Exploiting diffuse reflectance measurement uncertainty estimates in spatial frequency domain imaging

Spatial frequency domain imaging (SFDI) is a wide-field, noncontact diffuse optical imaging technique that has garnered significant interest for a variety of applications, including the monitoring of skin and breast lesions in clinical settings, and the progression of Alzheimer’s disease and drug delivery to the brain in mouse models. In most applications, diffuse reflectance measurements are used to quantify the optical absorption and reduced scattering coefficients of the turbid medium, and with these, chromophore concentrations of interest are extracted (e.g., hemoglobin in tissue). However, uncertainties in estimated absorption and reduced scattering values are rarely reported, and we know of no method capable of providing such uncertainties when look-up table-based inversion algorithms are used to recover the optical properties. Quantifying these uncertainties would have several important benefits. For example, they could be propagated forward to yield uncertainties in estimated chromophore concentrations, which could have profound implications for the interpretation of experimental results. They could also be employed to help guide the selection of spatial frequencies used for SFDI measurements, given the requirements of the specific application. In this work, we make two novel contributions. First, we show how knowledge of the accuracy of diffuse reflectance measurements from an SFDI instrument (i.e., diffuse reflectance uncertainty estimates) can be transformed to yield quantitative predictions of uncertainties for recovered absorption and reduced scattering values. Second, we use diffuse reflectance uncertainty estimates directly in a new algorithm for the recovery of optical properties. This algorithm performs equivalently to a standard look-up table-based approach but is up to ~200X faster (per pixel). To transform diffuse reflectance uncertainty estimates into uncertainty estimates for the absorption and reduced scattering coefficients, we employ the Cramer-Rao bound (CRB). The CRB is a lower bound that defines the best achievable precision (i.e., lowest variance) of any unbiased estimator for a given data model. It is often used in the statistical signal processing community, especially in the sonar and radar signal processing communities, to perform feasibility studies and system design. We calculate the CRBs for the absorption and reduced scattering coefficients and use them as our estimates of uncertainties for these parameters. We show that these estimates agree with results from Monte Carlo simulations to better than 0.1% for the common scenario where optical properties are computed with a look-up table using two spatial frequencies. We validate our simulations with tissue-mimicking phantom experiments and in vivo measurements on a human volunteer. This method of generating uncertainty estimates opens the door to several exciting possibilities. For example, the analytical form of the CRB calculation can be exploited to quickly generate “maps” of uncertainty estimates as a function of optical properties and spatial frequencies, thereby providing a tool that can be used to efficiently explore this trade space. The CRB-derived uncertainty estimates can also be propagated into chromophore uncertainty estimates. With knowledge of the spatial frequencies and wavelengths used for a given application, it is possible to pre-compute look-up tables of optical property and/or chromophore uncertainty estimates, which would be a significant advantage for applications requiring real-time performance. Diffuse reflectance uncertainty estimates can also be used to speed up optical property recovery with no performance penalty. We have developed a new algorithm to do this that in simulation performs equivalently to a standard look-up table-based approach employing linear interpolation but is up to ~200X faster (per pixel)

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 optical spectroscopic imaging reveals distinct early breast tumor hemodynamic responses to metronomic and maximum tolerated dose regimens.

BACKGROUND:Breast cancer patients with early-stage disease are increasingly administered neoadjuvant chemotherapy (NAC) to downstage their tumors prior to surgery. In this setting, approximately 31% of patients fail to respond to therapy. This demonstrates the need for techniques capable of providing personalized feedback about treatment response at the earliest stages of therapy to identify patients likely to benefit from changing treatment. Diffuse optical spectroscopic imaging (DOSI) has emerged as a promising functional imaging technique for NAC monitoring. DOSI uses non-ionizing near-infrared light to provide non-invasive measures of absolute concentrations of tissue chromophores such as oxyhemoglobin. In 2011, we reported a new DOSI prognostic marker, oxyhemoglobin flare: a transient increase in oxyhemoglobin capable of discriminating NAC responders within the first day of treatment. In this follow-up study, DOSI was used to confirm the presence of the flare as well as to investigate whether DOSI markers of NAC response are regimen dependent. METHODS:This dual-center study examined 54 breast tumors receiving NAC measured with DOSI before therapy and the first week following chemotherapy administration. Patients were treated with either a standard of care maximum tolerated dose (MTD) regimen or an investigational metronomic (MET) regimen. Changes in tumor chromophores were tracked throughout the first week and compared to pathologic response and treatment regimen at specific days utilizing generalized estimating equations (GEE). RESULTS:Within patients receiving MTD therapy, the oxyhemoglobin flare was confirmed as a prognostic DOSI marker for response appearing as soon as day 1 with post hoc GEE analysis demonstrating a difference of 48.77% between responders and non-responders (p < 0.0001). Flare was not observed in patients receiving MET therapy. Within all responding patients, the specific treatment was a significant predictor of day 1 changes in oxyhemoglobin, showing a difference of 39.45% (p = 0.0010) between patients receiving MTD and MET regimens. CONCLUSIONS:DOSI optical biomarkers are differentially sensitive to MTD and MET regimens at early timepoints suggesting the specific treatment regimen should be considered in future DOSI studies. Additionally, DOSI may help to identify regimen-specific responses in a more personalized manner, potentially providing critical feedback necessary to implement adaptive changes to the treatment strategy

High optode-density wearable diffuse optical probe for monitoring paced breathing hemodynamics in breast tissue

Significance: Diffuse optical imaging (DOI) provides in vivo quantification of tissue chromophores such as oxy- and deoxyhemoglobin ([Formula: see text] and HHb, respectively). These parameters have been shown to be useful for predicting neoadjuvant treatment response in breast cancer patients. However, most DOI devices designed for the breast are nonportable, making frequent longitudinal monitoring during treatment a challenge. Furthermore, hemodynamics related to the respiratory cycle are currently unexplored in the breast and may have prognostic value. Aim: To design, fabricate, and validate a high optode-density wearable continuous wave diffuse optical probe for the monitoring of breathing hemodynamics in breast tissue. Approach: The probe has a rigid-flex design with 16 dual-wavelength sources and 16 detectors. Performance was characterized on tissue-simulating phantoms, and validation was performed through flow phantom and cuff occlusion measurements. The breasts of [Formula: see text] healthy volunteers were measured while performing a breathing protocol. Results: The probe has 512 unique source–detector (S-D) pairs that span S-D separations of 10 to 54 mm. It exhibited good performance characteristics: [Formula: see text] drift of 0.34%/h, [Formula: see text] precision of 0.063%, and mean [Formula: see text] up to 41 mm S-D separation. Absorption contrast was detected in flow phantoms at depths exceeding 28 mm. A cuff occlusion measurement confirmed the ability of the probe to track expected hemodynamics in vivo. Breast measurements on healthy volunteers during paced breathing revealed median signal-to-motion artifact ratios ranging from 8.1 to 8.7 dB. Median [Formula: see text] and [Formula: see text] amplitudes ranged from 0.39 to [Formula: see text] and 0.08 to [Formula: see text] , respectively. Median oxygen saturations at the respiratory rate ranged from 82% to 87%. Conclusions: A wearable diffuse optical probe has been designed and fabricated for the measurement of breast tissue hemodynamics. This device is capable of quantifying breathing-related hemodynamics in healthy breast tissue

Cramer-Rao bounds for spatial frequency domain imaging

Matlab code (and associated files) for spatial frequency domain imaging Cramer-Rao bound calculation. Please see m-file for details. Code described in Pera et al., "Optical property uncertainty estimates for spatial frequency domain imaging," Biomedical Optics Express.<div><br></div

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