Ethan K. Murphy

Effect of Domain Shape Modeling and Measurement Errors on the 2-D D-Bar Method for EIT

The D-bar algorithm based on Nachmans 2-D global uniqueness proof for the inverse conductivity problem (Nachman, 1996) is implemented on a chest-shaped domain. The scattering transform is computed on this chest-shaped domain using trigonometric and adjacent current patterns and the complete electrode model for the forward problem is computed with the finite element method in order to obtain simulated voltage measurements. The robustness and effectiveness of the method is demonstrated on a simulated chest with errors in input currents, output voltages, electrode placement, and domain modeling.

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.

Towards a smart phone-based cardiac monitoring device using electrical impedance tomography

A novel framework for cardiac monitoring is presented that leverages a custom smart phone application and a wearable electrical impedance tomography (EIT) system. The smart phone application required to implement this framework has been designed and is described here. This technology could greatly improve telemonitoring of patients with chronic heart failure. A simulated portable EIT device was constructed that wirelessly sends data to the smart phone. The developed application receives wireless data transmission, performs EIT image reconstruction, and extracts a post-processing measure correlated to cardiac output. Data transmission rates of 4.2 MB/s were achieved between a simulated EIT system (server) and phone (client). Image reconstruction and post-processing implemented on a smart phone requires 332 ms, moderately longer than the 109 ms required on a modern laptop based implementation. The 332 ms is well within the approximately one second processing time needed to measure beat-to-beat cardiac output (i.e. assuming a 60 bpm heart rate).

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.

Signal-to-Noise Ratio Analysis of a Phase-Sensitive Voltmeter for Electrical Impedance Tomography

In this paper, thorough analysis along with mathematical derivations of the matched filter for a voltmeter used in electrical impedance tomography systems are presented. The effect of the random noise in the system prior to the matched filter, generated by other components, are considered. Employing the presented equations allow system/circuit designers to find the maximum tolerable noise prior to the matched filter that leads to the target signal-to-noise ratio (SNR) of the voltmeter, without having to over-design internal components. A practical model was developed that should fall within 2 dB and 5 dB of the median SNR measurements of signal amplitude and phase, respectively. In order to validate our claims, simulation and experimental measurements have been performed with an analog-to-digital converter (ADC) followed by a digital matched filter, while the noise of the whole system was modeled as the input referred at the ADC input. The input signal was contaminated by a known value of additive white Gaussian noise (AWGN) noise, and the noise level was swept from 3% to 75% of the least significant bit (LSB) of the ADC. Differences between experimental and both simulated and analytical SNR values were less than 0.59 and 0.35 dB for RMS values ≥ 20% of an LSB and less than 1.45 and 2.58 dB for RMS values < 20% of an LSB for the amplitude and phase, respectively. Overall, this study provides a practical model for circuit designers in EIT, and a more accurate error analysis that was previously missing in EIT literature.

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.

Simulation study for the design of an EIT system for cardiac output monitoring

This simulation study explores system design requirements needed for an EIT system that will be capable of accurately monitoring cadiac output. The 4D XCAT model is used to construct a realastic time-depedent conductivity profile of the chest. Forward and inverse simulations are calculated using Dartmouths NDRM EIT software package. Error analysis revealed that an SNR of 85-91 dB is preferred to confidently measure cardiac output.

Automated segmentation and feature extraction in cardiac electrical impedance tomography images

A non-invasive and accurate modality that can continuously monitor stroke volume (SV) for extended periods of time is desired to allow for more proactive care of an increasing population of patients living with heart failure. Electrical impedance tomography (EIT) has been proposed as a method for accurate, non-invasive, continuous, and long-term SV monitoring. While cardiac EIT has been explored, clinical translation has yet to occur and a standardized method for evaluation and comparison of cardiac EIT images is desired. This work explores an automated process for segmenting and extracting features from the images that allow for evaluation and comparison. A simulation study was conducted using the 4D XCAT model to evaluate the proposed method’s ability to automatically segment and extract features from images reconstructed at various phases of the cardiac cycle. The same procedure was then applied to EIT reconstructions on data collected from five healthy volunteers. The automated segmentation is able to accurately capture the heart region-of-interest (ROI) in various images and extract features, which allows comparison of desired signals across reconstructions. ROI mean conductivity, ROI area, sum of conductivities within the ROI, and ROI maximum conductivity were chosen as promising features from the simulation study, with R2 values of 0.61, 0.73, 0.75, and 0.66 for a single heart-cycle, and minimum SV distinguishability of 25.54, 12.16, 12.16, and 17.22 ml. In experimental data, the area feature showed the least variation across individual reconstructions while the sum feature showed the highest variation.