Spatial frequency domain imaging technology based on Fourier single-pixel imaging

SIGNIFICANCE

Optical properties (absorption coefficient and scattering coefficient) of tissue are the most critical parameters for disease diagnosis-based optical method. In recent years, researchers proposed spatial frequency domain imaging (SFDI) to quantitatively map tissue optical properties in a broad field of contactless imaging. To solve the limitations in wavebands unsuitable for silicon-based sensor technology, a compressed sensing (CS) algorithm is used to reproduce the original signal by a single-pixel detectors. Currently, the existing single-pixel SFDI method mainly uses a random sampling policy to extract and recover signals in the acquisition stage. However, these methods are memory-hungry and time-consuming, and they cannot generate discernible results under low sampling rate. Explorations on high performance and efficiency single-pixel SFDI are of great significance for clinical application.

AIM

Fourier single-pixel imaging can reconstruct signals with less time and space costs and has fewer reconstruction errors. We focus on an SFDI algorithm based on Fourier single-pixel imaging and propose our Fourier single-pixel image-based spatial frequency domain imaging method (FSI-SFDI).

APPROACH

First, we use Fourier single-pixel imaging algorithm to collect and compress signals and SFDI algorithm to generate optical parameters. Given the basis that the main energy of general image signals is concentrated in the range of low frequency of Fourier frequency domain, our FSI-SFDI uses a circular-sampling scheme to sample data points in the low-frequency region. Then, we reconstruct the image details from these points by optimization-based inverse-FFT method.

RESULTS

Our algorithm is tested on simulated data. Results show that the root mean square error (RMSE) of optical parameters is lower than 5% when the data reduction is 92%, and it can generate discernible optical parameter image with low sampling rate. We can observe that our FSI-SFDI primarily recovers the optical properties while keeping the RMSE under the upper bound of 4.5% when we use an image with 512  ×  512 resolution as the example for calculation and analysis. Not only that but also our algorithm consumes less space and time for an image with 256  ×  256 resolution, the signal reconstruction takes only 1.65 ms, and requires less RAM memory. Compared to CS-SFDI method, our FSI-SFDI can reduce the required number of measurements through optimizing algorithm.

CONCLUSIONS

Moreover, FSI-SFDI is capable of recovering high-quality resolvable images with lower sampling rate, higher-resolution images with less memory and time consumed than previous CS-SFDI method, which is very promising for clinical data collection and medical analysis.

Optical sampling depth in the spatial frequency domain

We present a Monte Carlo (MC) method to determine depth-dependent probability distributions of photon visitation and detection for optical reflectance measurements performed in the spatial frequency domain (SFD). These distributions are formed using an MC simulation for radiative transport that utilizes a photon packet weighting procedure consistent with the two-dimensional spatial Fourier transform of the radiative transport equation. This method enables the development of quantitative metrics for SFD optical sampling depth in layered tissue and its dependence on both tissue optical properties and spatial frequency. We validate the computed depth-dependent probability distributions using SFD measurements in a layered phantom system with a highly scattering top layer of variable thickness supported by a highly absorbing base layer. We utilize our method to establish the spatial frequency-dependent optical sampling depth for a number of tissue types and also provide a general tool to determine such depths for tissues of arbitrary optical properties.

Diffuse and nonlinear imaging of multiscale vascular parameters for in vivo monitoring of preclinical mammary tumors

Diffuse optical imaging (DOI) techniques provide a wide-field or macro assessment of the functional tumor state and have shown substantial promise for monitoring treatment efficacy in cancer. Conversely, intravital microscopy provides a high-resolution view of the tumor state and has played a key role in characterizing treatment response in the preclinical setting. There has been little prior work in investigating how the macro and micro spatial scales can be combined to develop a more comprehensive and translational view of treatment response. To address this, a new multiscale preclinical imaging technique called diffuse and nonlinear imaging (DNI) was developed. DNI combines multiphoton microscopy with spatial frequency domain imaging (SFDI) to provide multiscale data sets of tumor microvascular architecture coregistered within wide-field hemodynamic maps. A novel method was developed to match the imaging depths of both modalities by utilizing informed SFDI spatial frequency selection. An in vivo DNI study of murine mammary tumors revealed multiscale relationships between tumor oxygen saturation and microvessel diameter, and tumor oxygen saturation and microvessel length (|Pearson's ρ| ≥ 0.5, P < 0.05). Going forward, DNI will be uniquely enabling for the investigation of multiscale relationships in tumors during treatment.

Quantitative subsurface spatial frequency-domain fluorescence imaging for enhanced glioma resection

The rate of complete resection of glioma has improved with the introduction of 5-aminolevulinic acid-induced protoporphyrin IX (PpIX) fluorescence image guidance. Surgical outcomes are further enhanced when the fluorescence signal is decoupled from the intrinsic tissue optical absorption and scattering obtained from diffuse reflectance measurements, yielding the absolute PpIX concentration, [PpIX]. Spatial frequency domain imaging was used previously to measure [PpIX] in near-surface tumors under blue fluorescence excitation. Here, we extend this to subsurface [PpIX] fluorescence under red-light excitation. The decay rate of the modulation amplitude of the fluorescence signal was used to calculate the PpIX depth, which was then applied in a forward diffusion model to estimate [PpIX] at depth. For brain-like optical properties in phantoms with PpIX fluorescent inclusions, the depth can be recovered up to depths of 9.5 mm ± 0.4 mm, with [PpIX] ranging from 5 to 15 μg/mL within an average deviation of 15% from the true [PpIX] value.

Quantitative subsurface spatial frequency-domain fluorescence imaging for enhanced glioma resection

The rate of complete resection of glioma has improved with the introduction of 5-aminolevulinic acid-induced protoporphyrin IX (PpIX) fluorescence image guidance. Surgical outcomes are further enhanced when the fluorescence signal is decoupled from the intrinsic tissue optical absorption and scattering obtained from diffuse reflectance measurements, yielding the absolute PpIX concentration, [PpIX]. Spatial frequency domain imaging was used previously to measure [PpIX] in near-surface tumors under blue fluorescence excitation. Here, we extend this to subsurface [PpIX] fluorescence under red-light excitation. The decay rate of the modulation amplitude of the fluorescence signal was used to calculate the PpIX depth, which was then applied in a forward diffusion model to estimate [PpIX] at depth. For brain-like optical properties in phantoms with PpIX fluorescent inclusions, the depth can be recovered up to depths of 9.5 mm ± 0.4 mm, with [PpIX] ranging from 5 to 15 μg/mL within an average deviation of 15% from the true [PpIX] value.

Recovery of layered tissue optical properties from spatial frequency-domain spectroscopy and a deterministic radiative transport solver

We present a method to recover absorption and reduced scattering spectra for each layer of a two-layer turbid media from spatial frequency-domain spectroscopy data. We focus on systems in which the thickness of the top layer is less than the transport mean free path   (  0.1  -  0.8l  *    )  . We utilize an analytic forward solver, based upon the N'th-order spherical harmonic expansion with Fourier decomposition   (  SHEFN  )   method in conjunction with a multistage inverse solver. We test our method with data obtained using spatial frequency-domain spectroscopy with 32 evenly spaced wavelengths within λ  =  450 to 1000 nm on six-layered tissue phantoms with distinct optical properties. We demonstrate that this approach can recover absorption and reduced scattering coefficient spectra for both layers with accuracy comparable with current Monte Carlo methods but with lower computational cost and potential flexibility to easily handle variations in parameters such as the scattering phase function or material refractive index. To our knowledge, this approach utilizes the most accurate deterministic forward solver used in such problems and can successfully recover properties from a two-layer media with superficial layer thicknesses.

Two-layer inverse model for improved longitudinal preclinical tumor imaging in the spatial frequency domain

Spatial frequency domain imaging (SFDI) is a widefield, noncontact, and label-free imaging modality that is currently being explored as a new tool for longitudinal tracking of cancer therapies in the preclinical setting. We describe a two-layer look-up-table (LUT) inversion algorithm for SFDI that better accounts for the skin (top layer) and tumor (bottom layer) tissue geometry in subcutaneous tumor models. Monte Carlo (MC) simulations were conducted natively in the spatial frequency domain, avoiding discretization errors associated with Fourier or Hankel transforms of conventional MC simulation results. The two-layer LUT was validated using two-layer tissue mimicking optical phantoms, in which the optical property extractions of the bottom (tumor) layer were determined to be within 20% and 11% of the true values for μa and μs', respectively. A sensitivity analysis was conducted to evaluate how imperfect top layer estimates affect bottom-layer optical property extractions. Finally, the two-layer LUT was used to reanalyze a prior longitudinal data set, which revealed larger therapy-induced changes in optical scattering and a more hypoxic tumor environment compared to the homogeneous LUT. The two-layer LUT described here improves the accuracy of subcutaneous tumor imaging, and the general methodology can be applied for arbitrary multilayer SFDI applications.

Crack Detection in Concrete Tunnels Using a Gabor Filter Invariant to Rotation

In this article, a system for the detection of cracks in concrete tunnel surfaces, based on image sensors, is presented. Both data acquisition and processing are covered. Linear cameras and proper lighting are used for data acquisition. The required resolution of the camera sensors and the number of cameras is discussed in terms of the crack size and the tunnel type. Data processing is done by applying a new method called Gabor filter invariant to rotation, allowing the detection of cracks in any direction. The parameter values of this filter are set by using a modified genetic algorithm based on the Differential Evolution optimization method. The detection of the pixels belonging to cracks is obtained to a balanced accuracy of 95.27%, thus improving the results of previous approaches.

Ultrafast optical property map generation using lookup tables

Imaging technologies working in the spatial frequency domain are becoming increasingly popular for generating wide-field maps of optical properties, enabling rapid analysis of tissue parameters. While acquisition methods have become faster and are now performing in real-time, processing methods remain slow, precluding real-time display of information. We present solutions that rapidly solve the inverse problem for extracting optical properties by use of advanced lookup tables (LUTs). We present methods and results based on a dense, linearly sampled lookup table and an analytical representation that generate maps of absorption and reduced scattering in ?10??ms, which is 100× faster than the standard method, with ?4% error compared to the Monte-Carlo simulation. Combined with real-time acquisition methods, the proposed techniques enable video-rate feedback of real-time property maps, enabling full video-rate guidance in the clinic.

Separating melanin from hemodynamics in nevi using multimode hyperspectral dermoscopy and spatial frequency domain spectroscopy

Changes in the pattern and distribution of both melanocytes (pigment producing) and vasculature (hemoglobin containing) are important in distinguishing melanocytic proliferations. The ability to accurately measure melanin distribution at different depths and to distinguish it from hemoglobin is clearly important when assessing pigmented lesions (benign versus malignant). We have developed a multimode hyperspectral dermoscope (SkinSpect™) able to more accurately image both melanin and hemoglobin distribution in skin. SkinSpect uses both hyperspectral and polarization-sensitive measurements. SkinSpect’s higher accuracy has been obtained by correcting for the effect of melanin absorption on hemoglobin absorption in measurements of melanocytic nevi. In vivo human skin pigmented nevi (N=20) were evaluated with the SkinSpect, and measured melanin and hemoglobin concentrations were compared with spatial frequency domain spectroscopy (SFDS) measurements. We confirm that both systems show low correlation of hemoglobin concentrations with regions containing different melanin concentrations (R=0.13 for SFDS, R=0.07 for SkinSpect).

Enhancing in vivo tumor boundary delineation with structured illumination fluorescence molecular imaging and spatial gradient mapping

Fluorescence imaging, in combination with tumor-avid near-infrared (NIR) fluorescent molecular probes, provides high specificity and sensitivity for cancer detection in preclinical animal models, and more recently, assistance during oncologic surgery. However, conventional camera-based fluorescence imaging techniques are heavily surface-weighted such that surface reflection from skin or other nontumor tissue and nonspecific fluorescence signals dominate, obscuring true cancer-specific signals and blurring tumor boundaries. To address this challenge, we applied structured illumination fluorescence molecular imaging (SIFMI) in live animals for automated subtraction of nonspecific surface signals to better delineate accumulation of an NIR fluorescent probe targeting α4β1 integrin in mice bearing subcutaneous plasma cell xenografts. SIFMI demonstrated a fivefold improvement in tumor-to-background contrast when compared with other full-field fluorescence imaging methods and required significantly reduced scanning time compared with diffuse optical spectroscopy imaging. Furthermore, the spatial gradient mapping enhanced highlighting of tumor boundaries. Through the relatively simple hardware and software modifications described, SIFMI can be integrated with clinical fluorescence imaging systems, enhancing intraoperative tumor boundary delineation from the uninvolved tissue.

In vivo isolation of the effects of melanin from underlying hemodynamics across skin types using spatial frequency domain spectroscopy

Skin is a highly structured tissue, raising concerns as to whether skin pigmentation due to epidermal melanin may confound accurate measurements of underlying hemodynamics. Using both venous and arterial cuff occlusions as a means of inducing differential hemodynamic perturbations, we present analyses of spectra limited to the visible or near-infrared regime, in addition to a layered model approach. The influence of melanin, spanning Fitzpatrick skin types I to V, on underlying estimations of hemodynamics in skin as interpreted by these spectral regions are assessed. The layered model provides minimal cross-talk between melanin and hemodynamics and enables removal of problematic correlations between measured tissue oxygenation estimates and skin phototype.

Spatial mapping of drug delivery to brain tissue using hyperspectral spatial frequency-domain imaging

We present an application of spatial frequency-domain imaging (SFDI) to the wide-field imaging of drug delivery to brain tissue. Measurements were compared with values obtained by a previously validated variation of diffuse reflectance spectroscopy, the method of optical pharmacokinetics (OP). We demonstrate a crosscorrelation between the two methods for absorption extraction and drug concentration determination in both experimental tissue phantoms and freshly extracted rodent brain tissue. These methods were first used to assess intra-arterial (IA) delivery of cationic liposomes to brain tissue in Sprague Dawley rats under transient cerebral hypoperfusion. Results were found to be in agreement with previously published experimental data and pharmacokinetic models of IA drug delivery. We then applied the same scheme to evaluate IA mitoxantrone delivery to glioma-bearing rats. Good correlation was seen between OP and SFDI determined concentrations taken from normal and tumor averaged sites. This study shows the feasibility of mapping drug/tracer distributions and encourages the use of SFDI for spatial imaging of tissues for drug/tracer-tagged carrier deposition and pharmacokinetic studies.

Lookup-table method for imaging optical properties with structured illumination beyond the diffusion theory regime

Sinusoidally structured illumination is used in concert with a phantom-based lookup-table (LUT) to map wide-field optical properties in turbid media with reduced albedos as low as 0.44. A key advantage of the lookup-table approach is the ability to measure the absorption (mu(a)) and reduced scattering coefficients (mu(s) (')) over a much broader range of values than permitted by current diffusion theory methods. Through calibration with a single reflectance standard, the LUT can extract mu(s) (') from 0.8 to 2.4 mm(-1) with an average root-mean-square (rms) error of 7% and extract mu(a) from 0 to 1.0 mm(-1) with an average rms error of 6%. The LUT is based solely on measurements of two parameters, reflectance R and modulation M at an illumination period of 10 mm. A single set of three phase-shifted images is sufficient to measure both M and R, which are then used to generate maps of absorption and scattering by referencing the LUT. We establish empirically that each pair (M,R) maps uniquely to only one pair of (micro(s) ('),micro(a)) and report that the phase function (i.e., size) of the scatterers can influence the accuracy of optical property extraction.

Quantitation and mapping of tissue optical properties using modulated imaging

We describe the development of a rapid, noncontact imaging method, modulated imaging (MI), for quantitative, wide-field characterization of optical absorption and scattering properties of turbid media. MI utilizes principles of frequency-domain sampling and model-based analysis of the spatial modulation transfer function (s-MTF). We present and compare analytic diffusion and probabilistic Monte Carlo models of diffuse reflectance in the spatial frequency domain. Next, we perform MI measurements on tissue-simulating phantoms exhibiting a wide range of l values (0.5 mm to 3 mm) and (micro(s) (')micro(a)) ratios (8 to 500), reporting an overall accuracy of approximately 6% and 3% in absorption and reduced scattering parameters, respectively. Sampling of only two spatial frequencies, achieved with only three camera images, is found to be sufficient for accurate determination of the optical properties. We then perform MI measurements in an in vivo tissue system, demonstrating spatial mapping of the absorption and scattering optical contrast in a human forearm and dynamic measurements of a forearm during venous occlusion. Last, metrics of spatial resolution are assessed through both simulations and measurements of spatially heterogeneous phantoms.