Photoacoustic imaging of fluorophores using pump-probe excitation.

A pump-probe technique for the detection of fluorophores in tomographic PA images is introduced. It is based on inducing stimulated emission in fluorescent molecules, which in turn modulates the amount of thermalized energy, and hence the PA signal amplitude. A theoretical model of the PA signal generation in fluorophores is presented and experimentally validated on cuvette measurements made in solutions of Rhodamine 6G, a fluorophore of known optical and molecular properties. The application of this technique to deep tissue tomographic PA imaging is demonstrated by determining the spatial distribution of a near-infrared fluorophore in a tissue phantom.


Introduction
Photoacoustic (PA) imaging relies on the absorption of short optical pulses by tissue chromophores to generate broadband ultrasonic waves that are detected at the tissue surface [1,2]. From the measured PA signals, images of the initial pressure distribution are then obtained using reconstruction algorithms. For excitation pulses in the visible and near-infrared wavelength region, these images typically show the vasculature since hemoglobin is the strongest absorber. If contrast agents such as fluorophores [3,4] or absorbing compounds [5][6][7] are present, the image will also contain their contribution to the initial pressure distribution. Their detection and visualization typically relies on multiwavelength techniques, which involve the acquisition of images at multiple excitation wavelengths and the use of spectral unmixing methods such as model-based inversion schemes [8]. These techniques can be computationally expensive and rely on accurate a priori information, such as the wavelength dependence of the specific absorption coefficient, to account for the spectral and spatial distortion of the fluence [9]. In fluorophores, however, the assumption that the PA spectrum is proportional to the specific absorption spectrum is not always valid. Fluorescence emission and ground state depopulation can reduce the amount of thermalized energy, and hence PA signal amplitude, generated during the typically short (ns), high peak power excitation pulses [10,11]. Since the relative contributions of these effects are also wavelength-dependent, they can compromise the accuracy of spectral unmixing methods. Despite these limitations, multiwavelength imaging approaches have been used in vivo to visualize exogenous fluorescent contrast agents [12,13], and genetically expressed fluorescent proteins in small translucent organisms [14] and in subcutaneous tumor xenografts [15,16].
Only non-radiative relaxations contribute to the thermalisation of the optical energy, and hence the PA effect. While PA pump-probe excitation of methylene blue has already been used to investigate the dependence of transient absorption on oxygen concentration [17,18], the technique presented in this paper is based on modulating the excited state lifetime of fluorophores by inducing stimulated emission (SE) which, in turn, results in a nonlinear modulation of the thermalized energy, and hence the PA signal amplitude. A theoretical model of the PA signal generation in fluorophores using pump-probe excitation is presented and experimentally validated on cuvette measurements made in solutions of a fluorophore of known optical and molecular properties. The application of this technique to deep tissue tomographic PA imaging is demonstrated by determining the spatial distribution of a nearinfrared fluorophore in a tissue phantom.

PA signal generation in fluorophores
The electronic and vibrational transitions in a fluorophore during pump photon excitation are illustrated in Fig. 1(a). The absorption of a pump photon, which occurs on a timescale of fs, promotes the molecule to an excited state, S 1 *, from where it relaxes vibrationally (within ps) to the lowest level of the excited electronic state, S 1 [19]. From S 1 , it then returns to the electronic ground state, S 0 , either via spontaneous emission of a photon, i.e. fluorescence, or via non-radiative processes, such as vibrational decay, internal conversion, or inelastic collisions. In fluorophores, this generally occurs on much longer timescales than vibrational relaxation, ranging from hundreds of ps to several ns [20,21]. A third possible relaxation pathway from S 1 to the ground state (not shown in Fig. 1(a)) is intersystem crossing via a triplet state, which may relax via phosphorescence or non-radiative relaxation on a timescale of ms. Though formally prohibited by the laws of quantum mechanics, this transition may still be observed in large fluorescent molecules, where strong spin-orbit coupling enables such spin-flip reactions.
Only non-radiative relaxations contribute to the thermalisation of the optical energy, and hence the PA effect. Non-fluorescent tissue chromophores, such as hemoglobin, water and lipids, relax via fast non-radiative processes (within ps), i.e. the optical energy is thermalized almost completely due to vibrational dissipation. In fluorophores, by contrast, the local thermalized energy is affected by (i) fluorescence, (ii) ground state depopulation [22], and (iii) intersystem crossing, which results in time-resolved PA signals that may differ in amplitude from those generated in non-fluorescent chromophores of equal absorption coefficient. First, the emission of fluorescence reduces the local thermalized energy. Second, ground state depopulation, which is caused by long excited state lifetimes, can lead to a transient reduction in the number of molecules in the ground state during ns excitation pulses. This has been shown to result in deviations from the linear dependence of the PA signal amplitude on absorber concentration [23], and in differences between the optical absorption and corresponding PA spectra [10]. Third, intersystem crossing may also reduce the signal amplitude since triplet state relaxation occurs on ms timescales, which does not fulfill the condition of thermal and stress confinement. However, for the fluorescent dyes used in this study, intersystem crossing is considered a weak effect [24] and is therefore neglected.
We propose to modulate the excited state lifetime of fluorescent molecules using PA pump-probe excitation, a qualitative observation of which we first reported in [25]. By selecting pump and probe wavelengths that coincide with the spectral region of maximum absorption and fluorescence emission, respectively, stimulated emission (SE) can be induced. SE accelerates the relaxation of the long-lived excited states to the ground state [26,27], which modulates the local thermal energy generated during an excitation pulse. By introducing a time delay between the pump and probe pulses, SE can be suppressed. The difference in the PA signal amplitude measured using simultaneous and time-delayed pumpprobe pulses provides a contrast mechanism that is unique to fluorophores since contributions from non-fluorescent chromophores are removed.

Materials and methods
In section 3.1, a 1-D forward model of the PA signal generation in fluorophores using pumpprobe excitation is introduced. The model predicts the PA signal amplitude as a function of input parameters such as fluorophore concentration, pump and probe fluence, fluorescence lifetime, and quantum yield. The experimental setup and the cuvette measurements are described in section 3.2 and 3.3, respectively. The setup and methods used for 3-D PA imaging of a fluorophore in a tissue phantom are presented in section 3.4.

Rate equations of the radiative and vibrational transitions
The electronic state of a molecule is determined by the total electron energy and the symmetry of the electron spin states. Each electronic state is subdivided into a number of vibrational and rotational energy levels associated with the motion of the atomic nuclei. A simplified schematic of the energy levels of a fluorophore is shown in Fig. 1(a). The photon absorption process is assumed to start from the ground state, S 0 , a spin-paired electronic singlet state. The interaction of the fluorophore with the incident pump and probe fields are modeled assuming that significant population densities are only found in the electronic ground state, S 0 , and in the first excited electronic state, S 1 . The vibrationally excited energy levels of the electronic states are denoted S 0 * and S 1 *. Transitions to the triplet state as well as excited state absorption processes are not expected to play a significant role for the fluorophores used in this study and are therefore neglected [24,28]. The time dependent changes in the population densities of the energy levels can then be described by a set of rate equations [29,30].  probe excitation (S 0 -electronic ground state, S 1 -first excited electronic state, S 0 * and S 1 *vibrationally excited energy levels, k vib -vibrational relaxation rate, k nr -non-radiative relaxation rate from S 1 to S 0 *, k f -rate of spontaneous fluorescence emission, k se -rate of SE). ΔE S1 , ΔE S10 , ΔE S0 indicate the relative energies of the transitions. (b) Wavelength dependence of the absorption cross section, σ a , and the SE cross section, σ se , of Rhodamine 6G.
The ground state, S 0 , is coupled to the vibrationally excited Franck Condon state, S 1 *, by a pump photon absorption process. The change in the respective population can be described by where N 1 * is the time-dependent population probability of S 1 *, N 0 is the relative population probability of S 0 , σ a is the wavelength-dependent absorption cross section in cm 2 ( Fig. 1(b)), Φ R pump the pump fluence rate (in mol cm −2 s −1 ), and k vib is the vibrational relaxation rate from S 1 * to S 1 . The first term describes the increase in N 1 * due to pump photon absorption, and also formally includes the possibility of SE (from S 1 * to S 0 ) induced by pump photons. However, this effect is unlikely to occur due to the fast vibrational relaxation from S 1 * to S 1 , which is described by the second term.
The rate of transition from S 1 to S 0 * is inversely proportional to the fluorescence lifetime, τ, given by where k nr is the non-radiative relaxation rate, which includes vibrational transitions and collisional energy transfer, and k f the rate of spontaneous fluorescence emission. The values of k nr and k f are of the same order of magnitude and are related through the quantum yield, η, which describes the relative probability of radiative transitions The rate equation that describes the temporal change of the population at S 1 is given by where N 1 is the population probability of S 1 , N 0 * is the population probability at S 0 *, σ se is the wavelength-dependent SE cross section in cm 2 ( Fig. 1(b)), and Φ R probe is the probe fluence rate (in mol cm −2 s −1 ). The first term describes the increase in the N 1 population due to vibrational relaxation from S 1 *, while the second term describes the reduction in N 1 due to spontaneous fluorescence emission and non-radiative relaxation processes. The third term describes the reduction in N 1 due to the stimulated emission induced by the probe pulse. As in Eq. (1), the third terms also formally includes the possibility of probe photon absorption and a transition from S 0 * to S 1 , which is unlikely to occur due to fast vibrational relaxation from S 0 * to the vibrational ground state, S 0 . The respective rate equations for N 0 * and N 0 are Since k vib >> τ −1 , it is assumed that k vib is the same for the vibrational transitions within the first electronically excited state and the electronic ground state. The sum of the population probabilities, N i (t), equals unity. The absolute population densities are calculated by multiplying N i (t) by the concentration of the fluorescent molecules, c (in cm −3 ).

Light propagation model
The pump and probe fluence rate distributions are described as a function of depth, x, and time, t, by using the Lambert-Beer absorption law for an optically homogeneous, nonscattering medium. The pump fluence rate distribution is given by Similarly, the probe fluence rate distribution can be expressed as where G(t) is a Gaussian function that describes the time course of the excitation pulses. Its full-width-half-maximum corresponds to the pulse duration. Φ R 0 pump and Φ R 0 probe are the fluence rate values at the surface of the sample. µ a (x,t) and µ se (x,t) are the depth-and timedependent absorption and SE coefficients, respectively, and are given by To describe the light propagation, the depth dependence of the populations, i.e. N i (x,t), is introduced. In order to calculate µ a (x, t) and µ se (x, t), Eqs. (9) and (10) are inserted in Eqs. (7) and (8), and the expressions for the pump and probe fluence rates are inserted into the coupled differential population rate Eqs. (1), (4), (5) and (6).

Calculation of the PA signal
In non-fluorescent chromophores, which typically exhibit rapid, non-radiative relaxation, the ground state can be considered fully populated during the excitation pulse, i.e. N 0 (x, t) = 1. In this case, µ a (x, t) is constant. For the case of negligible absorption at the probe wavelength, the initial pressure p 0 is then given by where Γ is the Grüneisen coefficient, which is a measure of the conversion efficiency of absorbed energy to pressure and Φ pump the pump fluence (in photons cm −2 ). The excitation pulse is assumed to correspond to a temporal delta function. In fluorescent molecules, the thermalized energy is affected by i) fluorescence emission, and ii) the space-and time-dependent population densities N i (x, t), which in turn determine µ a (x, t) and µ se (x, t). The initial pressure is therefore proportional to the number of vibrational and non-radiative transitions weighted by their relative energy level difference (as illustrated in Fig. 1(a)) integrated over the duration of the excitation pulses. The following expression then describes the initial pressure p 0 as a function of penetration depth ( ) * * S1 S10 S0 1 where ΔE S1 and ΔE S0 is the amount of energy that is thermalized due to the vibrational transitions from S 1 * to S 1 and S 0 * to S 0 , respectively. ΔE S10 is the energy of the transition from S 1 to S 0 *, and E is the energy of the transition S 0 to S 1 *, i.e. the energy of the absorbed pump photon. The energy level of S 1 can be estimated from the wavelength at which the absorption and fluorescence spectra intersect [31]. By solving the system of coupled rate equations, the initial pressure can be calculated using Eq. (12). The output of the forward model is the time-resolved PA signal amplitude, S(t), which is a function of fluorophore concentration, pump and probe fluence, pump-probe pulse time delay, Δt, and speed of sound, c s , in the sample: where Φ probe is the probe fluence (in photons cm −2 ), t 0 is the acoustic transit time between the illuminated surface of the sample and the acoustic detector. K is a scaling factor, which includes factors such as acoustic attenuation, the sensitivity of the transducer, and signal amplification. Fixed model input parameters are σ a (λ), σ se (λ), k vib , k f , k nr , ΔE S1 , ΔE S0 , and ΔE S10 . The generation of PA signals in fluorophore solutions using pump-probe excitation was investigated (i) by making measurements in cuvettes using PA spectroscopy and (ii) by acquiring 3-D tomographic images in a tissue phantom using an all-optical PA imaging system. A schematic of the experimental setup is shown in Fig. 2. A wavelength tunable OPO laser system (Newport Spectra Physics, USA) provided pump and probe excitation pulses of 7 ns duration at a repetition frequency of 50 Hz. Small portions of the excitation pulses were directed to an integrating sphere to measure the pulse energy with a wavelength-calibrated photodiode/integrator system and the wavelength with an USB spectrometer (Ocean Optics, USA). Prism reflectors mounted on an optical rail were used to control the time delay between the pump and probe pulses (Δt = 0.0 -7.7 ns).

Experimental setup
For the cuvette measurements, the signal and idler outputs of the OPO were coupled into a single fiber (1.5 mm core dia.) to homogenize and co-align the pump and probe beams. The output of the fiber was collimated and directed onto a custom made cuvette (5 mm path length) placed in a water bath. The beam diameter was approximately 4.5 mm. Neutral density (ND) filters were used to control the fluence. PA signals were detected using a planar piezoelectric transducer with a 10 MHz center frequency (Precision Acoustics, UK), amplified with a 40 dB voltage preamplifier (Femto, Germany), and recorded using a digitizer card (National Instruments, USA). For the PA imaging experiments in tissue phantoms, the output of the OPO was coupled into two separate fibers (1.5 mm core dia.) to direct the pump and probe pulses to an all-optical PA scanner based on a Fabry-Pérot etalon ultrasound sensor, which is described in detail elsewhere [32][33][34]. The PA imaging experiments are described in section 3.4.

Cuvette measurements
PA signals were measured using (a) pump pulse excitation, (b) probe pulse excitation, and (c) simultaneous pump and probe pulse excitation. The signals obtained in (a) and (b) were added and are subsequently referred to as 'signal without SE' while the signal obtained using simultaneous pump and probe pulses is referred to as 'signal with SE'. Figure 3 illustrates the initial compressive part (corresponding to the positive pressure generated in the absorbing sample in the cuvette) of a set of typical time-resolved PA signals. The signals were calculated using the forward model (Eq. (13)). The peak amplitude of a signal generated without SE is reduced compared to that generated in a non-fluorescent absorber of the same µ a due to the effects of fluorescence emission and ground state depopulation [22,23]. By contrast, a signal generated with SE can exhibit an increase in the peak signal amplitude. By subtracting the signals with and without SE, a difference signal is obtained. Its amplitude provides a measure of the change in the local thermalized energy due to SE and its effect on the excited state lifetime.  PA signals were measured in solutions of rhodamine 6G (Santa Cruz Biotechnology, USA) in methanol in a cuvette. Rhodamine 6G (R6G) is a fluorophore with well-known optical properties, such as radiative and non-radiative decay rates, and absorption and SE cross sections ( Fig. 1(b)) [35][36][37][38]. Its quantum yield is 0.9 and the fluorescence lifetime is 3.9 ns. For the measurements on R6G solutions, the pump and probe wavelengths were 532 nm and 560 nm, respectively. The R6G concentrations ranged from 42.5 to 170 µM (µ a = 1.2 -4.6 mm −1 at 532 nm). No evidence of photobleaching was found during the experiments. PA signals were measured in R6G solutions as a function of i) pump and probe fluence, ii) R6G concentration, iii) probe wavelength, and iv) time delay between the pump and probe pulse. The PA imaging setup is shown in Fig. 4. The tissue phantom was illuminated through the transparent Fabry-Pérot ultrasound sensor by the divergent output of the optical fibers, which produced a beam diameter of approximately 2 cm at the phantom surface. It consisted of a scattering lipid suspension (µ s ' ~1.5 mm −1 ) in which polymer capillary tubes (i.d. 600 µm, Paradigm Optics Inc., USA) were immersed. The tubes were filled with a fluorescent dye, Atto680 (Atto-tec GmbH, Germany) in aqueous solution (c = 160 μM, µ a = 4.6 mm −1 at 680 nm), or whole murine blood. Atto680 in water has a fluorescence lifetime of 1.7 ns and a quantum yield of 0.3. 3-D tomographic image data sets were acquired in backward mode using a pump fluence of 6 mJ/cm 2 at a wavelength of 680 nm and a probe fluence of 7 mJ/cm 2 at 742 nm. The x-y scan area was 22 mm by 4 mm. Two image data sets were acquired using (i) simultaneous pump-probe pulses and (ii) time delayed pump and probe pulses (Δt = 7.7 ns). Images of the initial pressure distribution were reconstructed using a time reversal image reconstruction algorithm [39]. A difference image was obtained by subtracting the images acquired using simultaneous and time delayed pulses. Figure 5 shows the initial compressive part of PA signals measured in an 85 µM R6G solution using different pump and probe pulse fluences together with signals calculated using the forward model. The model input parameters were the known concentration, the measured pump and probe fluences, and the optical properties of R6G, such as σ a (λ), σ se (λ), k vib , and k f [35][36][37][38]. Figure 5(a) shows the PA signals for Φ pump = 10 mJ/cm 2 and Φ probe = 28 mJ/cm 2 . Figure 5(b)-5(d) (left column) show the PA signals for decreasing Φ pump at constant Φ probe, while Fig. 5(e)-5(g) (right column) show the PA signals for decreasing Φ probe at constant Φ pump . In Fig. 5(a), the PA signal without SE does not show the typical exponential shape observed in non-fluorescent absorbers. The PA signal amplitude at t 0 = 4.45 µs, which corresponds to the region adjacent to the cuvette window, is lower than that at earlier times points around 4.2 µs, i.e. corresponding to deeper regions. This suggests that ground state depopulation is strong for high pump fluences. Under such conditions, a significant portion of the pump photons encounter molecules in an excited state and are therefore not absorbed.

Effect of pump and probe fluence
(1) (1) (1) (1) (1) These photons will propagate further into the sample, resulting in increased PA amplitude at greater depths. By contrast, the signal with SE has higher peak amplitude and is almost exponential in shape. This is because SE causes rapid relaxation to the ground state, which allows the repeated absorption and thermalisation of additional pump photons. The changes to the local thermalized energy are also evident from the difference signal, which shows negative amplitude close to the cuvette surface, i.e. an increase in thermalized energy, and positive amplitude at larger penetration depths, i.e. a reduction in thermalized energy. Figure  5(b)-5(d) show the effect of decreasing Φ pump , which decreases the difference signal amplitude. In addition, the shape of the PA signal without SE gradually approaches that of an exponential function. This suggests that ground state depopulation is less significant at low pump fluences. In this situation, the density of pump photons is sufficiently low to result predominately in ground state absorption. Figure 5(e)-5(g) show that by reducing Φ probe while keeping Φ pump constant the PA difference signal amplitude, and hence the effect of SE, is reduced. The experimental and the modeled data are in good agreement. Figure 6 shows PA signals measured in R6G solutions with concentrations of 42.5 µM, 85 µM, and 170 µM. At 170 µM (Fig. 6(a)), the pump pulse (Φ pump = 6 mJ/cm 2 ) is strongly absorbed as evidenced by the fast exponential increase in the PA signal amplitude. In addition, the difference between the signals acquired with and without SE (for Φ probe = 24 mJ/cm 2 ) is small compared to those at lower concentrations. At high concentrations, the pump photon density per fluorescent molecule is sufficiently low to prevent ground state depopulation, i.e. most pump photons encounter molecules in the ground state. The fluence distribution is therefore similar to that predicted by the Beer-Lambert law. In addition, the effects of SE are minimal since repeated absorption-relaxation cycles are unlikely. With decreasing concentration, the relative amplitude of the difference signal compared to the signal without SE increases from 15% at 170 µM ( Fig. 6(a)), to 40% at 85 µM ( Fig. 6(b)), and to almost 90% at 42.5 µM (Fig. 6(c)). At low concentrations, the pump photon density per fluorescent molecule is sufficiently large for ground state depopulation to occur, which in turn allows SE, and its effect on the thermalized energy, to become more evident. The measured signals and those predicted by the model are in good qualitative agreement in terms of the relative signal amplitudes with only minor differences observed in the signal shape.

Effect of probe wavelength
Figure 7(a) shows the difference signal amplitude (peak-to-peak) measured in R6G solution as a function of probe beam wavelength for constant pump-probe fluences together with that predicted by the forward model. The maximum difference signal was measured at a probe wavelength of 560 nm, which is close to the wavelength of maximum fluorescence emission. The difference signal decreases with increasing wavelength according to σ se (λ) of R6G, with experimental and modeled data showing good agreement. It was found that the agreement between model and data was improved further by selecting a quantum yield of 0.93, comparable to the value measured in ethanol solutions of R6G [37]. Figure 7(b) shows the difference signal amplitude (peak-to-peak) measured in an R6G solution as a function of time delay together with the model prediction (c = 170 µM, Φ pump = 4 mJ/cm 2 , and Φ probe = 10 mJ/cm 2 ). The difference signal decreases with increasing time delay, which is explained by the gradual suppression of SE. The measured and modeled data were found to be in good agreement.  Figure 8 shows the results of the tissue phantom imaging experiments. Figure 8(a)-8(c) show 2-D x-z cross sectional images of 3-D image data sets acquired using simultaneous pumpprobe pulses (Fig. 8(a)), time delayed pump-probe pulses ( Fig. 8(b)), from which a difference image was calculated (Fig. 8(c)). While Fig. 8(a) and 8(b) show the locations of all tubes, the difference image clearly shows the location the fluorescent dye. Importantly, the background signal originating from non-fluorescent absorbers, such as blood, is removed. From the 3-D image data sets corresponding to Fig. 8(b) and 8(c), a fused volume rendered 3-D image was created using ZIBAmira (Zuse Institut Berlin, Germany) to visualize the spatial distribution of the fluorophore and that of blood ( Fig. 8(d)).

Discussion
This study demonstrated that pump-probe excitation can be used to modulate the PA signal amplitude in fluorophores. The relative amplitude of the difference signal provided a measure of the modulation of the thermalized energy as a result of SE and was shown to depend strongly upon the ratio of fluorophore concentration and the local pump and probe fluences. In addition, the amplitude of the difference signal has been shown to depend on the cross section of SE and the pump-probe time delay.
The physical mechanism underlying the modulation of the PA signal amplitude using pump-probe excitation is the induction of SE, which strongly reduces the typically long excited state lifetime of fluorophores, accelerates the return of the molecules to the ground state, and therefore facilitates the absorption of additional pump photons during an excitation pulse. Under conditions of high probe fluence, i.e. efficient generation of SE, the number of absorption-relaxation cycles within the duration of an excitation pulse is primarily dependent upon the ratio of fluorophore concentration, c, and pump fluence, Φ pump . For low c/Φ pump , strong ground state depopulation and SE can result in multiple excitation-relaxation cycles during a ns excitation pulse. This accumulatively increases the amount of the local thermalized energy originating from the vibrational relaxations within the S 1 and S 0 states ( Fig. 1(a)).  This is observed as increase in the PA signal amplitude near the source where multiple absorption-relaxation cycles are supported by a high Φ pump , while the attendant increase in pump photon absorption and reduction in absorption-relaxation cycles lead to a decrease in signal amplitude at greater depths ( Fig. 5(a)). For large c/Φ pump , by contrast, ground state depopulation is comparatively weak since most pump photons will encounter molecules in the ground state while SE reduces the number of excited molecules that may otherwise have undergone non-radiative relaxation. Since multiple excitation-relaxation cycles are unlikely to occur under these conditions, SE results in a reduction in the amount of thermalized energy, and hence the PA signal amplitude. While a difference signal can be detected in both cases, in vivo PA imaging applications typically result in a combination of low fluorophore concentrations and high fluence, i.e. simultaneous pump-probe pulses would produce an increase in the PA signal amplitude compared to that generated using time-delayed pulses.
The output of a forward model of the PA signal generation in R6G solutions was found to be in good agreement with the measured data, thus experimentally validating the model. It should be noted that the fitting of model input parameters, apart from the normalization of the model predictions to the measured data, was not required to achieve good agreement, i.e. the relative PA signal amplitudes were accurately predicted by the model. This suggests that a rate equation model of the temporal changes in the population density of four energy states can be used to describe the PA signal generation in fluorophores. Small discrepancies between the measured and predicted PA signals were nevertheless observed. These can be attributed to uncertainties in the measurement of experimental parameters, such as the pulse energies, and differences between the fixed model input parameters and their true values, such as the beam profile and beam divergence. A minor adjustment of the quantum yield of R6G was found to improve the agreement between model and data, which is reasonable since the optical properties, such as the quantum yield, of most fluorophores are sensitive to environmental parameters, e.g. concentration, pH, oxygen saturation [40], and deviations from literature values on the order of a few percent are not uncommon [41].
Tomographic PA imaging of a near-infrared fluorophore using pump-probe excitation in tissue phantoms was demonstrated using fluences below the ANSI safety limit of maximum permissible exposure (MPE) of skin. This method provides a PA contrast mechanism that is unique to fluorophores and can therefore be exploited for their detection. For example, multiplexed imaging of fluorophores could be achieved using a combination of wavelength selective and pump-probe PA excitation. By calculating difference images, the PA contrast originating from non-fluorescent, endogenous absorbers is completely removed. This provides a detection method that is, in principle, limited by the noise floor of the PA image acquisition system. By contrast, the accuracy of fluorophore distributions recovered from multiwavelength images using spectral unmixing methods can also be adversely affected by uncertainties in the a priori information, such as the specific absorption spectra of fluorophores [10]. A further major advantage of this method lies in its simple experimental implementation, which requires the acquisition of two images with and without time delay between the pump and probe pulses, and the calculation of a difference image. In addition, the absorption and SE (or fluorescence) spectra of the near-infrared fluorophore coincide with the wavelength region where the optical penetration depth of biological tissue is at a maximum. Lastly, by detecting the spatial distribution of a fluorophore, this method may provide prior information for model-based inversion schemes for quantitative PA imaging with which the scale of the inverse problem could be reduced.

Conclusions
This study has demonstrated that dual wavelength pump-probe excitation can be used to induce SE in fluorescent molecules, which modulates the amount of thermalized energy, and thus the PA signal amplitude. A forward model of the PA signal generation in fluorophores based on rate equations was used to predict time-resolved signals generated in a cuvette which were found to be in good agreement with measured data. By acquiring tomographic PA difference images of a tissue phantom using pump-probe excitation, it was demonstrated that this contrast mechanism can be used to detect the location of fluorophores. This method may be suitable for in vivo PA imaging applications, such as preclinical imaging of exogenous or genetically expressed fluorescent labels in small animals.