence rate (mW/cm²) and cumulative fluence (J/cm²) is monitored at 7 different sites during the entire light treatment delivery. A dilute intralipid solution (1%) was placed in the pleural cavity as a light scattering agent. Seven isotropic detectors were sewn to the wall of the pleural cavity for monitoring the light dose in the following sites: Apex, anterior medial chest wall (ACW), posterior chest wall (PCW), posterior diaphragmatic sulcus (PS), anterior diaphragmatic sulcus (AS), posterior mediastinum (PM) and pericardium (Peri). The illumination was delivered under manual control until the prescribed dose of 60 J/cm² was reached at all sites.

In this study, we analyzed data for five patients. All patients were male, their ages varying from 59 to 72. All patients kept both lungs intact.

2.2 Theory of light fluence distribution in pleural cavity

Considering the case of additional absorption from the non-scattering medium inside the pleural cavity, e.g., due to bleeding, the light fluence rate can be calculated [2]:

$$\phi =\frac{4S}{A_s}\cdot \frac{\rho \cdot e^{-{\mu }_{a}r}}{1-\rho (1-f)}$$ (1)

where ma is the absorption coefficient of the non-scattering liquid and r is the mean radius of the pleural cavity. The diffuse reflectance can be calculated based on the optical properties of the thoracic wall [3]:

$$\rho =\frac{a^{\prime }}{2}(1+e^{-(4/3)A\sqrt{3(1-a^{\prime }}})e^{-\sqrt{3(1-a^{\prime })}}$$ (2)

Where $a^{\prime }={\mu }_s^{\prime }/({\mu }_a+{\mu }_s^{\prime })$ is the transport albedo, A, the internal reflection parameter is a function of the ratio of the index of reflection of the two media. For a water-tissue interface, one can determine that A = 1.25 using n_water = 1.33 and n_t =1.4.

Using the relationship between the time and total light fluence: Ψ = φ ·t and Eq. (1), one finds the relationship between the treatment time and the treatment area:

$$t=k\cdot A_s$$ (3)

Where

$$k=\frac{\mathrm{\psi }}{4S}\frac{e^{{\mu }_a\cdot r}}{\rho (1-f)(1+\rho (1-f)+{\rho }^2{(1-f)}^2+\dots )}=\frac{{\mathrm{\psi }}_{e^{{\mu }_{a}r}}}{4S}\left(\frac{1-\rho (1-f)}{\rho (1-f)}\right)$$ (4)

Where $f=\frac{A_{\mathit{\text{open}}}}{A_{\mathit{\text{total}}}}=0.25$, Y = 15 - 22.5 J/cm² is the total fluence, S is the laser power (see table 2), r is the mean radius of the cavity, we estimated r = 8 cm for the patient population studied, and r is the diffuse reflectance, which is a function of tissue optical properties (μ_a and μ_s′)

Table 2.

Treatment time vs treatment area and volume.

SN	V(m3)	time (s)	S (cm2)	k (s/cm2)	Φ (J/cm2)	S (W)	μ (cm-1)
1	N/A	1924	---	---	15.0	8	---
2	N/A	1450	---	---	15.0	6	---
3	1.60	4654	661	7.04	15.0	5	0.27
4	1.60	4135	661	6.26	15.0	6	0.17
5	3.00	4233	1006	4.21	22.5	7	0.04
avr	2.07	3279.2	776.0	5.84	16.5	6.4	0.16

2.3 Determination of tissue optical properties

The optical properties before and after PDT treatment were determined by analyzing the diffuse reflectance spectra measured in four channels of the detection probe using an algorithm that quantifies the scattering spectrum and contributions to absorption of hemoglobin and photofrin [4].

The optical properties of various tissues in the thoracic cavity were measured using and optical probe consisting of a source fiber illuminated by a white light source and a series of detection fibers, as described previously [5]. The optical properties before and after PDT treatment were determined by analyzing the diffuse reflectance spectra measured in four channels of the detection probe using an algorithm introduced by Finlay and Foster [5, 6]. From these parameters, the best-fit optical properties at the wavelength of treatment (630nm) can be determined. Table 1 lists the minimum, maximum, and mean values of each parameter from among the 5 patients made on various tissue types.

Table 1.

Summary of measured in-vivo optical properties in pleural PDT patients.

		μa			μs′			μeff
		min	max	mean	min	max	mean	min	max	mean
pat1	Aorta	0.35	0.66	0.47	3.80	6.99	5.22	2.32	3.88	2.80
	Chestwall	0.13	0.96	0.50	9.83	345.38	155.70	7.44	18.21	12.83
	Diaph	0.02	0.73	0.42	6.26	67.24	22.74	8.35	22.26	15.08
	Lung	0.18	2.01	0.85	21.50	822.50	358.98	10.82	30.58	21.35
	Pericardium	0.01	1.02	0.38	11.32	514.28	242.10	4.71	12.79	9.28
	Skin	0.41	1.26	0.67	5.20	21.17	9.58	2.59	8.79	4.40
	esoph	0.30	1.45	0.85	15.33	221.27	86.29	6.69	13.81	10.38
pat2	Aorta	0.15	4.31	1.61	2.98	304.69	90.80	4.56	16.54	9.31
	Chestwall	0.13	2.39	0.88	3.80	31.93	12.29	1.85	8.76	4.13
	Diaph	0.03	1.44	0.55	7.75	116.77	50.21	3.47	7.20	5.34
	Lung	0.26	2.70	1.60	20.32	112.81	58.00	6.14	18.81	11.63
	Pericardium	0.32	0.74	0.48	10.85	51.29	28.26	3.96	8.42	5.50
	Serratus	0.95	3.47	1.89	4.21	32.73	12.74	4.23	17.75	8.77
pat3	Aorta	0.18	1.58	0.75	8.18	95.72	46.15	6.99	17.20	11.62
	Chestwall	0.11	2.01	0.79	9.68	218.48	138.66	4.26	87.60	33.34
	Diaphragm	0.20	1.20	0.61	11.06	351.43	131.05	4.76	14.41	9.97
	Lung	0.25	2.51	1.32	57.35	87.76	72.14	12.26	24.75	18.59
	Pericardium	0.17	1.91	1.10	24.04	175.43	93.76	8.62	21.96	14.25
	Skin	0.35	1.55	0.83	2.99	5.08	3.68	1.94	5.55	3.32
	Seratus	0.48	2.81	1.55	14.95	61.71	35.44	11.34	22.44	16.53
pat4	Chestwall	0.36	1.51	1.08	2.75	11.99	6.07	2.34	5.35	4.07
	Diaphragm	0.37	6.86	3.51	0.00	105.53	27.31	10.64	17.86	13.66
	Lung	2.20	10.67	5.19	0.00	107.88	71.51	14.50	21.81	18.10
	Pericardium	0.24	12.27	3.67	4.30	347.48	186.13	15.05	25.59	20.04
	Serratus	0.57	1.41	0.99	4.16	9.35	6.01	2.98	5.86	4.45
pat5	Chestwall	0.68	0.70	0.69	4.36	6.27	5.32	3.20	3.83	3.52
	Diaphragm	0.99	1.56	1.27	5.96	7.30	6.63	4.86	5.86	5.36
	Lung	1.23	2.63	1.93	5.74	6.42	6.08	4.98	8.43	6.70
	Pericardium	1.09	1.65	1.37	9.29	12.56	10.92	6.47	7.56	7.01

3. Results and Discussion

3.1 Relationship between treatment time and the treatment area

Light dosimetry was performed for each PDT light delivery to monitor the dose delivered to the cavity. For a uniform dose distribution isotropic detectors were measuring the fluence rate during the entire treatment. The isotropic detectors were sewed onto the thoracic wall. The relationship between the time needed to deliver the prescribed dose as a function of the volume and surface of the treated cavity were studied. K value was found to be 5.8 as shown in table 2. The time for light delivery varied from 1450s to 4654s. The volume of the treated pleural cavity was measured during PDT using water volume and varied from 1600cm³ to 3000cm³. The surface of the treated cavity was calculated assuming the cavity is a perfect sphere and it varied from 661 to 1006cm², as shown in table 2. The calculated area of the pleural cavity based on CT data agrees to within 10% to that estimated by the measured volume.

Figure 1 shows a wire-plot of the treated cavity wall for patient #4, with the corresponding volume and area of the structure. The lung itself was kept intact and deflated to about 20% of its normal size for all patients treated.

Figure 1.

Wire-plot of treated cavity wall for patient #4.

The accuracy of Eq. 2 for the calculation of diffuse reflectance has been verified in an intralipid phantom [7]. They have shown excellent agreement between theory and experiment. Figure 4b shows the measured diffuse reflectance based on the measured in-vivo optical properties, they vary between 0.2 and 0.9. The square in the figure corresponding to the mean optical properties measured in the pleural cavity.

Figure 4.

(a) Cumulative fluence plot of fluence vs time; (b) plot of fluence rate vs. time.

From figure 2, patient 1 has the highest mean diffuse reflectance while patient 5 has the lowest mean diffuse reflectance. The higher the transport albedo, the higher the diffuse reflectance.

Figure 2.

Calculated diffuse reflectance vs. μ_eff based on the measured optical properties as shown in table 1.

Using the measured diffuse reflectance and Eq. 4, one can calculate the linear coefficient between the treatment time and the treatment area. While the k values generally decrease with increasing effective attenuation coefficient, there is a wide spread because of the distribution of absorption and scattering coefficients. The mean values of μ_eff are always lower than the theoretical prediction unless we assume that the saline inside the lung cavity has a lot of absorption (diamond), due to the lung filling most of the cavity. Under this condition, they can be made exactly to agree with each other for μ_a = 0.22 cm^-1. It is clear that treating the thoracic cavity with uniform dose is a difficult task, given the very complex geometry of the thoracic wall.

The attenuation coefficient in saline changes significantly between patients, which is the dominant factor that determines the k value. On the other hand, the higher the diffuse reflectance, the lower the k value given μ is fixed.

3.3 Summary of light fluence rate results

The average fluence rate delivered among the studied patients was 46.31mW/cm². The calculated average fluence rate, based on the prescribed dose and time for delivery was 6.06mW/cm², as shown in table 3.

Table 3. Mean light dosimetry for each treated site.

SN	Apex	PS	AS	ACW	PCW	Peri	PM	Avr	Calc
1	64.42	88.51	63.93	56.56	34.26	83.70	52.74	63.45	7.80
2	65.54	82.14	64.75	56.60	34.03	83.70	51.99	62.68	10.34
3	41.88	37.41	30.94	18.84	22.50	29.72	40.02	31.62	3.22
4	39.01	67.10	48.07	23.22	26.95	41.27	29.27	39.27	3.63
5	32.63	45.46	57.15	24.69	22.95	27.01	32.01	34.56	5.32

An example of dose monitoring during treatment delivery is shown in figure 6. Figure 6a is a plot of the cumulative fluence for each of the seven sites monitored by isotropic detectors. Figure 6b shows the fluence rate received by each of the detectors. The fluence rate varies during the treatment; an average overall fluence rate 34.56mW/cm² was determined.

4. Conclusions

We have established a theory to correlate the treatment time with the treated area. Active patient study is ongoing to determine the coefficient for HPPH mediated pleural PDT. The results are discussed using an integrating sphere theory and the measured tissue optical properties. The result can be used as a clinical guideline for future pleural PDT treatment.

Figure 3.

Comparison between the theory and the measurement for linear coefficient between the treatment time and the area of treatment (Eq. 3), for patient #3 (a), patient #4 (b) and patient #5 (c).