Fourier transform fluorescence recovery after photobleaching (FT-FRAP) with patterned illumination is theorized and demonstrated for quantitatively evaluating normal and anomalous diffusion. Diffusion characterization is routinely performed to assess mobility in cell biology, pharmacology, and food science. Conventional FRAP is noninvasive, has low sample volume requirements, and can rapidly measure diffusion over distances of a few micrometers. However, conventional point-bleach measurements are complicated by signal-to-noise limitations, the need for precise knowledge of the bleach beam profile, potential for bias due to sample heterogeneity, and poor compatibility with multi-photon excitation due to local heating. In FT-FRAP with patterned illumination, the time-dependent fluorescence recovery signal is concentrated to puncta in the spatial Fourier domain through patterned bleaching, with substantial improvements in signal-to-noise, mathematical simplicity, representative sampling, and multiphoton compatibility. A custom nonlinear-optical beam-scanning microscope enabled patterned illumination for photobleaching through two-photon excitation. Measurements in the spatial Fourier domain removed dependence on the bleach profile, suppressing bias from imprecise knowledge of the point spread function. For normal diffusion, the fluorescence recovery produced a simple single-exponential decay in the spatial Fourier domain, in excellent agreement with theoretical predictions. Simultaneous measurement of diffusion at multiple length scales was enabled through analysis of multiple spatial harmonics of the bleaching pattern. Anomalous diffusion was characterized by FT-FRAP through a nonlinear fit to multiple spatial harmonics of the fluorescence recovery. Constraining the fit to describe diffusion over multiple length scales resulted in higher confidence in the recovered fitting parameters. Additionally, phase analysis in FT-FRAP was shown to inform on flow/sample translation. Statement of SignificanceFourier transform fluorescence recovery after photobleaching (FT-FRAP) with patterned illumination greatly improves the accuracy of diffusion assessments and simultaneously accesses information on both normal and anomalous diffusion in a single experiment..

Single-particle tracking of crystal growth performed in situ enables substantial improvements in the signal-to-noise ratio (SNR) for recovered crystal nucleation and growth rates by nonlinear optical microscopy. Second harmonic generation (SHG) is exquisitely sensitive to noncentrosymmetric crystals, including those produced by many homochiral active pharmaceutical ingredients (APIs). Accelerated stability testing at elevated temperatures and relative humidity informs design of pharmaceutical formulations. In the present work, we demonstrate reduction in the Poisson noise associated with the finite number of particles present in a given field of view through continuous monitoring during stability testing. Single-particle tracking enables recovery of crystal growth rates of individual crystallites and enables unambiguous direct detection of nucleation events. Collectively, these capabilities provide significant improvements in the signal-to-noise for nucleation and crystal growth measurements, corresponding to approximately an order of magnitude reduction in anticipated measurement time for recovery of kinetics parameters.

The use of periodically structured illumination coupled with spatial Fourier-transform fluorescence recovery after photobleaching (FT-FRAP) was shown to support diffusivity mapping within segmented domains of arbitrary shape. Periodic "comb-bleach" patterning of the excitation beam during photobleaching encoded spatial maps of diffusion onto harmonic peaks in the spatial Fourier transform. Diffusion manifests as a simple exponential decay of a given harmonic, improving the signal to noise ratio and simplifying mathematical analysis. Image segmentation prior to Fourier transformation was shown to support pooling for signal to noise enhancement for regions of arbitrary shape expected to exhibit similar diffusivity within a domain. Following proof-ofconcept analyses based on simulations with known ground-truth maps, diffusion imaging by FT-FRAP was used to map spatiallyresolved diffusion differences within phase-separated domains of model amorphous solid dispersion spin-cast thin films. Notably, multi-harmonic analysis by FT-FRAP was able to definitively discriminate and quantify the roles of internal diffusion and exchange to higher mobility interfacial layers in modeling the recovery kinetics within thin amorphous/amorphous phase-separated domains, with interfacial diffusion playing a critical role in recovery. These results have direct implications for the design of amorphous systems for stable storage and efficacious delivery of therapeutic molecules.

Seeded growth rates of ritonavir in copovidone at 75% relative humidity (RH) and 50 °C were evaluated by single-particle tracking second harmonic generation (SHG) microscopy and found to be ∼3-fold slower for crystallites at the surface compared to the bulk. The shelf lives of final dosage forms containing amorphous solid dispersions (ASDs) are often dictated by the rates of active pharmaceutical ingredient crystallization. Upon exposure to elevated RH, the higher anticipated water content near the surfaces of ASDs has the potential to substantially impact nucleation and growth kinetics relative to the bulk. However, quantitative assessment of these differences in growth rates is complicated by challenges associated with discrimination of the two contributions (supersaturation and molecular mobility) in ensemble-averaged measurements. In the present study, "sandwich" materials were prepared, in which sparse populations of ritonavir single-crystalline seeds were pressed between two similar ASD films to assess bulk crystallization rates. These sandwich materials were compared and contrasted with analogously prepared "open-faced" samples, without the capping film, to assess the surface crystallization rates. Single-particle analysis by SHG microscopy time-series during in situ crystallization produced average growth rates of 3.8 μm/h for bulk columnar crystals with a particle-to-particle standard deviation of 0.9 μm/h. In addition, columnar crystal growth rates for surface particles were measured to be 1.3 μm/h and radiating crystal growth rates for surface particles were measured to be 1.0 μm/h, both with a particle-to-particle deviation of 0.4 μm/h. The observed appearance of radiating crystals upon surface seeding is attributed to reduced ritonavir solubility upon water adsorption at the interface, leading to higher defect densities in crystal growth. Despite substantial differences in crystal habit, correction of the surface growth rates by a factor of 4 from geometric effects resulted in relatively minor but statistically significant differences in the growth kinetics for the two local environments. These results are consistent, with viscosity being a relatively weak function of water absorption coupled with primarily diffusion-limited growth kinetics.

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