Aditya Mahara

An Inverse Problems Approach to MR-EPT Image Reconstruction

Magnetic Resonance-Electrical Properties Tomography (MR-EPT) is an imaging modality that maps the spatial distribution of the electrical conductivity and permittivity using standard MRI systems. The presence of a body within the scanner alters the RF field, and by mapping these alterations it is possible to recover the electrical properties. The field is time-harmonic, and can be described by the Helmholtz equation. Approximations to this equation have been previously used to estimate conductivity and permittivity in terms of first or second derivatives of RF field data. Using these same approximations, an inverse approach to solving the MR-EPT problem is presented here that leverages a forward model for describing the magnitude and phase of the field within the imaging domain, and a fitting approach for estimating the electrical properties distribution. The advantages of this approach are that 1) differentiation of the measured data is not required, thus reducing noise sensitivity, and 2) different regularization schemes can be adopted, depending on prior knowledge of the distribution of conductivity or permittivity, leading to improved image quality. To demonstrate the developed approach, both Quadratic (QR) and Total Variation (TV) regularization methods were implemented and evaluated through numerical simulation and experimentally acquired data. The proposed inverse approach to MR-EPT reconstruction correctly identifies contrasts and accurately reconstructs the geometry in both simulations and experiments. The TV regularized scheme reconstructs sharp spatial transitions, which are difficult to reconstruct with other, more traditional approaches.

3D Microendoscopic Electrical Impedance Tomography for Margin Assessment During Robot-Assisted Laparoscopic Prostatectomy

Radially configured microendoscopic electrical impedance probes intended for intraoperative surgical margin assessment during robot-assisted laparoscopic prostatectomy (RALP) were examined through simulation, bench-top experimentation, and ex vivo tissue studies. Three probe designs with 8, 9, and 17 electrodes, respectively, were analyzed through finite element method based simulations. One mm diameter spherical inclusions ( σinclusion = 1 S/m) are positioned at various locations within a hemispherical background ( σbackground = 0.1 S/m) of radius 5 mm. An 8-electrode configuration is not able to localize the inclusion at these positions while 9 and 17-electrode configurations are able to accurately reconstruct the inclusion at maximum depth of 1 mm and 3 mm, respectively. All three probe designs were constructed and evaluated using saline phantoms and ex vivo porcine and human prostate tissues. The 17-electrode probe performed best in saline phantom studies, accurately reconstructing high contrast, 1-mm-diameter metal cylindrical inclusions in a saline bath ( σsaline = 0.1 S/m) with a position and area error of 0.46 mm and 0.84 mm2, respectively. Additionally, the 17-electrode probe was able to adequately distinguish cancerous from benign tissues in three ex vivo human prostates. Simulations, bench-top saline experiments, and ex vivo tissue sampling suggest that for intraoperative surgical margin assessment during RALP, the 17-electrode probe (as compared to an 8 and 9 electrode probe) will be necessary to provide sufficient accuracy and sensitivity.

Absolute Reconstructions Using Rotational Electrical Impedance Tomography for Breast Cancer Imaging

A rotational Electrical Impedance Tomography (rEIT) methodology is described and shown to produce spatially accurate absolute reconstructions with improved image contrast and an improved ability to distinguish closely spaced inclusions compared to traditional EIT on data recorded from cylindrical and breast-shaped tanks. Rotations of the tank without altering the interior conductivity distribution are used to produce the rEIT data. Quantitatively, rEIT was able to distinguish two inclusions that were 1.5 cm closer together than traditional EIT could achieve for inclusions placed 2 to 3 cm from the center for the cylindrical tank, and rEIT was able to distinguish two tumor-like inclusions where traditional EIT could not reliably do so. Mathematical analysis showed that rEIT improves the number of stable singular vectors by up to 4.2 and 4.7 times than that of traditional EIT for the cylindrical and breast-shaped tanks, respectively, which is an indication of improved resolution. Direct investigations into measurements revealed minimum rotation angles that should yield data uncorrupted by noise. Two inverse approaches (one that inverts then fuses the data (I/DF) and one that fuses the data then inverts (DF/I)) and two mesh modeling approaches were considered. It was found that DF/I produces far better results compared to I/DF and a rotated-mesh approach produces further improvements. The ability to obtain improved absolute reconstructions using rEIT on a practical clinical scenario (breast-shaped tank experiment) is an important step towards using rEIT to improve previous EIT results in medical applications.

Prostate Cancer Detection Using Composite Impedance Metric

Prostate cancer (PCa) recurrences are often predicted by assessing the status of surgical margins (SM)- positive surgical margins (PSM) increase the chances of biochemical recurrence by 2-4 times which may lead to PCa recurrence. To this end, an electrical impedance acquisition system with a microendoscopic probe was employed in an ex-vivo study of human prostates. This system measures the tissue bioimpedance over a range of frequencies (1 kHz to 1 MHz), and computes a number of Composite Impedance Metrics (CIM). A classifier trained using CIM data can be used to classify tissue as benign or cancerous. The system was used to collect the impedance spectra from 14 excised prostates, which were obtained from men undergoing radical prostatectomy, for a total of 23 cancerous and 53 benign measurements. The data revealed statistically significant (p <; 0.05) differences in the impedance properties of the benign and tumorous tissues, and among the measurements taken on the apical, base, and lateral surface of the prostate. Further, in the leave-one-patient-out cross validation, a maximum predictive accuracy of 90.79% was achieved by combining high frequency CIM phase data to train a support vector machine classifier with a radial basis function kernel. The observations are consistent with the physiology and morphology of benign and malignant prostate tissue. CIMs were found to be an effective tool in distinguishing benign from cancerous tissues.

Towards intraoperative surgical margin assessment and visualization using bioimpedance properties of the tissue

Prostate cancer (PCa) has a high 10-year recurrence rate, making PCa the second leading cause of cancer-specific mortality among men in the USA. PCa recurrences are often predicted by assessing the status of surgical margins (SM) with positive surgical margins (PSM) increasing the chances of biochemical recurrence by 2-4 times. To this end, an SM assessment system using Electrical Impedance Spectroscopy (EIS) was developed with a microendoscopic probe. This system measures the tissue bioimpedance over a range of frequencies (1 kHz to 1MHz), and computes a Composite Impedance Metric (CIM). CIM can be used to classify tissue as benign or cancerous. The system was used to collect the impedance spectra from excised prostates, which were obtained from men undergoing radical prostatectomy. The data revealed statistically significant (p<0.05) differences in the impedance properties of the benign and tumorous tissues, and between different tissue morphologies. To visualize the results of SM-assessment, a visualization tool using da Vinci stereo laparoscope is being developed. Together with the visualization tool, the EIS-based SM assessment system can be potentially used to intraoperatively classify tissues and display the results on the surgical console with a video feed of the surgical site, thereby augmenting a surgeon’s view of the site and providing a potential solution to the intraoperative SM assessment needs.

Comparative study of separation between ex vivo prostatic malignant and benign tissue using electrical impedance spectroscopy and electrical impedance tomography

OBJECTIVE Currently no efficient and reliable technique exists to routinely assess surgical margins during a radical prostatectomy. Electrical impedance spectroscopy (EIS) has been reported as a potential technique to provide surgeons with real-time intraoperative margin assessment. In addition to providing a quantified measure of margin status, a co-registered electrical impedance tomography (EIT) image presented on a surgeons workstation could add value to the margin assessment process. APPROACH To investigate this, we conducted a comparative study between EIS and EIT to evaluate the potential these technologies might have for margin assessment. EIS and EIT data was acquired from ex vivo human prostates using a multi-electrode endoscopic impedance acquisition probe. MAIN RESULTS EIS and EIT show good predictive performance with a 0.76 and 0.80 area-under-curve (AUC), respectively, when considering discrete frequencies only. A machine learning (ML) algorithm is implemented to combine features, which improves the AUCs of EIS and EIT to 0.84 and 0.85, respectively. Single-step EIT takes significantly less time to reconstruct than multi-step EIT, yet provides similarly accurate classification results, making the single-step approach a potential candidate for real-time margin assessment. While the ML-based approach clearly exhibits benefits as compared to the single feature assessment, the decision to use EIS versus EIT is unclear since each approach performs better for different subsets of tissue classifications. SIGNIFICANCE The results presented in this paper corroborate our previous studies and present the strongest evidence yet that an intraoperative-capable impedance probe can be used to distinguish benign from malignant prostate tissues. An in vivo study with a large cohort will be necessary to definitively determine the preferred approach and to show the clinical effectiveness of using this technology for margin assessment.

Phantom experiments using soft-prior regularization EIT for breast cancer imaging

OBJECTIVE A soft-prior regularization (SR) electrical impedance tomography (EIT) technique for breast cancer imaging is described, which shows an ability to accurately reconstruct tumor/inclusion conductivity values within a dense breast model investigated using a cylindrical and a breast-shaped tank. APPROACH The SR-EIT method relies on knowing the spatial location of a suspicious lesion initially detected from a second imaging modality. Standard approaches (using Laplace smoothing and total variation regularization) without prior structural information are unable to accurately reconstruct or detect the tumors. The soft-prior approach represents a very significant improvement to these standard approaches, and has the potential to improve conventional imaging techniques, such as automated whole breast ultrasound (AWB-US), by providing electrical property information of suspicious lesions to improve AWB-USs ability to discriminate benign from cancerous lesions. MAIN RESULTS Specifically, the best soft-regularization technique found average absolute tumor/inclusion errors of 0.015 S m-1 for the cylindrical test and 0.055 S m-1 and 0.080 S m-1 for the breast-shaped tank for 1.8 cm and 2.5 cm inclusions, respectively. The standard approaches were statistically unable to distinguish the tumor from the mammary gland tissue. An analysis of false tumors (benign suspicious lesions) provides extra insight into the potential and challenges EIT has for providing clinically relevant information. SIGNIFICANCE The ability to obtain accurate conductivity values of a suspicious lesion (>1.8 cm) detected from another modality (e.g. AWB-US) could significantly reduce false positives and result in a clinically important technology.

A Novel Regularization Technique for Microendoscopic Electrical Impedance Tomography

A novel regularization technique is developed for endfired microendoscopic electrical impedance tomography using the dual-mesh method. The new regularization technique coupled with appropriate forward modeling and inverse mesh design is shown to produce dramatically improved reconstructions over previous methods. 3D absolute and difference reconstructions from measured saline tank and ex vivo adipose and muscle tissue experiments are used to validate the approach. The ex vivo experiments are used as a surrogate for prostate tissue, which is the primary clinical application for the probe. Inclusion center of mass errors were less than 0.47 mm for tank experiments with inclusion depths and radial offsets ranging less than 3 mm and 1.5 mm, respectively. Absolute 3D reconstructions on the tissue show quantitatively good accuracy and the ability to spatially distinguish small tissue features (adipose strands of approximately 2.5 mm in width). The reconstruction algorithm developed provides strong evidence for the promise of surgical margin detection using microendoscopic EIT.

Electrical impedance map (EIM) for margin assessment during robot-assisted laparoscopic prostatectomy (RALP) using a microendoscopic probe

Positive surgical margins (PSMs) found following prostate cancer surgery are a significant risk factor for post-operative disease recurrence. Noxious adjuvant radiation and chemical-based therapies are typically offered to men with PSMs. Unfortunately, no real-time intraoperative technology is currently available to guide surgeons to regions of suspicion during the initial prostatectomy where immediate surgical excisions could be used to reduce the chance of PSMs. A microendoscopic electrical impedance sensing probe was developed with the intention of providing real-time feedback regarding margin status to surgeons during robot-assisted laparoscopic prostatectomy (RALP) procedures. A radially configured 17-electrode microendoscopic probe was designed, constructed, and initially evaluated through use of gelatin-based phantoms and an ex vivo human prostate specimen. Impedance measurements are recorded at 10 frequencies (10 kHz - 100 kHz) using a high-speed FPGA-based electrical impedance tomography (EIT) system. Tetrapolar impedances are recorded from a number of different electrode configurations strategically chosen to sense tissue in a pre-defined sector underlying the probe face. A circular electrical impedance map (EIM) with several color-coded pie-shaped sectors is created to represent the impedance values of the probed tissue. Gelatin phantom experiments show an obvious distinction in the impedance maps between high and low impedance regions. Similarly, the EIM generated from the ex vivo prostate case shows distinguishing features between cancerous and benign regions. Based on successful development of this probe and these promising initial results, EIMs of additional prostate specimens are being collected to further evaluate this approach for intraoperative surgical margin assessment during RALP procedures.