112 10  Metabolic Mapping

From studies on expected fundus fluorophores as well as those on ocular structures, the technical parameters can be derived for excitation, emission and for the time range of decay times. Taking into account the transmis-

10  sion of the ocular media, the optimal excitation of fundus fluorophores is around 440 nm up to 490 nm. A certain discrimination of fluorophores is possible if the emission is detected within a short wavelength range of 490–560 nm and within a long wavelength range of 560–700 nm. The fluorescence of NADH, AGE, FAD and connective tissue (collagen, elastin) contributes to the emission in the short wavelength interval. The possibility of the fluorescence of the lens covering the fundus fluorescence to a certain degree cannot be excluded. As a consequence, different results can be expected from eyes with crystalline lens and those with implanted intra-ocular lens. The fluorescence in the long wavelength range is dominated by lipofuscin. The influence of all other fluorophores is considerably reduced. As the longest detected lifetime was about 4 ns, 12.5 ns was sufficient time between the two excitation pulses according to a repetition rate of 80 MHz.

The autofluorescence signal is very weak. The number of fluorescence photons as a result of excitation has been calculated by Schweitzer et al. [20]. Less than one fluorescence photon can be expected when the fundus is excited by a series of ten pulses near the maximal permissible exposure [21]. This result leads to two conclusions. First, the signal is too weak to measure the fluorescence decay in the frequency domain [22]. In the frequency domain, the fluorescence lifetime is calculated from the phase shift or demodulation between the modulated excitation laser radiation and the modulated fluorescence light. This principle would require at least three fluorescence photons for construction of a half wave. The very weak detectable fundus fluorescence signal is optimally suited for the application of the time-correlated single photon counting technique (TCSPC) [22, 23]. In the TCSPC, the time is measured between the excitation pulse and the first and only fluorescence photon detected. According to this time, the content of the added photons in the corresponding time channel is increased by number 1 for each detected photon. After a certain measuring time, the content in all the time channels represents the probability density function of the fluorescence decay from the excited singlet state S1 to the ground state S0. According to this principle, the original decay process is transformed from the subnanosecond decay in the well-detectable time scale of seconds or minutes. The goal is now to detect such decay signals in the fundus fluorescence images for each pixel in, for example, a 150 × 150 pixel matrix. It can be estimated that the measuring time would have to last for several minutes to get a good SNR. As this detection of single photons is a Poisson process, the SNR is equal to the square root of the signal. That is, 10, 000 photons are required for SNR = 100.

The second consequence of the weak detectable signal and the long measuring time that is necessary is the application of the methods of image registration. That is, each fluorescence photon detected must be collected in the right image pixel in the corresponding time channel, despite the eye movements. From these basic investigations, the fluorescence lifetime mapper was developed.

10.4  Fluorescence Lifetime Mapping

Ophthalmoscopy

10.4.1  Technical Solution

A fluorescence lifetime laser scanner ophthalmoscope was developed at the Department of Experimental Ophthalmology at the University Eye Clinic, Jena, Germany. It works in the time domain. According to previous investigations, all parameters required for the discrimination of fluorophores are combined. Thus, two wavelengths can be used for excitation, and the timeresolved autofluorescence is measured within two spectral ranges in the TCSPC technique. Furthermore, an online image registration is realised, allowing measurements over a period of minutes despite eye movements and blinking. A short technical description follows.

The opto-mechanical basis is a laser scanner ophthalmoscope (HRA II; Heidelberg Engineering, Heidelberg, Germany). This device was added by a unit for the fibre adoption of pulse laser diodes (HLD 440 or HLD 470; Lasos, Jena, Germany; Becker & Hickl, Berlin, Germany). These diodes emit pulses at 448 or 468 nm (75 ps FWHM, 80 MHz). The fibre end (3 µm) is imaged at the fundus during the scanning process. The average radiation power is about 120 µW in the corneal plane. Thus, the applied exposure is about 1% of the maximal permissible exposure. The fluorescence light is confocally detected via a 100 µm fibre. In addition, the fundus is irradiated by an IR Laser (820 nm) permitting contrast-rich fundus images, also in cases of cataracts. As the acquisition time is short for single images, it is unlikely that eye movements will interfere with the measurement. Subsequent images are registered in relation to the IR reference image. The calculated image transformation is also used for the registration of weak images of the dynamic fluorescence. As shown in Fig. 10.4, the IR light is separated from fluorescence light by a dichroic mirror, DM1. The excitation light is blocked by a razor filter (Laser 2000, Wesseling, Germany) at 488 nm from the fluorescence light. The fluorescence light is separated by a second dichroic mirror, DM2, in two spectral ranges, K1 = 490–560 nm and K2 = 560–700 nm. In both channels, the time-resolved fluorescence is detected by a multi-channel photomultiplier (MCP-PMT, HAM-R 3809U-50; Hamamatsu, Herrsching, Germany).

A TCSPC board SPC 150 (Becker & Hickl, Berlin, Germany) detects the fluorescence decay. This board works in first-in first-out mode and has direct memory access. Thus, continuous measurements are possible and no interruption is required for data-saving. During the measuring process, online image registration is performed in both channels. The measuring time is determined by the number of collected photons required for the evaluation of the decay process. The number of collected photons in each time channel depends on the time resolution and spatial resolution selected. In the case of a constant width of the time channels, the smallest expected fluorescence lifetime determines the number of time channels. As the time between the two excitation pulses is divided into 1,024 time channels, the time resolution is 12.5 ps in the device described.

The better the image resolution, the longer the measuring time. A good compromise is a 40 µm × 40 µm resolution in 30 fundus images. This spatial resolution corresponds to one-fourth of a vessel diameter. Regions of changed metabolism are much more extensive. On the other hand, a thrombus or deposits in the retinal vessels are smaller than a vessel diameter. If a large number of photons is required for the calculation of lifetime parameters, several small pixels can be added to one extended pixel.

10.4.2  Calculation of the Parameters of Time-

Resolved Fluorescence

As result of measurements of dynamic fluorescence, histograms of fluorescence decay are detected at each pixel in the fundus image. These histograms represent the decay of fluorescence intensity as the function of time.

The process is mostly assumed to be exponential decay, which can be approximated by a sum of e-functions (10.3):

where:

ai is the pre-exponential factor of exponent i or amplitude

ti is the lifetime of exponent i b is the background

p is the degree of exponential function

As the excitation is not a Dirac pulse, the measured decay of fluorescence is the convolution of the excitation pulse with the decay process. Hence, the criterion for the fitting process is the minimisation of cr2 (10.4):

In this equation, N(tj) is the number of photons measured in the time channel j. Nc(tj) is the number of expected photons, which is calculated by the convolution of the instrumental response function and the model function. n is the number of time channels and q is the number of free parameters (ai, ti, b).

If the detection of the photons is a Poisson process, the mean square root error between the detected photons and the calculated photons is equal to the square root of the detected events:

Thus, the ratio in the sum of (10.4) is 1 for each time channel and the sum is n, that is, the limiting value of cr2 is 1.