2.1.

Principle of Nanoscale Photoacoustic Tomography

nPAT uses two laser beams for signal generation and detection. The excitation beam is tuned to an absorbance peak of the primary molecule being used as a contrast agent (532 suffices in the case of Hb). The excitation and detection wavelengths are kept below the ANSI safety limit if dynamic imaging of biological samples is desired. The detection beam is ideally tuned to a wavelength of maximum reflectance but can also be of the same wavelength as the excitation wavelength. Pump–probe detection of the excitation beam-induced acoustic signal is then performed in the axial direction.^24,25 Optical detection as opposed to detection by an ultrasound transducer enables nPAT to detect extremely high-frequency signals.^25–29 This allows for nPATs axial resolution to surpass that of conventional PAM as the axial resolution is dependent on the bandwidth of ultrasound detection.³⁰ This extends the theoretical resolution of nPAT into the nanometer range. The high resolution achieved by nPAT is not a result of optical focusing, but instead the extremely high bandwidths that are achievable in laser-based pump–probe systems. As a result, the resolution of nPAT should ultimately only depend on the excitation pulse duration and sound velocity.

The experimental setup of nPAT requires the use of a pulsed laser, several beam splitters, two focusing lenses of sufficiently high numerical aperture, an optical delay line, mirrors, and detection electronics (e.g., photodiodes). The laser beams are close to confocal on the sample, with the pump being less finely focussed than the probe so as to enable a large axial field of view. A schematic of an nPAT setup is available in our previous studies.²⁴

The primary axial resolution limitations in current photoacoustic imaging techniques such as PAM are the bandwidth of the detecting ultrasound transducer and the laser pulse duration.^30–33 Typical transducers are capable of detecting photoacoustic signals on the order of tens of MHz. However, the physical photoacoustic signal is theoretically broadband, with relevant contributions in the GHz range for excitation pulses on the order of picoseconds.³⁴ These GHz signals contain information about higher resolution imaging, and the ability to detect them is directly tied to the resolution of the final image. Therefore, to detect such high-frequency pulses and obtain nanometer resolution in the axial direction, a piezoelectric transducer is insufficient. For this reason, nPAT uses a pump–probe signal detection method, allowing for the detection of high bandwidths.

2.2.

Resolution of Nanoscale Photoacoustic Tomography

To calculate the maximum achievable resolution of nPAT, we begin by considering the excitation pulse laser. For a Gaussian laser pulse, the intensity as a function of time can be written as

Let $\tau ={\frac{(t-\frac{r}{v})}{\theta }}^{}$. Then, substituting this into Eq. (1):

The photoacoustic pressure produced by a point source as a function of $r$ and $\tau$ has been derived by Calasso et al.³⁵ In the case of delta function heating and linear thermal expansion, it is given as

Substituting in Eq. (2) into Eq. (3) yields

This function has maxima/minima at $\tau =\pm \frac{1}{\sqrt{2k}}$, which corresponds to $t=\pm \frac{\theta }{\sqrt{2k}}+\frac{r}{c}$. Applying the Rayleigh criterion, the temporal diffraction limit of two such point sources will occur when the minimum pressure of one point signal coincides with the maximum pressure of another. This is equivalent to the distance between the maximum and minimum of the photoacoustic point source. Time between the maxima and minima is then $\frac{2\theta }{\sqrt{2k}}$. The Rayleigh spatial resolution is given by converting this time into a distance by multiplying by the sound speed. Then, the maximum theoretical resolution achievable by a point source is given as

For a pulse duration of 7 ps and $v=1549.3\mathrm{m}/\mathrm{s}$, this corresponds to a maximum achievable axial resolution of 9.2 nm.

2.3.

Sensitivity of Nanoscale Photoacoustic Tomography

The sensitivity of nPAT is an important parameter in the assessment of its potential. Whereas an ultrasonic transducer benefits from higher sensitivities at the cost of lower bandwidth, acoustic detection via a laser pulse is the opposite scenario. The sensitivity of probe laser detection will be less than that of an ultrasound transducer at comparable distances from the source. The probe beam acts similar to a high-bandwidth transducer, and detects acoustic waves at the point at which it is focused. In this way, the focused probe beam can detect acoustic waves traveling through the focal point, and the pump beam can generate these acoustic waves. The two beams, pump and probe, can be focused very close to each other, making it easier to detect an nPAT signal very close to the source as compared with PAM. The sensitivity of nPAT can be estimated based on the theoretical change in refractive index caused by the acoustic pressure.

We assume that the sound wave (for simplicity’s sake) is a box function in one-dimension and propagates outward in three-dimensions. Then, the resultant change in refractive index induced related to the wave intensity is given as³⁶

It is assumed that $M$ for water and blood plasma remains the same. We also know that, for blood plasma, $\rho =1025\mathrm{kg}/{\mathrm{m}}^3$, $v=1549.3{\mathrm{m}\mathrm{s}}^{-1}$, $n=1.333$ using 532-nm light. This corresponds to $\widehat{p}=10.5$.

Simulations have suggested that acoustic waves produced by RBCs can reach amplitudes as high as 2500 pa.³⁴ For such a pressure, the resulting change in the refractive index is $\mathrm{\Delta }{n}_0=1.775\times {10}^{-5}$. In pump–probe imaging, the corresponding reflectance change, $\delta R$, induced by $\mathrm{\Delta }{n}_0$ is the probed quantity and can be given by evaluating the usual Fresnel equation

Substituting Eqs. (7) and (8) into Eq. (9) yields $\delta R\approx -2.17\times {10}^{-6}$. If instead we wish to go in the opposite direction and calculate the minimum detectable pressure (i.e., the sensitivity of nPAT), then we must isolate for pressure. Rearranging Eq. (9), we have

As $n_a-n_b=0.333$, and the magnitude of $\mathrm{\Delta }{n}_0$ will not exceed 0.333 (this would correspond to a pressure of 46 MPa, which is unreasonably high), the right side will be negative prior to taking the absolute value. Then, substituting in Eqs. (7) and (8) into Eq. (9) provides an equation for the pressure, as follows:

The pump–probe method’s sensitivity to reflectivity is theoretically limited to a reflectivity ratio change on the order of $-{10}^{-6}$, which corresponds to a reflectance change of $\delta R=2.04\times {10}^{-8}$.³⁷ Substituting this into Eq. (11) yields a noise equivalent pressure (NEP) of 21 pa, whereas ultrasound transducers can detect pressures as small as $<1\mathrm{P}\mathrm{a}$.³⁸

The number of molecules (NEN) required to generate this pressure, known as the noise equivalent NEN, is given by dividing this pressure by the pressure generated by a single molecule, $p_s$.³² For Hb, this pressure is given by the equation

However, Eq. (12) does not hold for indefinitely small pulse widths, and at pulse widths extending to shorter than stress confinement, the dependence on pulse-width vanishes, with shorter pulse widths no longer increasing signal amplitude.³² As compared with PAM, which uses an ultrasonic transducer, nPAT will benefit from typically higher NEN due to the fact that nPAT’s pump–probe detection method allows for $r$ to be very close to the source itself. However, laser-based detection is less sensitive than an ultrasound transducer at comparable distances from the source. For pulse widths comparable with PAM (30 ns) and fluence operating at the ANSI safety limit, the NEN for $r=1\mu \mathrm{m}$ is 292, which is a lower NEN than typically reported in PAM. This number can be further decreased by increasing the fluence or shortening the pulse.

3.1.

Sample Selection

To demonstrate the imaging capabilities of nPAT, we chose simulation geometries based on x-ray microscopy image data obtained and generously provided by Dr. Saibil of Hale et al.³⁹ We chose these samples, because they were obtained with x-ray microscopy and can serve as extremely high-resolution digital phantoms for physical simulations. Also, these samples show the malaria parasites clearly, in addition to the parasitophorous vacuole, digestive vacuole, and RBC membrane. The samples also show the RBC at different life cycle stages. The simulation geometries are outlined below.

3.2.

Simulation Geometry

We performed simulations on experimental data obtained by Hale et al.³⁹ via soft x-ray microscopy. These images depict a malaria-infected RBC treated with the broad-spectrum cysteine protease inhibitor E64. This treatment allows for the rupture of the parasitophorous vacuole membrane (PVM) but prevents RBC membrane rupture. The end result is merozoites that would otherwise egress, being trapped in the RBC.^40,41

These tomograms could then be used to construct a simulation geometry that was suitable for the photoacoustic imaging of the specimen. A sample slice from the segmented tomogram is shown in Fig. 1(a). This slice was transformed into a simulation geometry by filling in the segmented regions and assigning to each color a different absorption coefficient. A sample slice of the resultant geometry is shown in Fig. 1(b), along with the axially focused laser beam and the direction in which it scans. Scanning along the slice yields a series of 1-D images that can be combined and segmented to form a 2-D image. This can be repeated over the entire 3-D x-ray tomogram to yield a series of 2-D images, which can be combined into a 3-D image. Hale et al.³⁹ also used x-ray microscopy to image earlier stage malaria within RBCs by fixing with selective PKG inhibitor compound 2 (C2) to reversibly inhibit egress prior to the rounding up stage. These 3-D tomograms could also be similarly utilized and segmented to simulate nPAT imaging of malaria at this earlier stage. We performed simulations on this geometry in the same way as outlined above for the E64 fixed schizonts. The C2 tomograms consisted of 43 slices, and the E64 tomograms consisted of 27 slices. For both geometries, the distance between each slice was 80 nm and the pixel size in each slice was $16\times 16\mathrm{nm}$.

Fig. 1

(a) Segmented slice from E64 treated RBC infected with malaria imaged with x-ray microscopy, (b) simulation geometry slice showing the laser spatial dimensions and scan direction; each color of the RBC is assigned a different absorption coefficient. Green bar represents the laser, and green arrow is the scanning direction. Cyan: merozoite membrane, yellow: PVM, brown: digestive vacuole, red: RBC membrane, and white: additional vacuole, as identified by Hale et al.³⁹

3.3.

Wave Propagation

Once the simulation geometry was created, the k-wave^42,43 toolbox in MATLAB was used to simulate the propagation of all waves throughout the simulation. This toolbox solves the photoacoustic wave equation in both time and space using a pseudospectral method and therefore allows for the modeling of acoustic wave propagation in a user-friendly and computationally efficient manner.

The k-wave simulation was run in 2-D for the E64 simulation model to conduct slice-by-slice imaging of the RBC. The detector was placed at the top of the excitation laser pulse. To simulate a focused probe beam of 200 nm, signals arriving at a detector array at the top of the laser beam in Fig. 1(b) were averaged in time to yield a single waveform. The resulting pressure versus time A-line scans were set beside one another for the reconstruction of initial pressure in each slice for simple morphological imaging. Following this, the resulting images were manually segmented to obtain outlines of the differentiable merozoites and RBC membrane. For functional imaging, the detected pressures were corrected for $r^2$ amplitude decay using a correction algorithm.⁴⁴ This was not done for morphological images because the contrast was suitable for segmentation without this correction, and the raw pixel values do not reveal any morphological information. The pressures were assumed to be higher in the cytoplasm than in the parasites themselves as the cytoplasm contains the most Hb. For functional imaging, Hz amplitude was assumed to be 10 times that of the cytoplasm amplitude,⁴⁵ with little to no initial pressure in the parasites (corresponding to low absorber concentration).

3.4.

Functional Imaging Parameters and Geometry

To simulate functional imaging, we have replicated conditions in which the Hz and Hb concentrations are not uniform throughout the cell, with Hz only present in the digestive vacuole of the parasites. We have simulated nPAT RBC imaging at two different wavelengths, one at which Hb and Hz both absorb strongly and another at which only Hz absorbs strongly.

The reason for difference imaging is that Hb optical absorption is strong at 532 nm; however, Hz absorption can be more than an order of magnitude higher than Hb at this wavelength.^45–47 Therefore, if Hz were evenly distributed throughout the RBC, it would be the only optical absorber that stands out as compared with the background and would render Hb concentration mapping impossible. Fortunately, Hz formation and storage occurs entirely inside the digestive vacuole of the cell.⁴⁸ Additionally, Hb absorption is around four orders of magnitude less than that of Hz at wavelengths of around 670 nm. Therefore, PA signals imaging at 670 nm would almost entirely originate from Hz. The drastic difference in Hb absorption at these two wavelengths (532 and 670 nm), and the strong absorption of Hz at both of these wavelengths, presents an opportunity for difference imaging. Our simulations have been performed accordingly, with one simulation featuring both Hz and Hb absorptions, and a second image featuring only Hz absorption. The difference between these two images reveals the Hb concentration distribution throughout the cell.

4.1.

Morphological Imaging

X-ray tomograms of E64 treated schizonts just prior to egress were used as the simulation geometry to determine the initial acoustic pressure, which was then allowed to propagate to a linear detector array with element size of 200 nm (corresponding to the diffraction limit of 532-nm light, representing the focused probe beam). For the sake of simplicity, detected A lines were converted to images by simply mapping the intensity of the detected waveforms back onto the image space. These images were in turn manually segmented to identify parasites within the cell. The maximum supported frequency of the grid was 46.7864 GHz, and the detectors were not given any restrictions on bandwidth to simulate the high bandwidth of the pump–probe detection. This is in contrast to a PAM simulation, in which the detectors would have to be assigned some bandwidth of detection. This high bandwidth is what allows nPAT to achieve higher resolutions suitable for cellular imaging. The output of the k-wave simulation (a series of pressure versus time plots) represents detected signals in nPAT at different positions of laser scanning.

A 2-D slice from a simulated nPAT image is shown in Fig. 2(b). This figure shows that the merozoite images in nPAT have comparable resolution to those in x-ray microscopy. Merozoites (manually outlined in blue) are clearly visible within the RBC membrane (outlined in red). However, if this image was obtained by an nPAT imaging device, it would be an in-vivo image of the merozoites without necessitating fluorescent labeling. In addition, two of the vacuoles identified by Hale et al. are also visible.³⁹

Fig. 2

Simulation 2-D output (a) simulation geometry from segmented x-ray micrographs provided by Hale et al.³⁹ and (b) nPAT simulated image of samples slice in (a); outlines of merozoites and RBC can be made, as well as the larger vacuoles. Manual segmentation was performed to the image in order to outline key features.

This image was generated assuming Hb concentrations in the RBC according to the biological parameters. It has been shown that malaria cells digest up to 65% of the Hb in their host cell,⁴⁹ and so the absorption coefficient inside the merozoites was modeled as being $\sim 30\%$ smaller than that of the surrounding cytoplasm. Although the actual Hb may well be broken down and sent to the digestive vacuole for biocrystallization into Hz, the ultimate effect of this difference is that there is a much weaker photoacoustic signal from the malarial cells as opposed to the cytoplasm because that they have far less Hb.⁵⁰ This contrast is present regardless of where the Hb ends up as long as there is less Hb inside the merozoites than inside the cytoplasm. Hb that enters the merozoites is broken down via proteolysis, and the waste products are in turn transported to the digestive vacuole.^49,50 It is reasonable to expect that the Hb concentration inside merozoites will be substantially lower than that in the cytoplasm. nPAT can, therefore, differentiate between subcellular merozoites in malaria-infected RBCs and the cytoplasm of the RBC. As Hz is localized in the digestive vacuole (which can be removed via subtraction imaging at a different wavelength), the absorption of Hz was ignored for anatomical imaging simulations. However, it should be noted that in the experiment the suppression of this background will require multiwavelength laser imaging, taking advantage of the large difference in absorption of Hz and Hb at the wavelength of 700 nm and comparing with images from wavelengths at which Hb exhibits a peak. It can be seen that the stronger signals are near the “edge” of the merozoites. This is not to be confused with an edge effect; however, this is a consequence of the tight packaging of merozoites at this stage. The erythrocyte cytoplasm is visible entirely and all parts of it produce a signal. The appearance of signals originating from membranes alone is due to the high density of merozoites in the cell. As Hb concentration inside the merozoites is modeled to be smaller than that of the cytoplasm, the absence of a signal is used to identify merozoites. Merozoites are tightly packed within the cell, these signals are only strong in the small areas between merozoites, leading to what appears to be an edge effect but is in fact simply Hb absorption.

Two-dimensional slice-by-slice imaging can enable 3-D imaging and rendering of biological phenomenon. In this way, nPAT can achieve 3-D imaging through repeated tomographic imaging of 2-D slices. These 2-D slices can be segmented and then a mesh can be formed from segmented features to render 3-D images. The E64 nPAT tomogram was put through this process to model a sample nPAT 3-D image. The resultant image (shown in Fig. 3) was generated by meshing segmented merozoites, vacuoles, and the RBC membrane.

Fig. 3

E64 simulated 3-D nPAT image after slice segmentation and meshing: merozoites (blue) can be easily distinguished. The RBC outline (red) is also visible. The 3-D tomogram shows structural features with nanometer resolution throughout the RBC.

The shapes of the merozoites are apparent in high resolution. This image displays the 3-D imaging capabilities of nPAT to image malaria-infected RBCs. As nPAT is a noninvasive test, this imaging could theoretically be done during the live development of malaria without the need for E64 fixation to prevent egress, allowing for visualization of malarial development in living RBCs. The primary constraint of in vivo imaging will be in obtaining a high signal-to-noise ratio while simultaneously achieving fast raster scanning to allow for dynamic visualization. In this context, fast pump–probe scanning techniques such as asynchronous optical sampling can be combined with fast raster scanning techniques such as those used in photoacoustic remote sensing microscopy (PARS) to increase speeds and potentially enable dynamic imaging for small fields of views.

Different stages of malarial development can also be imaged with nPAT, allowing it to record, in vivo and without fluorescent labels, malarial development after cell infection. A C2 fixed cell was imaged with an x-ray microscope by Hale et al.³⁹ These tomograms, as in the E64 case, can serve as inputs to a k-wave simulation of nPAT imaging. The 2-D sample geometry with segmentation is shown in Fig. 4(a), and the resulting simulated nPAT image of this sample is subsequently shown in Fig. 4(b). It can be seen that the rough morphology of the RBC and the PVM is both preserved and visible in nPAT.

Fig. 4

(a) Segmented slice from C2 treated RBC infected with malaria imaged with x-ray microscopy, (b) simulated and segmented nPAT image of (a); outlines of the PVM and RBC membrane are visible (yellow: PVM, red: RBC membrane).

The resulting 3-D tomographic image is shown in Fig. 5. The yellow parasitophorous vacuole is clearly visible. However, the packaged malarial parasites could not be consistently differentiated from the parasitophorous vacuole in all 2-D slices. Nevertheless, the shape of the vacuole can be assumed to roughly resemble the shape of the parasites themselves as demonstrated by Hale et al.³⁹ This image demonstrates that nPAT is capable of imaging not just late stage but also early stage malarial development in vivo.

Fig. 5

Three-dimensional image of C2 fixed schizont after slice segmentation and meshing, demonstrating nPAT’s high-resolution imaging of early stage malarial development. Parasitophorous vacuole is shown in yellow with RBC membrane shown in red.

4.2.

Functional Imaging

Figure 6(a) shows the resulting image from functional imaging simulations at a wavelength where Hb and Hz absorb strongly. Due to the even stronger absorption of Hz, it can be seen that there is little contrast near the digestive vacuole from Hb, and the cell appears very dim compared with the strong signal coming from the digestive vacuole. Imaging at a wavelength where only Hz absorbs will essentially only produce an image of Hz concentration itself as shown in Fig. 6(b). To see the Hb image with the Hz interference removed, subtraction imaging can be done by taking the difference between Figs. 6(a) and 6(b), which is shown in Fig. 6(c). With the Hz signal subtracted, Fig. 6(c) is a relative concentration map of Hb only, therefore demonstrating the functional information that can be obtained from nPAT.

Fig. 6

Simulated functional imaging via nPAT. (a) Full absorber image, including both Hb and Hz. (b) Hz image showing relative concentration map. (c) Difference image of subtracting (b) from (a), revealing relative Hb concentration in the cell.