1.

Introduction

Interest in optical characteristics of the human prostate is mainly related to recent efforts in developing photodynamic therapy (PDT) into a modality for treatment of localized prostate cancer. Initial preclinical work on PDT of prostate carcinoma appeared during the 1980s (Refs. 1, 2) and (first) clinical work was published³ as early as 1990. For the development and optimization of the technique, several studies have since been performed on canine^{4, 5, 6} and rat^{1, 7} models. Clinical results from various research groups are now available. ^{8, 9, 10, 11, 12, 13} Altogether, these results have shown a great potential of PDT in the management of prostate cancer.^{14, 15}

PDT, in general, relies on a process where light excites (i.e., activates) a photosensitizer, which induces cytotoxic oxygen species. Thus, PDT relies on the presence of light, a photosensitizer, and oxygen. The corresponding dosimetry is therefore a complex matter, involving measurement and/or prediction of sensitizer and oxygen concentrations as well as light fluence (light dose). Since full treatment of diseased regions is crucial, these issues must be carefully addressed. Accordingly, PDT dosimetry has been the main focus of numerous papers (see, e.g., Star¹⁶), of which a few are closely related to the particular case of PDT of prostate cancer. ^{17, 18, 19, 20, 21} One fundamental aspect in this context is the tissue optical properties, e.g., absorption and scattering coefficients. Not only do they together determine the light dose distribution, but in vivo access to absorption coefficients can be used to estimate, for example, sensitizer concentrations, hemoglobin concentration, and tissue oxygenation. In addition, due to dynamic changes during PDT treatment, it is sometimes argued that on-line monitoring is required to achieve optimal treatment.^{22, 23}

For the case of prostate tissue, several papers have addressed the issue of optical properties, e.g., the effective attenuation coefficient ${\mu }_{\mathrm{eff}}$ and in some cases also absorption and reduced scattering coefficients ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ , respectively. ^{4, 18, 24, 25, 26, 27, 28, 29, 30, 31} Most of them rely on interstitial fiber optic steady state fluence rate measurements at multiple source-detector separations. By measuring relative fluence rate in a range of source-detector separations larger than a few millimeters (i.e., the diffuse regime), the diffusion approximation of light transport can be employed to determine ${\mu }_{\mathrm{eff}}$ . Since ${\mu }_{\mathrm{eff}}$ depends on both ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ , additional data is required to reach information on absorption and scattering separately. One option is to determine ${\mu }_{\mathrm{t}}^{\prime }={\mu }_{\mathrm{a}}+{\mu }_{\mathrm{s}}^{\prime }$ by measuring relative radiance at multiple, but short, source-detector separations.³² A second option, avoiding the need of short source-detector separations, is to measure absolute (instead of relative) fluence rate in the diffuse regime.³³ Data evaluation, by means of curve fitting, then yields ${\mu }_{\mathrm{eff}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ . Hence, both options enable estimation of absorption and scattering coefficients.

Previously published values on optical properties of the human prostate, together with the results obtained in this study, are given in Sec. 3. The first published work presents ex vivo steady state measurements of ${\mu }_{\mathrm{eff}}$ and ${\mu }_{\mathrm{t}}^{\prime }={\mu }_{\mathrm{a}}+{\mu }_{\mathrm{s}}^{\prime }$ , at $633\mathrm{nm}$ , in three whole, nonmalignant human prostates.²⁴ Another post mortem study estimates prostate optical properties ( ${\mu }_{\mathrm{a}}$ , scattering coefficient ${\mu }_{\mathrm{s}}$ , scattering anisotropy $g$ , and ${\mu }_{\mathrm{s}}^{\prime }$ ) at $1064\mathrm{nm}$ , by measuring through thin prostate slices.²⁵ In vivo effective attenuation in prostates diagnosed with benign prostatic hyperplasia (BPH) or prostatic carcinoma (PC) has been estimated at 630, 633, and $665\mathrm{nm}$ , by employing steady state fluence rate measurements.^{26, 28, 29} Other studies rely on absolute fluence rate measurements to determine both absorption and scattering coefficients. By measuring fluence rates along a linear channel ( $5\mathrm{mm}$ away from the source fiber), one such study presents optical properties at $732\mathrm{nm}$ , before and after motexafin-lutetium-mediated PDT of locally recurrent prostate cancer.³⁴ In a similar study, optical fibers are kept fixed (five source fibers and three detector fibers), and absolute fluence rate data is collected for 15 source-detector separations (at $762\mathrm{nm}$ ). Measurements were in that case performed in connection with TOOKAD-mediated PDT of recurrent prostate cancer.³⁰ Regarding hemoglobin monitoring in human subjects, only very limited data have been published.^{30, 31}

This study employs interstitial time-resolved spectroscopy to characterize human prostate tissue in vivo. Conceptually, this approach is very different from those chosen in previously published work related to prostate tissue. By analyzing the temporal broadening of picosecond laser pulses due to propagation through tissue, this technique provides reliable estimations of absorption and reduced scattering coefficients. The use of multiple wavelengths enables spectroscopic determination of total hemoglobin concentration (THC) and oxygen saturation $\left({\mathrm{S}}_{\mathrm{t}}{\mathrm{O}}_2\right)$ . The technique has previously been used in various areas of biomedical optics. ^{35, 36, 37, 38, 39}

The aim of the paper is to provide information on parameters of dosimetric importance, as well as to introduce time-resolved spectroscopy as a tool in PDT research. In particular, the aim is to achieve separate information on ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ , as well as quantitative information on hemoglobin parameters. We also wish to give a proper indication on intra- and intersubject variation, for the case of untreated prostate cancer. These parameters are important for PDT dosimetry calculations, and are not extensively explored in previous studies.

Nine patients diagnosed with prostate cancer were included in the study, and all measurements were performed before primary treatment. By inserting three optical fibers, three tissue volumes were probed, yielding information on prostate tissue heterogeneity.

2.

Material and Methods

2.1.

Instrumentation

Time-resolved data were acquired using a compact $(50\times 50\times 30\mathrm{cm})$ and portable time-domain photon migration instrument primarily intended for spectroscopy of biological tissues in clinical environments.^{39, 40} A schematic illustration is given in Fig. 1 .

Fig. 1

Schematic of the instrumentation in interstitial mode.

The system is based on diode laser technology and time-correlated single-photon-counting (TCSPC). A laser driver (SEPIA PDL 808, PicoQuant, Germany) controls four pulsed diode lasers (LDH, PicoQuant at 660, 786, 916, and $974\mathrm{nm}$ ). Wavelengths are chosen to enable monitoring of important tissue constituents (hemoglobin, water, and lipids) and properties (tissue oxygenation). Lasers are typically operated at 1 to $2\mathrm{mW}$ , generating pulses about $70\mathrm{ps}$ wide (FWHM). Four wavelength pulse trains are generated at a repetition frequency of $40\mathrm{MHz}$ . This is accomplished by separating the individual pulses in time $(\sim 6\mathrm{ns})$ , using electric cables of different lengths.

The light emitted from each diode laser is individually coupled into a separate $200\text{-}\mathrm{\mu }\mathrm{m}$ graded-index (GRIN) fiber (G 200/280 N, ART Photonics, Germany). A four-to-one coupler is used to couple all light into a single $600\text{-}\mathrm{\mu }\mathrm{m}$ GRIN fiber (G 600/840 P, ART Photonics), which serves as the light source. A second fiber collects light and delivers it to the detector. Each of these two fibers is approximately $2\mathrm{m}$ long. To fit into 1-mm inner diameter brachytherapy needles, a thin polyimide layer acts as the only fiber coating at the fiber endings. Remaining parts are protected in polyolefin tubing.

Proper photon levels are achieved by sending collected light through an adjustable gradient neutral density (ND) filter. Remaining photons are sent to a cooled microchannel plate photomultiplier tube (MCP-PMT; R3809-59, Hamamatsu Photonics, Japan). A TCSPC computer card (SPC-300, Becker&Hickl, Germany) is used to obtain time-dispersion histograms with channel widths of approximately $25\mathrm{ps}$ .

Broadening in the fibers and the detector yields an instrument response function (IRF) that is about $100\mathrm{ps}$ wide. The IRF is measured by inserting source and detector fibers into a chamber so that the end facets are separated by $150\mathrm{mm}$ and face each other. The chamber is made of black delrin, and contains a pinhole that is inserted between the two fibers to block reflected stray light.

2.2.

Modeling

Experimental data are modeled using the diffusion approximation of transport theory. More specifically, data are fitted to the analytical solution of the time-dependent diffusion equation for the case of a homogenous and infinite medium.⁴¹ Accordingly, the fluence rate $\Phi$ due to a infinitely short light pulse from an isotropic point source can be written as

Eq. 1

$$\Phi (r,t)=c^{\prime }{E}_0{\left(4\pi c^{\prime }Dt\right)}^{-3∕2}\exp (-\frac{r^2}{4c^{\prime }Dt}-{\mu }_{\mathrm{a}}{c}^{\prime }t),$$

where $E_0$ is the pulse energy, $r$ is the distance from the point source, $c^{\prime }$ is the speed of light within the material, and $D$ is the diffusion coefficient. The refractive index is assumed to be $n=1.4$ . To comply with recent work concerning the diffusion coefficient, it is defined as in Eq. 2, rather than in the traditional (absorption-dependent) way^{42, 43}:

Eq. 2

$$D=\frac{1}{3{\mu }_{\mathrm{s}}^{\prime }}.$$

The form of Eq. 1 enables deduction of both ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$ from experimental data without requiring absolute measurements of light fluence. This is achieved by considering temporal shapes only. That is, experimental data are fitted using an expression similar to that given in Eq. 1, but in which amplitude information is contained in a free parameter $k$ . This expression is given as

Eq. 3

$$y({\mu }_{\mathrm{a}},{\mu }_{\mathrm{s}}^{\prime },k,t)=k{t}^{-3∕2}\exp (-\frac{3{\mu }_{\mathrm{s}}^{\prime }{r}^2}{4c^{\prime }t}-{\mu }_{\mathrm{a}}{c}^{\prime }t).$$

The best fit is reached iteratively using a Levenberg-Marquardt algorithm, where ${\mu }_{\mathrm{s}}^{\prime }$ , ${\mu }_{\mathrm{a}}$ , and $k$ are varied to minimize a ${\chi }^2$ error norm.⁴⁴ Final values of ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$ are then estimations of the reduced scattering coefficient and absorption coefficient, respectively. Note that the IRF, being about $100\mathrm{ps}$ wide, cannot be regarded as infinitely short in comparison to the tissue response. Therefore, each iteration in the curve-fitting procedure involves a convolution of analytical data and IRF. It should also be noted that fitting is performed using the part of experimental data between times given by the 50% of maximum on the rising edge, and 20% on the falling edge (see Fig. 5 in Sec. 3).

Fig. 5

Fitting of 786-nm time-resolved data from patient 4 (26.5-mm fiber separation). Dispersion data used in fitting are marked by solid dots. Weighted residuals are shown below, together with the zero level (solid line) and the $[-1.96,1.96]$ prediction interval of standardized normal distributions (dashed lines).

The previous studies of human prostate optical properties mentioned in the introduction used the same theoretical framework. However, by employing steady state techniques, they rely on a stationary solution rather that the time-dependent solution given in Eq. 1. The stationary solution of the diffusion equation for an infinite homogenous medium is given as

Eq. 4

$$\Phi \left(r\right)=\frac{3{\mu }_{\mathrm{s}}^{\prime }{P}_0}{4\pi r}\exp (-{\mu }_{\mathrm{eff}}r).$$

Here, $P_0$ is the power of the point source, $r$ is the distance from the source, and ${\mu }_{\mathrm{eff}}$ the effective attenuation. The effective attenuation is defined as

Eq. 5

$${\mu }_{\mathrm{eff}}={({\mu }_{\mathrm{a}}∕D)}^{1∕2}={\left(3{\mu }_{\mathrm{a}}{\mu }_{\mathrm{s}}^{\prime }\right)}^{1∕2}$$

From the form of Eq. 4, we see that ${\mu }_{\mathrm{eff}}$ can be deduced from relative fluence measurements at multiple source detector separations. Only if absolute fluence rate is measured, it can be used to get information on reduced scattering and absorption separately. Absolute measurement of fluence rate in living tissue is of course a difficult matter (especially in interstitial settings). Note also that ${\mu }_{\mathrm{eff}}$ is a primary parameter when using the steady state technique. Time-resolved experiments provide estimations of ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ which in a second step can be used to calculate ${\mu }_{\mathrm{eff}}$ .

2.4.

Clinical Procedure

Clinical data were collected at the Lund University Hospital adhering to a protocol approved by the regional ethics committee. All nine patients involved in the study were undergoing primary treatment of prostate cancer. Measurements were performed in connection with brachytherapy (low-dose seed implantation). This fact limits our study to patients suitable for this treatment, that is, patients fulfilling the following requirements: (1) Gleason index $<6$ , (2) prostate specific antigen (PSA) $<10$ , (3) no tumor obstruction of urethra, and (4) prostate volume of the order of 20 to $40{\mathrm{cm}}^3$ . Such patients are often referred to as low-risk patients.

This type of brachytherapy of prostate cancer involves permanent implantation of radioactive seeds (internal radiotherapy). The procedure takes place in an operating theater, while patients are under general anesthesia. At the Lund University Hospital, the first step in this procedure is to image the prostate gland using transrectal ultrasound. When the physician has marked important boundaries in these images (prostate, urethra, and rectum), a radiotherapist performs dosimetric calculations. Dosimetric calculations open a time window of about $20\min$ in which the time-resolved measurements were performed without interfering with the routine procedures. Three standard brachytherapy needles were then inserted, all to the same depth (using transrectal ultrasound guidance). A standard transperineal brachytherapy needle matrix handles lateral positioning ( $5\times$ 5-mm grid spacing). Three sterilized optical fibers were inserted through the three needles so that they were located edge to edge with the needle tips (this positioning is achieved by premarking the fibers). Fiber separations are inferred from ultrasound images (B-K Medical Hawk 2102 EXL with transducer 8658-T operating at 6.5 to $7.5\mathrm{MHz}$ ). Figure 2 shows two authentic ultrasound images.

Fig. 2

Two ultrasound images showing three needles inserted into the prostate. For clarity, the needles are marked by circles. Shadows behind the needles are due to their high reflectivity. The fairly homogenous image (a) originates from patient 5, while the heterogenous structure in (b) was exhibited by patient 6.

By using three needles, it is possible to probe three fairly nonoverlapping prostate tissue volumes. Fiber separations were in the range of 10 to $30\mathrm{mm}$ . The three fiber separations used within each patient were chosen to differ, and typically set in a triangular pattern to approximately 15, 20, and $25\mathrm{mm}$ . The longest fiber separation corresponds to a more central volume of the prostate, bordering the urethra. Typical fiber positioning is schematically illustrated in Fig. 3 . In addition, this figure also indicates sampling volumes by displaying⁴⁸ PHDs.

Fig. 3

Schematic drawing of fiber positioning [compare with Fig. 2a]. The needle template has 5-mm grid spacing. Three optical fibers are inserted to the same depth. Fiber separations are 15, 20, and $25\mathrm{mm}$ . The three tissue volumes being probed are indicated using calculations of photon-hitting densities (PHDs) at the plane of fiber tips ( ${\mu }_{\mathrm{s}}^{\prime }=8.7$ and ${\mu }_{\mathrm{a}}=0.49{\mathrm{cm}}^{-1}$ ). Isocurves indicate where the PHD is 50% of the value exhibited halfway between source- and detector fibers.

Since the instrumentation used in this study supports only one source and one detector fiber at a time, three sequential measurements must be performed. The total data acquisition time was approximately $3\min$ per patient ( $1\min$ per tissue volume). To detect unexpected changes during data acquisition, measurements were performed in $1\mathrm{s}$ increments. After completion of the tissue measurements, the IRF is measured using the same set of fibers. To ensure system stability (e.g., avoid drifts due to temperature changes), this step is conducted while the system is in the operating theater.

3.

Results

Analysis of collected data reveals that time-resolved spectroscopy can provide consistent optical and physiological characteristics of human prostate tissue. Data were collected at four wavelengths: 660, 786, 916, and $974\mathrm{nm}$ . For each patient and wavelength, raw data consist of three dispersion curves (tissue response) corresponding to the three utilized fiber separations (in total, 27 time-resolved data sets from nine patients). Since the fiber separations within a patient are chosen to be different, e.g., 15, 20, and $25\mathrm{mm}$ , the obtained curves are significantly different. For the range of fiber separations used in this study, most detected light travels a time less than $1.5\mathrm{ns}$ through tissue (corresponding to maximum path lengths of about $30\mathrm{cm}$ ). An example of raw data, for the case of $660\mathrm{nm}$ , is given in Fig. 4 .

Fig. 4

Acquired time-resolved data at $660\mathrm{nm}$ for patient 5 (after background subtraction). Data are shown in both linear (upper axes, normalized) and logarithmic scale (lower axes). Corresponding 660-nm IRFs are also shown. Input laser pulses are broadened from $90\mathrm{ps}$ (IRF) to 222 (14.8), 264 (17.7), and $291\mathrm{ps}$ $\left(23.3\mathrm{mm}\right)$ .

By means of curve fitting, optical properties were extracted for 660, 786, and $916\mathrm{nm}$ from all 27 time-resolved data sets. Unfortunately, high absorption at $974\mathrm{nm}$ prevented analysis of data acquired at that wavelength. A typical fitting example, for the case of $786\mathrm{nm}$ , is shown in Fig. 5 .

A summary of the results of this study is given in Table 2 , in which previously published data are presented for comparison. A detailed report on measured optical (at 660 and $786\mathrm{nm}$ ) and physiological characteristics are given in Table 3 . In the following, graphical representation of data from Table 3 is used to illustrate and support further analysis.

Table 2

Optical properties (given in inverse centimeters) of human prostate tissue as reported in various published studies; the number of involved patients is also given (N) ; note differences regarding wavelength.

No pronounced correlation between estimated values of ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ was seen for any wavelength, implying that results do not suffer from ${\mu }_{\mathrm{s}}^{\prime }$ to ${\mu }_{\mathrm{a}}$ crosstalk. This is shown in Fig. 6 , where results from $660\mathrm{nm}$ are presented. A general comment is, however, helpful in interpreting the pattern shown. Three measurements (21.5 and $26.4\mathrm{mm}$ from patient 6, and $25.0\mathrm{mm}$ from patient 8) resulted in very low values of both absorption and reduced scattering (leading to a THC less than $100\mathrm{\mu }\mathrm{M}$ ). In these cases, note that an extremely low degree of bleeding was noted during the measurements (almost no blood stains on the used fibers, while the average fiber was heavily stained after a measurement). Thus, it is likely that these measurement outcomes correspond to a particular tissue composition, rather than a systematic error such as ${\mu }_{\mathrm{s}}^{\prime }$ to ${\mu }_{\mathrm{a}}$ crosstalk.

Fig. 6

Scatterplot showing correlation between derived ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$ at $660\mathrm{nm}$ . The three points in the lower left correspond to the three measurement cases exhibiting a low degree of bleeding and low THC ( $r=0.31$ if disregarded).

The influence of fiber separation on derived optical properties is illustrated in Fig. 7 . Although derived optical properties show no strict dependence on the fiber separation, there might be a tendency toward measuring lower ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ for large fiber separations. Such a tendency may be related to the fact that the longest fiber separation (for each patient) corresponds to a central prostate volume, while the two shorter correspond to outer volumes. For comparison, note that studies on intralipid phantoms having prostate-like optical properties were performed. In these, the selection of fiber separation had no systematic influence on derived optical properties.

Fig. 7

Scatterplot showing the correlation between utilized fiber separation and derived optical properties at $660\mathrm{nm}$ . Correlation coefficients $r$ are added for reference. The three points with ${\mu }_{\mathrm{a}}<0.25$ correspond to the three measurement cases exhibiting a low degree of bleeding and low THC.

As we can see in Fig. 8 , derived hemoglobin concentrations show a behavior similar to that of ${\mu }_{\mathrm{a}}$ , while oxygen saturation showed no correlation to utilized fiber separation.

Fig. 8

Scatterplot showing the correlation between utilized fiber separation and THC and ${\mathrm{S}}_{\mathrm{t}}{\mathrm{O}}_2$ , respectively. Correlation coefficients $r$ are added for reference.

Turning to inter- and intrapatient variations, an important general observation is that patients 2 to 5 exhibited homogenous ultrasound images, while obvious inhomogeneities due to calcifications are found in images from patients 1 and 6 to 9. As we can see in Figs. 9, 10, 11 , this fact correlates to measured intrasubject variations. A second general observation is that all derived parameters, except oxygen saturation, can be subject to a fairly large spread, even within individual patients. Figure 9 presents inter- and intrapatient variations of 660-nm optical properties.

Fig. 9

Inter- and intrapatient variations in 660-nm optical properties. Patients 2 to 5 exhibited homogenous ultrasound images. Solid lines marks the average values, and dashed lines correspond to $\pm$ one standard deviation.

Fig. 10

Inter- and intrapatient variations in 660-nm effective attenuation. Patients 2 to 5 exhibited homogenous ultrasound images. The solid line mark the average value, and dashed lines correspond to $\pm$ one standard deviation.

Fig. 11

Inter- and intrapatient variations in hemoglobin parameters. Patients 2 to 5 exhibited homogenous ultrasound images. Solid lines mark the average values, and dashed lines correspond to $\pm$ one standard deviation.

Effective attenuation, being an important parameter in PDT dosimetry, was calculated from extracted ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ and is presented in Fig. 10.

Hemoglobin concentrations and oxygen saturation were spectroscopically determined using absorption coefficients as measured at 660 and $786\mathrm{nm}$ . As we can see in Fig. 11, THC exhibit substantial inter- and intrasubject variations. Oxygen saturation, on the other hand, displays only minor variations.

One alternative to deriving hemoglobin concentrations from 660- and 786-nm data only, would be to include 916-nm data (still assuming that the prostate contains 70% water and 10% lipids). If this procedure is followed, resulting THC values deviate by $+1.5\pm 8.7\%$ , and ${\mathrm{S}}_{\mathrm{t}}{\mathrm{O}}_2$ by $+1.1\pm 4.1\%$ from the values calculated from 660- and 786-nm data only. In terms of overall impact, derived THC changes from $215\pm 65$ to $215\pm 56\mathrm{\mu }\mathrm{M}$ (the rounded average is coincidentally conserved), and ${\mathrm{S}}_{\mathrm{t}}{\mathrm{O}}_2$ from $76\pm 4$ to $77\pm 4\%$ . These fairly small changes can also be understood by analyzing the difference between measured 916-nm ${\mu }_{\mathrm{a}}$ , and the predicted 916-nm ${\mu }_{\mathrm{a}}$ , as calculated from derived hemoglobin levels (estimated from 660- and 786-nm data) in combination with the assumption of 70% water and 10% lipids. Such analysis show that measured 916-nm ${\mu }_{\mathrm{a}}$ deviates by $2\pm 11\%$ from predicted values.

A synthetic absorption spectra can be constructed using derived hemoglobin concentrations and assumed concentrations of water and lipids. Figure 12 presents the average composite absorption spectra of the prostate, as derived in this study.

Fig. 12

Synthetic average absorption spectra (bold solid) together with derived absorption coefficients at 660, 786, and $916\mathrm{nm}$ (mean $\pm$ standard deviation). It is constructed using $215\mathrm{\mu }\mathrm{M}$ THC at 76% oxygen saturation, 70% water and 10% lipids. Contribution spectra are also shown: $51.6\text{-}\mathrm{\mu }\mathrm{M}$ Hb (dashed), $163.4\text{-}\mathrm{\mu }\mathrm{M}$ ${\mathrm{HbO}}_2$ (dotted), 70% water (solid), and 10% lipid (dash-dotted).

Table 3

Detailed report on optical and physiological characteristics of human prostate tissue in vivo, as measured by our time-resolved instrumentation; prostate volumes (V) are determined from ultrasound images.

4.

Discussion

Reliable optical dosimetry is an important issue in the development of PDT into a modality for treatment of prostate cancer. Whether reliable dosimetry means on-line monitoring of certain parameters, individual pretreatment planning, or general knowledge on intra- and intersubject variations remains an open question. By employing time-resolved spectroscopy, this study was able to generate estimations of optical and physiological characteristics ( ${\mu }_{\mathrm{a}}$ , ${\mu }_{\mathrm{s}}^{\prime }$ , ${\mu }_{\mathrm{eff}}$ , total hemoglobin concentration, and oxygen saturation) for all involved patients, and thus providing a reliable indication on intra- and intersubject variations for the case of untreated prostate cancer. In fact, as we can see in Table 3, all measurements resulted in quality data. In addition, by requiring only two fixed fibers for a single measurement, the time-resolved technique is accompanied with fairly simple clinical procedures.

Calculations of PHDs suggest that sampling volumes are kept within the prostate. Results are consistent and imply that the prostates of the patient group under consideration exhibit moderate intra- and intersubject variations. However, the following observation calls for a separate discussion: derived ${\mu }_{\mathrm{s}}^{\prime }$ at $916\mathrm{nm}$ exceeds those at $786\mathrm{nm}$ in 23 out of 27 measurements. According to the general theory of tissue optics, a reduction of ${\mu }_{\mathrm{s}}^{\prime }$ is expected. Such behavior was only seen in 4 out of 27 measurements (three out of nine patients). The explanation is very likely to be related to the high absorption and low scattering at $916\mathrm{nm}$ . In fact, analysis of Monte Carlo simulations indicates a breakdown of diffusion approximation in this regime. Derived ${\mu }_{\mathrm{s}}^{\prime }$ is closely related to the rising flank of the dispersion curve (early photons), and may be particularly sensitive. Another aggravating circumstance is that such optical properties yield a low degree of broadening (and thus fewer data points), which in turn reduces the performance of the fitting procedure. Refined data evaluation may solve this problem, one option being implementation of Monte-Carlo-based evaluation.

When comparing our results to previously published data, two important facts must be noted. First, differences in patient groups must be taken into account (e.g., untreated or recurrent prostate cancer). The prostate physiology changes drastically upon radiation therapy. An experienced physician can feel such differences during the insertion of brachytherapy needles. Second, previous studies of prostate tissue have employed steady state techniques. Note that the ambiguous appearance of published steady state ${\mu }_{\mathrm{s}}^{\prime }$ data may indicate a difficulty in separating absorption and scattering using steady-state techniques (cf the published values of ${\mu }_{\mathrm{s}}^{\prime }$ stated in Table 2). Unfortunately, differences in patient groups prevent these results from being compared to the results of this study. It would thus be very interesting to employ time-resolved spectroscopy also in cases of locally recurrent prostate cancer. On the other hand, in the 600-nm range, ${\mu }_{\mathrm{eff}}$ were measured using steady state techniques in patient groups similar to ours. In this respect, the two techniques seem to produce similar data (most derived ${\mu }_{\mathrm{eff}}$ values are between 3 and $4{\mathrm{cm}}^{-1}$ ).

To discuss the correctness of our approach, a few general remarks are given in the following. First, the model used in this study is valid for photon fluence rates. Detected light is collected by cleaved optical fibers, and is thus not a direct measure of fluence rate. Since data evaluation considers only temporal shapes, this fact is, however, not a source of error if the proportionality constant between actual fluence rate and collected light is the same for all photon times of flight. Moreover, the model applies for homogenous media. The prostate is, of course, heterogenous, and out of all detected photons, those that have traveled through regions of low attenuation will be overrepresented. One should therefore be careful in interpreting the derived values as true volume averages.

Second, the choice of data range involved in curve fitting occasionally has an influence on the outcome. Finding an optimal fitting range is, however, a complex issue, since the correctness of our model varies with the photon time of flight. For example, early photons are often disregarded since diffusion theory does not describe them very well. In this study, we focus on regions with fairly high photon count rates by choosing to cut the tail of late photons at 20% of maximum (see Sec. 2.2). The reason why later photons are excluded is to avoid a region with many data points at a low signal level, where even small absolute systematic measurement/model errors will have a significant impact on fitted parameters.

Third, as we can see in Eq. 3, the fiber separation is an important parameter in time-resolved spectroscopy. The inferring of fiber separations from ultrasound images is, of course, afflicted with some errors. However, it is unlikely that the error between true and measured separation, $r_{\mathrm{true}}$ and $r_{\mathrm{meas}}$ , respectively, exceeds $1\mathrm{mm}$ . From Eq. 3, one finds that errors in fiber separation will produce errors only in derived reduced scattering coefficients. The optimal fit is expected when ${\mu }_{\mathrm{s}}^{\prime }$ is selected so that

Finally, the time-resolved approach, in contrast to steady state techniques, should be rather insensitive to bleedings around the needle tips. These bleedings can be thought of as random filters, and may therefore disturb measurements of fluence rate. However, all detected photons must pass the region of bleeding, leaving the temporal shape unchanged.

5.

Summary

This study clearly shows that time-resolved spectroscopy is a suitable tool for accessing information on human prostate tissue in vivo. By producing consistent estimations of absorption $\left({\mu }_{\mathrm{a}}\right)$ , reduced scattering $\left({\mu }_{\mathrm{s}}^{\prime }\right)$ , effective attenuation $\left({\mu }_{\mathrm{eff}}\right)$ , hemoglobin concentrations, and tissue oxygenation, this technique was able to generate the most complete in vivo optical characterization of human prostate tissue published so far. By measuring across three tissue volumes in each prostate, both inter- and intrasubject variations were examined. All derived parameters, with the exception of tissue oxygen saturation, are subject to fairly large intrasubject variation. Interestingly, these variations correlate with the heterogeneity exhibited by acquired ultrasound images.