2.1.

Excitation Simulation

Simulations of the excitation light at $488\mathrm{nm}$ were performed with an illumination radius of $0.1\mathrm{cm}$ for the laser scanner excitation and $0.5\mathrm{cm}$ for the broad-field excitation method. Illumination was uniform within a circular area. Figure 2 shows the different excitation and collection methods used. The fluence produced by a radial section containing 200 beams normal to the tissue surface was expressed with a homogenous grid system in radial and depth coordinates (i.e., the grid was constructed with uniform increments in the coordinates). All results presented used a grid with increments of $2.5\mu \mathrm{m}$ . We used 1000 elements in the depth direction to represent a tissue thickness of $0.25\mathrm{cm}$ , which is comparable to ventricular free wall thicknesses in rabbit hearts. For each depth, the excitation fluence values were recorded at all grid elements within a radius of $0.25\mathrm{cm}$ . Contours of the normalized excitation fluence in the tissue did not change when we repeated a simulation with $1\times {10}^6$ , $2\times {10}^6$ , and $3\times {10}^6$ incident photons in the radial section. In all results presented, the excitation simulations used $2\times {10}^6$ incident photons, which corresponded to energy densities of 26 and $1\mathrm{pJ}∕{\mathrm{cm}}^2$ for the laser and broad-field excitation methods, respectively. Simulations used the values for absorption coefficient $({\mu }_a=5.2∕\mathrm{cm})$ , scattering coefficient $({\mu }_s=232∕\mathrm{cm})$ , and scattering anisotropy $(g=0.94)$ that were previously measured for a light wavelength of $488\mathrm{nm}$ in heart tissue stained with the transmembrane voltage-sensitive dye,⁶ di-4-ANEPPS. In additional simulations, the scattering and anisotropy properties were held constant while the absorption coefficient at $488\mathrm{nm}$ was changed from the measured value of $5.2∕\mathrm{cm}$ to 1.8, 15.6, and $52∕\mathrm{cm}$ . This indicated the effects of $1∕3$ -, 3-, and 10-fold changes in absorption coefficient of excitation light.

Fig. 2

Diagrams of simulated excitation and collection methods: (a) broad-field excitation and (b) laser scanner excitation. The maximum illumination radius (solid horizontal arrows directed onto tissue from left) was larger for the broad-field excitation. The fluence was recorded using a cylindrical coordinate system and grids with depth and radial increments of $2.5\mu \mathrm{m}$ (single grid element shown). Fluorescent photons that escaped the tissue within a narrow radius at the illuminated or opposite tissue surface (maximum radius indicated with dotted arrows) were collected for broad-field excitation. All fluorescence photons that escaped a surface were collected for the laser scanner excitation. Escaping fluorescence photons had variable directions of travel (not shown).

2.2.

Fluorescence Simulation

To study the fluorescence propagation, simulations were performed with optical properties of tissue for light at a wavelength of $669\mathrm{nm}$ . During fluorescence simulations each grid element within the recording radius was regarded as a point source from which fluorescence originated. The weight assigned to fluorescence photons launched at each element was directly proportional to the fluence of the excitation light to represent fluorescence produced by the single-photon excitation process.⁹ The initial direction of travel of launched fluorescence photons was isotropic [i.e., the direction was determined randomly with all directions having the same probability, Fig. 1a].

In pilot simulations, we launched one fluorescence photon at each element. To lessen irregularities in contours of the interrogated regions, we also performed simulations in which the number of launched fluorescence photons was increased to 10, 100, and finally 1000 per element. The increases from 1 to 100 improved smoothness of contours. However, results were similar when the number was increased from 100 to 1000. All results presented used 1000 photons launched per element.

We selected $669\mathrm{nm}$ to represent fluorescence because this is near^{10, 11} the wavelength of peak fluorescence emitted from the transmembrane voltage-sensitive dye di-4-ANEPPS. Also, values of the optical properties at this wavelength ( ${\mu }_a=1.0∕\mathrm{cm}$ , ${\mu }_s=218∕\mathrm{cm}$ , $g=0.96$ ) have been measured⁶ in heart tissue stained with di-4-ANEPPS. In different simulations, the scattering and anisotropy properties were held constant while the absorption coefficient at $669\mathrm{nm}$ was changed from the measured value of $1∕\mathrm{cm}$ to 0.3, 3, and $10∕\mathrm{cm}$ . This indicated the effects of $1∕3$ -, 3-, and 10-fold changes in absorption of fluorescence.

During fluorescence simulations, weights of fluorescence photons that exited each of the surfaces (epi- and transillumination, respectively) of the tissue and the locations of their origin inside the tissue were saved in memory. For simulations of the laser scanner excitation method, all photons exiting a given surface were collected to represent the large collection area of a photomultiplier tube.⁴ For simulations of the broad-field excitation method, only the photons exiting a given surface within a radius of 0.05, 0.1, or $0.25\mathrm{cm}$ were collected. We chose to show the results for the $0.1\text{-}\mathrm{cm}$ exit radius because this is comparable to the size of a photodiode array element used in mapping with broad-field excitation.²

We used locations of the origin of collected fluorescence photons to evaluate the interrogated region, defined as the specific region in radial and depth coordinates inside the tissue from which a given percentage of the total collected fluorescence originated.^{6, 8}

Our analysis determined interrogated regions based on fractions of the total collected fluorescence so that the size of the regions was independent of factors that alter fluorescence yield such as concentration of fluorescent dye. This was confirmed by similarity of interrogated regions (except for noise) when simulations were repeated with different numbers of launched fluorescence photons at each element. To reduce effects of random noise, all results shown were spatially smoothed by binning fluorescence contributions from $40\times 40$ neighboring grid elements, which resulted in plots of interrogated regions with $100\text{-}\mu \mathrm{m}$ resolution.

2.3.

Applicability to Multisite Cardiac Optical Mapping

Our simulations with the laser excitation method used a single laser beam to predict the interrogated region, while in cardiac optical mapping experiments the laser beam scans sequentially to multiple sites.⁴ During laser scanning of the heart with 128 spots at a sampling rate of $1\mathrm{kHz}$ for each spot as performed in our laboratory, samples of light corresponding to consecutive spots were collected $7.8\mu \mathrm{s}$ apart in time. However, the propagation and absorption of laser photons and the production of fluorescence at a given spot takes only a few nanoseconds. For example, Delpy ¹² have shown the largest transit time for a photon to propagate through a $1\text{-}\mathrm{cm}$ slab of brain tissue ( ${\mu }_a=0.456∕\mathrm{cm}$ and ${\mu }_s=60∕\mathrm{cm}$ ) is approximately $0.5\mathrm{ns}$ . Given this difference in time scales, the fluorescence produced by illumination at one spot will be unaffected by the illumination at other spots during scanning. Thus, we determined the size of the interrogated region for a single beam centered on the $z$ axis. We considered that the origin of a cylindrical coordinate system can be placed at any arbitrary location on the heart surface, so the size that we found in the simulation may apply to any location of the beam that occurs during scanning. Lateral movement of the laser beam to a different spot during scanning of the tissue produces corresponding movement of the interrogated region.

Similarly, our simulations with the broad-field excitation method use a single imaged site on a tissue surface from which fluorescence can be projected to an imaging array element to predict the size of the interrogated region. In cardiac optical mapping experiments, fluorescence photons from multiple imaged sites are projected to corresponding array elements. However, given that the origin of the model can be located arbitrarily, the size of the interrogated region may still apply to any imaged site on the tissue surface. Also the fact that illumination is simultaneous over a large surface area is taken into account in the simulations of the broad-field excitation method.

2.4.

Experimental Measurements

We performed experimental measurements with pairs of $0.1\text{-}\mathrm{cm}$ -thick rabbit cardiac slices between glass slides. Three experiments were performed using slices from three hearts. Each experiment included a control pair and a pair stained with a fluorescence absorber.

Figure 3 shows a schematic of the experimental setup. Experiments determined relative contributions of tissue at different depths to the signal measured with transillumination, and whether these contributions are altered by an increase in fluorescence absorption. Control pairs consisted of a slice stained with di-4-ANEPPS ( $15\min$ immersion in a solution containing $2\mathrm{mL}$ of di-4-ANEPPS-saturated ETOH in $100\mathrm{mL}$ water) and a nonstained slice. We oriented the tissue so that the stained slice was either near or far from the illuminated surface (i.e., shallow or deep). Since dye fluorescence may only originate in the stained slice, fluorescence measurements for the two orientations indicated approximate contributions of shallow and deep tissue.

Fig. 3

Schematic of setup for the experimental measurements. A laser beam $\left(488\mathrm{nm}\right)$ of approximately $0.3\mathrm{cm}$ diameter illuminated a pair of $0.1\text{-}\mathrm{cm}$ -thick cardiac tissue slices held between glass slides. Fluorescence light escaping the opposite surface of the tissue slices passed through a $530\text{-}\mathrm{nm}$ longpass or $670\pm 6\text{-}\mathrm{nm}$ bandpass emission filter into an integrating sphere ( $24.5\mathrm{cm}$ diameter) and was measured with a power meter.

The tissue was illuminated with an approximately $0.3\text{-}\mathrm{cm}$ -diam beam from an argon laser (Lexel 95, $488\mathrm{nm}$ , $40\text{to}80\mathrm{mW}$ ). Fluorescence exiting the far side of the tissue passed through a longpass (wavelengths $>530\mathrm{nm}$ ) or bandpass filter $(670\pm 6\mathrm{nm})$ into an integrating sphere (Labsphere, $24.5\text{-}\mathrm{cm}$ diameter). The longpass filter enabled us to collect light from a large portion of the fluorescence spectrum, whereas the bandpass filter provided measurements directly applicable to the fluorescence wavelength of $669\mathrm{nm}$ used in our Monte Carlo simulations. A power meter (Newport 840 with 4031 probe) attached to the sphere indicated transillumination-induced fluorescence intensity.

To examine the effect of increased red absorption, pairs of slices were initially stained with a fluorescence absorber (Signature Brand, blue 1, $0.3\mathrm{g}$ in $100\mathrm{mL}$ water), which produced visible darkening of specimens. One of the slices in each of these pairs was then stained with the di-4-ANEPPS. Measurements of the transillumination-induced fluorescence intensity were performed for the two orientations.

3.1.

Interrogated Region with Normal Optical Properties of Stained Hearts

Figures 4a and 4d show the interrogated regions for the broad-field excitation method with normal optical properties, i.e., the values that have been measured in di-4-ANEPPS-stained heart tissue.⁶ Figure 4a shows the results for epi-illumination while Fig. 4d shows the results for transillumination. The absorbed excitation light (total weight of excitation photons absorbed in tissue within the $0.25\text{-}\mathrm{cm}$ recording radius) was 21% of the total weight of all incident excitation photons. When expressed as a percentage of the weight of just those excitation photons incident within the recording radius, the absorbed excitation light was 84%.

Depths of interrogation for all the contours were greater for transillumination than for epi-illumination. For example, at a radius of $0.05\mathrm{cm}$ , the 80% contour in Fig. 4a had a depth of approximately $0.1\mathrm{cm}$ , while the corresponding depth in Fig. 4d was $0.25\mathrm{cm}$ (i.e., it included the entire tissue thickness). The maximum radius of interrogation was greater for the transillumination, e.g., maximum radius of the 80% contour was $0.13\mathrm{cm}$ for epi-illumination and $0.21\mathrm{cm}$ for transillumination. The total weight of collected fluorescence photons for transillumination was 38% of that for epi-illumination, consistent with greater travel distance and absorption of photons for transillumination.

Figure 5 shows the contributions to the collected fluorescence from different depths at a radius of $0.01\mathrm{cm}$ for the broad-field excitation method with the normal optical properties. Contributions are expressed as percentages of the total collected fluorescence that originated from all depths at that radius. Figure 5a shows the results for epi-illumination, while Fig. 5b shows the results for transillumination. The contributions for epi-illumination rapidly decrease at all depths shown, whereas contributions for transillumination decrease gradually.

Figures 6a and 6d show interrogated regions for the laser scanner excitation method with normal optical properties. The absorbed excitation light within the recording radius was 83% of the weight of incident excitation photons. Again, depth of interrogation for all contours was greater for transillumination compared with epi-illumination [e.g., at a radius of $0.05\mathrm{cm}$ the 80% contour in Fig. 6a had a depth of approximately $0.1\mathrm{cm}$ , while the corresponding depth in Fig. 6d was $0.15\mathrm{cm}$ ]. The total weight of collected fluorescence photons for transillumination was 61% of that for epi-illumination.

Figure 7 shows the contributions to the collected fluorescence from different depths at a radius of $0.01\mathrm{cm}$ for the laser scanner excitation method with the normal optical properties. As found for the broad-field excitation method, the largest contributions to the collected fluorescence occurred from tissue at shallow depth. Also the contributions for epi-illumination decreased more rapidly with depth than occurred for transillumination (e.g., at a depth of $0.15\mathrm{cm}$ for epi-illumination the contribution decreased to 6% of the maximum contribution, whereas for transillumination the contribution decreased to 17% of the maximum). For transillumination, however, the decrease found with the laser scanner excitation method was more rapid than that with broad-field excitation method [e.g., Fig. 7b versus Fig. 5b].

The total weight of collected fluorescence expressed as a percentage of the weight of excitation photons incident on the tissue surface within the recording radius was greater with the laser scanner excitation method compared with the broad-field method. For epi-illumination, this value for the laser scanner method in Fig. 6a was 9 times that for the broad-field method in Fig. 4a. For transillumination, the value in Fig. 6d was 14 times that in Fig. 4d.

3.2.

Effects of Altered Absorption Coefficients

Panels (b), (c), (e), and (f) in Figs. 4 and 6 show the interrogated regions when the absorption properties of the tissue at 488 or $669\mathrm{nm}$ were varied. Figure 4 shows results for the broad-field excitation method, while Fig. 6 shows results for the laser scanner excitation method. The center panels in each column show the effect of a threefold increase of the absorption coefficient of fluorescence, while the bottom panels show the effect of a threefold increase of the absorption coefficient of excitation light.

The increased fluorescence absorption coefficient produced a slight decrease in the interrogated depths for epi-illumination, e.g., at a radius of $0.05\mathrm{cm}$ , the 80% contour had a depth of approximately $0.1\mathrm{cm}$ for the normal conditions and $0.9\mathrm{cm}$ when the absorption was increased [Fig. 4b versus Fig. 4a and Fig. 6b versus Fig. 6a]. However, for transillumination the interrogated depths increased [Fig. 4e versus Fig. 4d and Fig. 6e versus Fig. 6d]. This was more pronounced for the broad-field excitation, for which the brightest collected fluorescence photons originated away from the illuminated surface [20% contour in Figure 4e]. Also the radius of interrogation decreased for the broad-field method.

The increased absorption coefficient of fluorescence did not affect the excitation light or its absorption in the models, however, the total weight of collected fluorescence decreased. The decreases, expressed as a percentage of the total weight of collected fluorescence for the heart tissue with normal absorption, were 25% for broad-field excitation with epi-illumination, 47% for broad-field excitation with transillumination, 43% for laser scanner excitation with epi-illumination, and 63% for laser scanner excitation with transillumination.

When we increased the absorption coefficient of the $488\mathrm{nm}$ excitation light threefold, the major effect on the interrogated regions was a decrease in the depth of interrogation, which was observed for all methods examined [panels (c) versus (a) and (f) versus (d) in Figs. 4 and 6]. The total weight of excitation photons absorbed inside the tissue increased to 93 and 94% of the excitation light incident within the recording radius (compared with the 84 and 83% described for the normal absorption with broad-field and laser scanner excitation methods, respectively). The total weight of collected fluorescence decreased by 57% for broad-field excitation with epi-illumination, 73% for broad field excitation with transillumination, 49% for laser scanner excitation with epi-illumination, and 63% for laser scanner excitation with transillumination.

In simulations already described, the amount of collected fluorescence (expressed as a percentage of the weight of excitation photons incident on the tissue surface within the recording radius) was consistently greater for the laser scanner excitation method compared with the broad-field method. With the threefold increased fluorescence absorption coefficient, it was greater by a factor of 6.8 times for epi-illumination and 10 times for transillumination. With the threefold increased excitation light absorption coefficient, the factor became 10.5 times for epi-illumination and 20 times for transillumination.

To further study the effects of variations in the absorption coefficient at 488 and $669\mathrm{nm}$ , we examined the depth of interrogation for a range of absorption coefficients that encompass normal values in myocardium stained with di-4-ANEPPS (Figs. 8 and 9 ). When the absorption coefficient of the fluorescence was increased (Fig. 8), the depth of interrogation decreased for epi-illumination (empty diamonds), while it increased for transillumination (filled squares). When the absorption coefficient of the excitation light was increased (Fig. 9), the depth of interrogation usually decreased.

Fig. 8

Maximum depth of the tissue from which the brightest 80% of the fluorescence photons originated at a radius of $0.05\mathrm{cm}$ . Simulations used different absorption coefficients for fluorescence light. Results are shown for (a) broad-field and (b) laser scanner excitation methods, with absorption coefficients of 0.3, 1, 3, and $10∕\mathrm{cm}$ . Each panel shows results for epi-illumination (open diamonds) and transillumination (filled squares). The vertical dotted line indicates normal absorption coefficient for cardiac tissue stained with di-4-ANEPPS. A depth of zero corresponds to the tissue surface nearer the incident excitation light, and a depth of $0.25\mathrm{cm}$ corresponds to the tissue surface away from the incident excitation light.

Fig. 9

Maximum depth of the tissue from which the brightest 80% of the fluorescence photons originated at a radius of $0.05\mathrm{cm}$ . Simulations used different absorption coefficients for excitation light. Results are shown for (a) broad-field and (b) laser scanner excitation methods, with absorption coefficients of 1.8, 5.2, 15.6, and $52∕\mathrm{cm}$ . Each panel shows results for epi-illumination (open diamonds) and transillumination (filled squares). The vertical dotted line indicates normal absorption coefficient for cardiac tissue stained with di-4-ANEPPS. A depth of zero corresponds to the tissue surface nearer the incident excitation light and a depth of $0.25\mathrm{cm}$ corresponds to the tissue surface away from the incident excitation light. Data points for epi-illumination and transillumination with an absorption coefficient of $52∕\mathrm{cm}$ in (a) are superimposed.

3.3.

Experimental Measurements

To test whether model predictions apply to optical measurements in heart tissue, we measured the contributions at two different depths to the collected fluorescence using differently stained tissue slices. We chose to examine the addition of a fluorescence absorber with transillumination because these conditions produced the greatest interrogated depth in our models.

For the slices that had no coloaded absorber (Tables 1, 2 , control), fluorescence intensity when the slice stained with di-4-ANEPPS faced away from the laser was 0.67 to 0.68 of the value found when the slice faced the laser. With the fluorescence absorber coloaded, fluorescence intensities decreased for both positions of the slice containing the di-4ANEPPS. This can be seen by comparing row 1 with row 2 in Tables 1, 2. However for both fluorescence filters tested, the decrease was smaller when the slice containing di-4-ANNEPS faced away from the laser, representing deeper tissue (from mean values of 0.67 to 0.53 in Table 1 and from 0.68 to 0.45 in Table 2, which are decreases of 21 and 34%, respectively) compared to the result found when the slice containing di-4ANEPPS faced the laser (from 1 to 0.66 in Table 1 and from 1 to 0.50 in Table 2, which are decreases of 34 and 50%). These results indicate that the coloaded fluorescence absorber increased the relative contribution of the deeper slice to the collected fluorescence.

Table 1

Intensity of fluorescence measured with transillumination using a longpass 530nm filter.

Table 2

Intensity of fluorescence measured with transillumination using a bandpass 670±6nm filter.

4.1.

Interrogation Depth

The interrogated region for transillumination was deeper than that for epi-illumination (Figs. 4 and 6). Deeper interrogation may occur with transillumination because the length of the path traveled by the photon and attenuation may be grater for those fluorescence photons launched near the illuminated surface, enabling other fluorescence photons launched deeper in the tissue to contribute a greater percentage to the total collected fluorescence. This result is consistent with conclusions from a 1-D model.³ We also found the depth for transillumination was smaller with the laser scanner excitation method compared with the broad-field method, which may be due to differences in the excitation fluence distribution as well as the fluorescence collection. The excitation fluence for a narrow laser beam might attenuate more rapidly with depth due to lateral travel of scattered photons.

Results indicate an increase of absorption coefficient of the fluorescence light increased the depth of interrogation for transillumination (Figs. 4e versus 4d and Figs. 6e versus 6d), while it decreased depth for epi-illumination [Figs. 4b versus 4a and Figs. 6b versus 6a]. This suggests cardiac optical mapping of tissue coloaded with a fluorescence absorbing dye would help to localize interrogation either near the illuminated surface for epi-illumination or deeper in the tissue for transillumination. Our results indicate such coloading is possible by adding a blue dye to cardiac bathing solution.

An increase in absorption coefficient of the excitation light decreased depth of interrogation for all methods tested [Figs. 4c versus 4a, Figs. 4f versus 4d, Figs. 6c versus 6a, and Figs. 6f versus 6d]. This suggests coloading the heart with a red dye may be useful to localize interrogation near the illuminated surface for epi-illumination. However, this would not enhance the interrogation depth for transillumination.

4.2.

Experimental Measurements

Predicted effects of coloading with a fluorescence absorber are supported by experimental measurements. When the fluorescence absorber was coloaded, we found the collected fluorescence intensity decreased in our measurements with the di-4-ANEPPS slice away from or facing the laser to represent deeper and shallower tissue, respectively (Tables 1, 2). This is comparable to the 47 to 63% decrease in the total weight of collected fluorescence produced by increasing the absorption coefficient for $669\text{-}\mathrm{nm}$ light threefold in our Monte Carlo models for transillumination using the broad-field and laser scanner methods. While the similarity suggests we produced similar changes in absorption in the model and experiments, the amount of decrease will depend on the amount of fluorescence-absorbing dye added experimentally or the absorption coefficient in a model.

For the control data, the contribution of the deeper slice (i.e., measurement with di-4-ANEPPS away from the laser) was 67 to 68% of the contribution of the shallow slice (di-4-ANEPPS facing the laser). A smaller contribution of deeper tissue is consistent with the models for transillumination with broad-field and laser scanner excitation in which the interrogated region was primarily in the tissue nearer the illuminated surface representing shallow tissue [Figs. 4d and 6d]. With a fluorescence absorber coloaded, the contribution of the deeper slice was still less than the contribution of the shallow slice, consistent with the model results in which the interrogated region remained closer to the illuminated surface [80% contour in Fig. 4e and all contours in Fig. 6e]. However, with the coloaded absorber, the fluorescence intensity when the slice stained with di-4-ANEPPS faced away from the laser was 80 to 90% (column 2 versus 1, row 2, of both tables) of the intensity found when the slice faced the laser, whereas the corresponding values were only approximately 68% in the control data (column 2 versus 1, row 1 of both tables). This agrees with the relative increase in depth of interrogation in the models with the addition of the fluorescence absorber [compare Figs. 4e versus 4d and Figs. 6e versus 6d].

4.3.

Absorbed Excitation Light

The predicted 83 to 84% of excitation photons absorbed in the heart tissue stained with di-4-ANEPPS in our models is largely accounted for by the absorption coefficient for excitation light in the tissue. For example, given the absorption coefficient of $5.2∕\mathrm{cm}$ at $488\mathrm{nm}$ , ignoring scattering, the exponential law of absorption would indicate 73% of the excitation light is absorbed over a photon pathlength of $0.25\mathrm{cm}$ . By accounting for additional distance of travel due to scattering, the Monte Carlo models are expected to absorb a greater percentage.

An increased absorption coefficient of excitation light produced a rise in the total amount of excitation light absorbed to approximately 94%, which is less than the rise expected from the absorption alone (with an absorption coefficient of $15.6∕\mathrm{cm}$ and a pathlength of $0.25\mathrm{cm}$ , ignoring scattering, the exponential law predicts 98% of the light is absorbed). The lower value in our Monte Carlo models may be due to effects of loss of photons by backscattering near the illuminated surface, which may prevent the value from approaching 100%.

4.4.

Collected Fluorescence

An increase in the absorption coefficient for the fluorescence decreased the total weight of fluorescence collected by 25 to 63% for the four methods modeled. This was most pronounced for transillumination with the laser scanner excitation method. A decrease for the transillumination can be expected, given that some fluorescence photons that exit the far side of the tissue will have a longer travel distance and hence more chance to become absorbed in the tissue compared with photons that exit the illuminated surface.

The finding that an increased absorption coefficient for either excitation light or fluorescence decreased the total collected fluorescence intensity indicates the fluorescence light detector must be more sensitive when an absorber is used. For example, in all of our models with a threefold increase in the absorption coefficient for excitation light or fluorescence, we found the total weights of collected fluorescence decreased by 25 to 73%. This predicts, in the worst case for the $0.25\text{-}\mathrm{cm}$ thickness modeled, the sensitivity of the detector must increase approximately fourfold to produce the same output signal level found without coloading an absorber. This increase can be achieved by additional electron gain or transconductance amplification with photomultiplier tubes or photodiodes. Also the intensity of the incident excitation light can be increased if needed to produce more fluorescence. A small fluorescence intensity may become a more important limitation of transillumination for cases in which tissue thickness or absorption are greater than those in our models.

4.5.

Lateral Interrogation

While results from a single radius at various depths (Figs. 5 and 7) are similar to Fig. 7 of Baxter, ³ our results also show lateral distributions of interrogated regions. The width of interrogation due to photon scattering inside the tissue is greater for transillumination compared with epi-illumination (most notably for the broad-field excitation method, e.g., Fig. 4). This is consistent with more scattering events for the transillumination, since fluorescence photons may travel greater distances before exiting the tissue. Also Fig. 4 shows that the radius of interrogation for the broad-field excitation is sensitive to changes in absorption coefficients.

Interestingly, the interrogated regions differ from results obtained with other metrics of spatial resolution. Estimates of lateral resolution as simply the imaging array element size divided by the magnification underestimate the interrogated region. This underestimation has been attributed to scatter of photons within the tissue and is expected to prolong the action potential upstroke even if a very small area of the surface is imaged.^{5, 6, 13} Also, the distribution of fluorescence exiting the tissue surface that originates from a point source in tissue at a given distance from the surface is identical for subsurface imaging compared with transillumination [e.g., Figs. 2(a)—2(c) of Ref. 14].

4.6.

Implications for Cardiac Optical Mapping

Electrophysiological studies that would benefit from mapping inside cardiac tissue include experiments with conduction block, fibrillation, regional ischemia, and electrical defibrillation.^{3, 4, 15, 16} Of the methods analyzed here, results indicate broad-field excitation with transillumination and coloading of a fluorescence absorber [Fig. 4e] provides the deepest interrogation. However, the increased range of tissue depths included in an interrogated region with transillumination is a limitation for studies of action potential upstroke velocity to assess rapid inward sodium current, microreentry, or defibrillation-shock-induced transmembrane potential changes on a microscopic spatial scale. Of all the methods analyzed, the smallest range of depths in an interrogated region was found with epi-illumination using the laser scanner method and addition of an excitation light absorber [Fig. 6c]. This may be useful in studies that require surface mapping with a smaller depth.