System and method of noninvasively monitoring electrical properties within the body using a reduced sensor array and deep neural network

Abstract

Aspects of the present invention relate to a method for using electrical impedance tomography (EIT) to reconstruct electrical property distributions in a patient subjected to an electrode array, including the steps of measuring electrode outputs from the electrode array configured to an anatomical position of the patient, and mapping the electrical property distributions of the measured electrode outputs with a deep neural network (DNN).

Description

[0001] SYSTEM AND METHOD OF NONINVASIVELY MONITORING ELECTRICAL PROPERTIES WITHIN THE BODY USING A REDUCED SENSOR ARRAY AND DEEP NEURAL NETWORK

[0002] CROSS-REFERENCE TO RELATED APPLICATIONS

[0003] This application claims priority to U.S. Provisional Application No. 63 / 585,410 filed on September 26, 2023, incorporated herein by reference in its entirety.

[0004] BACKGROUND OF THE INVENTION

[0005] Electrical impedance tomography (EIT) provides means to image and discriminate critical physiological properties and processes occurring within the body [Adler & Holder, Electrical impedance tomography: methods, history and applications. CRC Press, 2021], EIT systems typically comprise a network of electrodes (16 or 32) attached to one or more planes of the body surface. A sequence of currents is applied to a subset of electrodes within the network, and the electrical fields created within the body are also measured on the network. Reconstruction of internal electrical properties from surface measurements is characteristically very difficult. However, the large electrical contrast between different tissue types and the sensitivity of electrical measurements to small changes partially mitigates the highly ill-posed reconstruction problem. EIT systems can image and monitor lung and cardiovascular function and are presently used to inform lung ventilation strategies by determining differences in properties of oxygenated and injured lungs, amongst many other applications [Adler et al., Physiological measurement, 30(6):S35, 2009; Inez Frerichs, Physiological measurement, 21(2):R1, 2000; Rapin et al., IEEE Transactions on Biomedical Engineering, 66(3):810- 820, 2018],

[0006] Due to blood having a much higher conductivity than many abdominal tissues (about six times), another possible clinical application of EIT is the monitoring of acute intra-abdominal hemorrhages (IAH) [Brian H Brown, Journal of medical engineering & technology, 27(3):97-108, 2003; Tucker et al., In Journal of Physics: Conference Series, volume 224, page 012063. IOP Publishing, 2010; Tucker et al., Physiological Measurement, 32: 151, 2010], IAH is a common consequence of blunt trauma caused by automobile accidents, falls, or detonations and may be undetected from normal clinical signs [Barbara A Gaines, Journal of Trauma and Acute Care Surgery, 67(2):S135-S139, 2009], Ultrasounds and computed tomography (CT) are frequently used in trauma management to detect internal bleeding but cannot easily be used to monitor the bleeding state and are often not available in low-resource environments. EIT monitoring strategies can be used without interrupting treatment, and EIT systems can be miniaturized and used during transport. EIT systems are also much cheaper than other imaging techniques. A sensitive EIT monitoring system could detect whether or not a patient is bleeding at a rate indicative of significant blood volume loss before hypovolemic shock occurs, causing loss of consciousness and more serious sequelae [Dutton et al., Journal of Trauma and Acute Care Surgery, 52(6): 1141-1146, 2002],

[0007] EIT has been demonstrated to discriminate clinical bleeding rates below clinically significant thresholds using a circumferential network of 16 electrodes applied to a single plane of the abdomen of subjects undergoing peritoneal dialysis [Sadleir & Fox, IEEE transactions on biomedical engineering, 48(4):484-491, 2001], However, many subjects with blunt trauma may also have spinal injuries. This indicates a need for an approach that does not involve lifting the patient to place the electrode array, such as applying fewer electrodes to only the anterior surface of the abdomen. Using such a ‘hemiarray’ configuration produces severe artifacts in reconstructed EIT images, with the worst characterization of conductivity properties far away from electrodes [Sadleir et al., Physiological measurement, 29(8):913, 2008; Tucker et al., Physiological Measurement, 32: 151, 2010],

[0008] However, quantities derived from images such as the sum of pixel values were well correlated with the amount of conductive dialysis fluid infused and the lowest detectable bleeding rate was similar for hemiarrays and circumferential arrays [Tucker et al., Physiological Measurement, 32:151, 2010], These initial findings showed good promise for the hemiarray configuration. Nonetheless, for the hemiarray configuration to replace other methods (CT and MRI), the reconstructions must not only produce meaningful derived quantities but must also have an accurate representation of the actual conductivity distribution. Moreover, the metrics produced by both hemi- and circumferential arrays should be consistent wherever bleeding occurs, so that radiological interpretation is not required.

[0009] The literature on novel methods in EIT aims to produce better solutions to the inverse problem; that is, the methods generally focus on reconstructing the internal conductivity based on boundary voltage measurement [Adler & Holder, Electrical impedance tomography: methods, history and applications. CRC Press, 2021], Over the years, several methods have emerged, demonstrating varying degrees of success. Nonetheless, they all have their issues. Methods that deal with the ill-posedness of the inverse problem, such as truncated singular value decomposition (TSVD), b ackprojection, and Tikhonov regularization, struggle with sharp boundaries in conductivity often observed from internal bleeds and other anomalies [Adler & Holder, Electrical impedance tomography: methods, history and applications. CRC Press, 2021], Other edge-preserving methods based on total variation regularization developed to fix this smoothing problem may become trapped in local extrema, resulting in poor overall accuracy [Adler & Holder, Electrical impedance tomography: methods, history and applications. CRC Press, 2021; Mueller & Siltanen. Linear and nonlinear inverse problems with practical applications. SIAM, 2012],

[0010] Thus, there is a need in the art for improved EIT systems and methods. The present invention meets this need.

[0011] SUMMARY OF THE INVENTION

[0012] Aspects of the present invention relate to a method for using electrical impedance tomography (EIT) to reconstruct electrical property distributions in a patient with an electrode array including measuring electrode outputs from the electrode array configured to monitor an anatomical portion of the patient, mapping the electrical property distributions of the measured electrode outputs with a deep neural network (DNN), the DNN comprising computing code executed by at least one processor for providing the DNN, the processor communicatively connected to a providing apparatus of the EIT, and the computing code stored in at least one dedicated computing memory communicatively connected to the at least one processor and being configured to carry out the steps of receiving, by the DNN, a plurality of boundary voltage inputs, weighting at least a portion of the plurality of boundary voltage inputs based on training of the DNN by comparing reconstructions of the electrical property distributions by the DNN for a plurality of samples, ones of which have randomly placed circular and square anomalies with various conductivities in the reconstructed electrical property distributions, to reconstructions for the plurality of samples provided by a second neural network (SNN) trained for a full array EIT, randomly assigning weighting in the training of the DNN for the remaining boundary voltage inputs of the plurality of boundary voltage inputs, reconstructing, by the DNN, the electrical property distributions received by the electrode array based on a pass of the electrode outputs through the DNN after training by the DNN of the receiving step, the weighting step, and the assigning step.

[0013] In some embodiments, the electrode array is selected from the group consisting of: a reduced-number electrode array, a standard-number electrode array, an electrode full-array, an electrode hemiarray, and an anterior region electrode hemiarray. In some embodiments, the anatomical position is selected from the group consisting of anterior, posterior, superior, inferior, lateral, medial, and combinations thereof. In some embodiments, the electrode array is configured to any of a transverse configuration, a coronal configuration, a sagittal configuration, or combinations thereof.

[0014] In some embodiments, the method further includes applying current patterns to the electrode array. In some embodiments, the current pattern includes applying current between other electrodes in the array. In some embodiments, the current pattern includes an adjacent current injection pattern, wherein current is applied between adjacent electrodes in the array.

[0015] In some embodiments, the method further includes the step of finetuning the training of the DNN in one or more epochs of batches of 100 of the plurality of samples. In some embodiments, the method further includes the step of checking for data overfitting using finer mesh filtering of outputs of the finetuning.

[0016] In some embodiments, the DNN and SNN each have a series of connected layers with one or more nodes in each layer, wherein the layers include input, hidden and output layers. In some embodiments, the hidden layers have between 10 and 500 nodes.

[0017] In some embodiments, the hidden and output layers utilize one or more activation functions. In some embodiments, the one or more activation functions are selected from: non-linear activation function, rectified linear unit (ReLU) activation function, hyperbolic tangent (tanh) activation function, and logistic sigmoid activation function.

[0018] In some embodiments, the finetuning step includes randomly removing nodes from at least one of the layers. In some embodiments, the nodes are removed from the input and hidden layers.

[0019] In some embodiments, one or more learning techniques are applied to the networks selected from the group consisting of unsupervised learning techniques, supervised learning techniques, L2 regularization, loss function penalty, weight decay, Tikhonov regularization, Greedy layer-wise pretraining, noise reduction, autoencoder stacking, data augmentation, dropout, and any combinations thereof.

[0020] In some embodiments, a portion of the plurality of voltage inputs are weighted. In some embodiments, the plurality of voltage inputs include between 5 and 208 voltage inputs, and wherein between 5 and 100 voltage inputs are weighted.

[0021] In some embodiments, the step of finetuning the training of the DNN further includes utilizing one or more evaluation metrics selected from the group consisting of amplitude response (AR), position error (PE), resolution (RES), shape deformation (SD), ringing (RNG), quality index (QI), mean squared error (MSE), and any combinations thereof.

[0022] In some embodiments, the plurality of samples includes at least 12,000 samples and the one or more epochs include 200 pretraining epochs and 50 finetuning epochs. In some embodiments, the plurality of samples includes between 100 and 100,000 samples, and the one or more epochs have between 8 and 800 epochs.

[0023] In some embodiments, the electrode array is an electrode hemiarray, and the SNN is configured to simulate an electrode full-array representation of the electrode hemiarray.

[0024] BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The following detailed description of embodiments of the invention will be better understood when read in conjunction with the appended drawings. It should be understood, however, that the invention is not limited to the precise arrangements and instrumentalities of the embodiments shown in the drawings. FIG. 1 A and FIG. IB are diagrams depicting exemplary training mesh and electrode layouts or arrays for a system and method of noninvasively monitoring electrical properties within the body using electrical impedance tomography (EIT). FIG. 1A depicts an exemplary full-array configuration. FIG. IB depicts an exemplary hemiarray configuration.

[0026] FIG. 2A and FIG. 2B are diagrams depicting an exemplary voltage gathering process and exemplary network (e.g., deep neural network (DNN)) topology for the fullarray configuration according to aspects of the present invention. FIG. 2A is a diagram for an exemplary voltage gathering process displaying how the full-array gathers boundary voltage measurements by injecting adjacent electrodes with current in a pattern and produces a plurality of boundary voltage measurements or outputs (e.g., 208 boundary voltage measurements). FIG. 2B is a diagram of exemplary network topology for the full-array showing that the boundary voltage measurements are used to reconstruct a discretized internal conductivity distribution with a plurality of elements (e.g., 576 elements).

[0027] FIG. 3A and FIG. 3B are diagrams depicting an exemplary voltage gathering process and exemplary network (e.g., deep neural network (DNN)) topology for the hemiarray configuration according to aspects of the present invention. FIG. 3A is a diagram of an exemplary voltage gathering process displaying how the boundary voltage measurements are collected using the adjacent current injection pattern. FIG. 3B is a diagram of exemplary network topology displaying that the hemiarray network, except for its input layer, share the same topology as the full-array configuration.

[0028] FIGs. 4A-4C are a set of plots arranged in columns displaying the results of full- and hemiarray reconstructions of simulated data. FIG. 4A shows the true internal conductivity. FIG. 4B shows the reconstructions produced by Tikhonov (TK), truncated singular value decomposition (TSVD), and the full-array deep neural network (FA- DNN), respectively, using the full-array configuration. FIG. 4C shows reconstructions produced by TK, TSVD, and the half-array deep neural network (HA-DNN), respectively, using the hemiarray configuration.

[0029] FIGs. 5A-5F are a set of plots displaying the average values of each figure of merit for reconstructing small conductive anomalies. FIGs. A, 5B, and 5C shows the results for a fullarray configuration. FIGs. 5D, 5E, and 5F shows the results for a hemiarray configuration. Bold lines indicate the mean value of each figure of merit for all radial positions at a given angle. Shaded regions show two standard errors (one-fifth standard deviation) above and below the mean value, indicating the models’ robustness to changes in anomaly radial positions. Quantity Index (QI) subplots have a black dashed line representing the normalized true QI at each angle. QI values are averages over the entire mesh in units of S / m.

[0030] FIGs. 6A-6D are a set of plots arranged in rows displaying the hemiarray reconstructions of internal conductivity based on actual voltage measurements, with the true placement of cylindrical anomalies superimposed. FIGs. 6A and 6B show plots depicting metal anomalies. FIGs. 6C and 6D show plots depicting plastic anomalies. Note that anomaly locations are described in terms of the electrode or angular location, i .e., anomaly ‘ 1’ is at the same angle as electrode 1, or 90°, and ‘7’ is at the angle of electrode 7 (225°). FIG. 6D further shows an exemplary electrical impedance tomography (EIT) device utilized to collect the data and a depiction of all anomalies within an elliptical boundary.

[0031] FIG. 7A and FIG. 7B are a set of plots showing a Graz consensus Reconstruction algorithm for EIT (GREIT) figure of merit metrics for DNN phantom data reconstructed on disk mesh. FIG. 7A is a plot corresponding to metal anomaly measures. FIG. 7B is a plot showing plastic anomaly values. QI values are averages over entire mesh in S / m.

[0032] FIGs. 8A-8D are a set of plots arranged in rows displaying the hemiarray reconstructions of internal conductivity based on phantom data, with the true placement of cylindrical anomalies superimposed. FIGs. 8A and 8B are plots depicting metal anomalies. FIGs. 8C and 8D are plots depicting plastic anomalies. FIG. 8D is an exemplary EIT device utilized to collect the data and a depiction of all anomalies within an elliptical boundary.

[0033] FIG. 9 is a plot displaying the QI expressed as average conductivity over mesh for elliptical reconstructions for each anomaly type.

[0034] FIG. 10 is a diagram depicting a computer architecture for a computer for practicing the various embodiments of the invention. DETAILED DESCRIPTION

[0035] It is to be understood that the figures and descriptions of the present invention have been simplified to illustrate elements that are relevant for a clear understanding of the present invention, while eliminating, for the purpose of clarity many other elements found in related systems and methods. Those of ordinary skill in the art may recognize that other elements and / or steps are desirable and / or required in implementing the present invention. However, because such elements and steps are well known in the art, and because they do not facilitate a better understanding of the present invention, a discussion of such elements and steps is not provided herein. The disclosure herein is directed to all such variations and modifications to such elements and methods known to those skilled in the art.

[0036] Definitions

[0037] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the invention pertains. Although any methods and materials similar or equivalent to those described herein can be used in the practice for testing of the present invention, exemplary materials and methods are described herein. In describing and claiming the present invention, the following terminology will be used.

[0038] It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting.

[0039] The articles “a” and “an” are used herein to refer to one or to more than one (i.e., to at least one) of the grammatical object of the article. By way of example, “an element” means one element or more than one element.

[0040] “About” as used herein when referring to a measurable value such as an amount, a temporal duration, and the like, is meant to encompass the specified value, and variations of ±20%, ±10%, ±5%, ±1%, or ±0.1% from the specified value, as such variations are appropriate.

[0041] The terms “patient,” “subject,” “individual,” and the like are used interchangeably herein, and refer to any animal amenable to the systems, devices, and methods described herein. The patient, subject or individual may be a mammal, and in some instances, a human.

[0042] Ranges: throughout this disclosure, various aspects of the invention can be presented in a range format. It should be understood that the description in range format is merely for convenience and brevity and should not be construed as an inflexible limitation on the scope of the invention. Accordingly, the description of a range should be considered to have specifically disclosed all the possible subranges as well as individual numerical values within that range. For example, description of a range such as from 1 to 6 should be considered to have specifically disclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 6, from 3 to 6 etc., as well as individual numbers within that range, for example, 1, 2, 2.7, 3, 4, 5, 5.3, and 6. This applies regardless of the breadth of the range.

[0043] System and Method of Noninvasively Monitoring Electrical Properties within the Body The disclosed invention provides a system and method of non-invasively monitoring electrical properties within the body of a subject using electrode arrays and deep learning with neural networks. In some embodiments, the disclosed system may be used for Electrical impedance tomography (EIT) and utilizes one or more EIT reconstruction algorithms or methods. Electrical impedance tomography (EIT) is a noninvasive type of medical imaging in which the electrical conductivity, permittivity, and impedance of a part of the body is inferred from surface electrode measurements and used to form a tomographic image of that part. Electrical conductivity varies considerably among various biological tissues (absolute EIT) or the movement of fluids and gases within tissues (difference EIT). In some embodiments, any disclosed systems and methods may apply small alternating currents at a single frequency for EIT, however, in some embodiments may use multiple frequencies to better differentiate between normal and suspected abnormal tissue within the same organ (multifrequency-EIT or electrical impedance spectroscopy).

[0044] In some embodiments, the disclosed system and method utilize one or more networks (e.g., deep neural network (DNNs)) configured to measure or capture signals from an electrode array. Exemplary networks may include hemi array deep neural network (HA-DNN) and full-array deep neural network (FA-DNN), although any neural network known in the art may be used herein. In some embodiments, each network processes or reconstructs data from an electrode array (i.e., performs EIT reconstruction) configured on a subject. In some embodiments, the networks comprise a second neural network (SNN), and each network may be interconnected and / or utilize methods for sharing or correlating data between the networks. For example, in some embodiments, transfer learning is implemented by utilizing the learned information from the FA-DNN as the initial starting point for the HA-DNN, to ensure the consistency of the HA-DNN reconstruction with the FA-DNN.

[0045] In some embodiments, the system and method simulates an electrode array, such as a simulated electrode full array or hemiarray, that may be representative of and used in conjunction with a physical electrode full array or hemiarray. In some embodiments, the disclosed system and method mitigates the challenges of reconstructing anomalies in posterior regions of a patient, with a performance advantage consistently observed across reconstructions of phantom data. Further disclosed herein are experimental results where the performance of disclosed DNNs are compared against other popular methods, such as truncated singular value decomposition (TSVD) and Tikhonov regularization. Furthermore, the results are evaluated using the Graz consensus Reconstruction algorithm for EIT (GREIT) figures of merit, specifically designed to assess the consistency and visibility of EIT reconstruction algorithms.

[0046] Referring now to FIGs. 1A-1B, shown is a set of diagrams depicting exemplary electrode layouts or arrays for the full-array (FIG. 1 A) and hemiarray (FIG. IB) configurations for the disclosed system and / or method. Each array comprises one or more electrodes positioned in a shape, layout or pattern, or along a path, in one or more rows, and configured to measure or capture signals from an anatomical region or portion of a patient. In some embodiments, each array comprises any number of electrodes, or between 1 and 250 electrodes. In some embodiments, suitable arrays may have 1-200 electrodes, or 1-150 electrodes, or 1-100 electrodes, or 1-50 electrodes, or 50-100 electrodes, or 1-25 electrodes, or 10-20 electrodes, or 20-40 electrodes, or any other suitable number of electrodes. In some embodiments, the path or shape of the electrodes forms a boundary, wherein a training mesh is applied to the region within the boundary. In some embodiments, an exemplary full-array arrangement comprises electrodes that cover more than half of a circumference or border of the layout, and the hemiarray arrangement comprises electrodes that cover half, or less than half of a circumference or border. In some embodiments, a portion of the electrodes in the full-array coincide or correlate to a portion of the electrodes in the half-array.

[0047] In some embodiments, the electrode layouts or arrays comprise one or more rows of electrodes, or multiple rows of electrodes. In some embodiments, the output of each electrode of each row, or the output of each row may be combined with the output of another electrode or row. In some embodiments, the electrodes may be arranged as multiple rows, and the output of each electrode, or one or more electrodes, may be measured using a combination of electrodes (e.g., 4 electrodes) of the total combination of electrodes, or the total number of electrodes may be grouped into groupings of electrodes, wherein each grouping has between 2 and 20 electrodes, or about 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ,13 14, 15, 16, 17, 18, 19, or about 20 electrodes. In some embodiments, some or all of the electrodes in one or more of the arrays may be regularly or similarly spaced apart from one another, or irregularly or differently spaced from one another. In some embodiments, a first subset of the electrodes in one or more of the arrays may be spaced differently from one another with respect to a second subset of the electrodes in one or more of the arrays. In some embodiments, the spacing or distance between each electrode is between 1 mm and 10 cm, or between 1 cm and 25 cm, or about 1 mm, 2 mm, 3 mm, 4 mm, 5, 6 mm, 7 mm, 8 mm, 9, mm, 10 mm, or about 0.25 cm, 0.5 cm, 0.75 cm, 1 cm, 1.25 cm, 1.5 cm, 1.75 cm, 2 cm, 2.25 cm, 2.5 cm, 2.75 cm, 3 cm, 3.25 cm, 3.5 cm, 3.75 cm, 4 cm, 4.25 cm, 4.5 cm, 4.75 cm, 5 cm, 5.25 cm, 5.5 cm, 5.75 cm, 6 cm, 6.25 cm, 6.5 cm, 6.75 cm, 7 cm, 7.25 cm, 7.5 cm, 7.75 cm, 8 cm, 8.25 cm, 8.5 cm, 8.75 cm, 9 cm, 9.25 cm, 9.5 cm, 9.75 cm, or about 10 cm. Any electrode having any shape, size or material known by one of ordinary level of skill in the art may be used with the disclosed system and method.

[0048] Although exemplary electrode arrays are provided, the electrode arrays may comprise any electrode array or device known by one of ordinary level of skill in the art for reading, measuring, monitoring or capturing signals from an anatomical position, portion or region of a patient. In some embodiments, the electrode array comprises a reduced-number electrode array, a standard-number electrode array, an electrode hemiarray, an anterior region electrode hemiarray, or combinations thereof. In some embodiments, the anatomical portion or region of the patient is selected from the group consisting of: anterior, posterior, superior, inferior, lateral, medial, or combinations thereof. In some embodiments, the electrode array may be configured to a patient or anatomical region in one or more configurations. In some embodiments, the configurations are any of a transverse configuration, a coronal configuration, a sagittal configuration, or combinations thereof.

[0049] Aspects of the present invention relate to one or more full- and hemiarray electrode configurations for the disclosed electrode arrays. In some embodiments, the pattern or shape of the electrodes is formed along a circular boundary of the anatomical portion or region of the patient. For example, FIGs. 1 A-1B display electrodes in exemplary full-array and hemiarray configurations arranged around a circular boundary. In some embodiments, the full-array (FIG. 1A) comprises one or more electrodes (e.g., 16 electrodes) each spaced by a distance or angle (e.g., 22.5°). In some embodiments, the hemiarray (FIG. IB) comprises one or more electrodes (e.g., 8 electrodes) each spaced by a distance or angle. In some embodiments, the angle ranges between 1° and 300°, or about 22°. In some embodiments, the full- and hemi-array share the same spacing except for the 8thand 1stelectrodes, which are separated by 202.5°. In some embodiments, a mesh or training mesh is applied to the region inside the boundary of each electrode configuration. In some embodiments, the mesh is a tessellation covering the region contained within the boundary using tiles having any geometric shape. In some embodiments, the mesh uses at least one pattern (e.g, "c2C" or “d2C” pattern). In some embodiments, the mesh comprises of one or more elements, pixels or voxels.

[0050] The disclosed system or method comprises one or more networks (e.g., an FA- DNN and HA-DNN) configured to receive boundary voltage inputs from one or more electrode arrays. In some embodiments, each network is a neural network utilizing one or more learning techniques. In some embodiments, each network comprises one or more layers. In some embodiments, the one or more layers comprise at least an input layer, one or more hidden layers, and an output layer. In some embodiments, the hidden layers comprise at least three layers, or ranging between 3 layers and 20 layers. In some embodiments, the hidden layers comprise three hidden, fully connected layers. Tn some embodiments, each layer comprises at least one node. In some embodiments, the hidden layers comprise a plurality of nodes (e.g., 50 or 60 nodes) and utilizes at least one function (e.g., a logistic sigmoid function) as an activation function. In some embodiments, each of the hidden layer and output layer comprises or utilizes at least one activation function. In some embodiments, the one or more layers comprise an input layer connected to one or more hidden layers (e.g., 3 hidden layers), and an output layer, in a series of connected layers. In some embodiments, the plurality of nodes in the hidden layers comprise at least 2 nodes, or ranging between 2 nodes and 1000 nodes, or about 50 nodes, 100 nodes, 150 nodes, 200 nodes, 250 nodes, 300 nodes, 350 nodes, 400 nodes, 450 nodes, 500 nodes, 550 nodes, 600 nodes, 650 nodes, 700 nodes, 750 nodes, 800 nodes, 850 nodes, 900 nodes, 950 nodes, or about 1000 nodes.

[0051] In some embodiments, the nodes of the input and output layers correlate to the number of electrodes in the respective array, or to a number of boundary voltages for the array. In some embodiments, an exemplary FA-DNN comprises a deeper architecture with up to 20 layers, varying nodes between 2 and 1,000, and using one or more multilayer perceptron (MLP), one or more convolutional neural network (CNN)s, artificial neural network (ANN), deep neural network (DNN), second neural network (SNN), or one or more transformer based models. In some embodiments, activation functions such as non-linear activation functions, rectified linear unit (ReLU) activation function or hyperbolic tangent (tanh) activation functions may be used. In some embodiments, regularization techniques such as dropout (0.2 to 0.5) or L2, and optimizers such as Adam optimization or root mean square propagation (RMSProp) may be used.

[0052] Aspects of the present invention relate to the input and output layers for the one or more layers. In some embodiments, the input layer comprises or receives a plurality of boundary voltage measurements or outputs (e.g., 208 boundary voltage measurements) from an electrode array, while the output layer calculates or outputs a conductivity (e.g., an internal conductivity) of some or all of the pixels, voxels, or elements (e.g., 576 pixels) in the training mesh. Any number of voltage measurements or outputs from an electrode array may be used. Referring now to FIG. 2A and FIG. 2B, shown are diagrams depicting an exemplary voltage gathering process and exemplary network (e.g., DNN) topology for the full-array configuration according to aspects of the present invention. FIG. 2A is a diagram for an exemplary voltage gathering process displaying how, in some embodiments, the full-array gathers outputs or boundary voltage measurements by injecting adjacent electrodes with current. FIG. 2B is a diagram of exemplary network topology for the full-array configuration. In some embodiments the boundary voltage measurements are used to reconstruct a discretized internal conductivity distribution with a plurality of elements (e.g., 576 elements).

[0053] Referring now to FIG. 3A and FIG. 3B, shown are diagrams depicting an exemplary voltage gathering process and exemplary network topology for the hemiarray configuration according to aspects of the present invention. FIG. 3 A is a diagram of an exemplary voltage gathering process displaying how the boundary voltage measurements are collected using the adjacent current injection pattern. In some embodiments, the hemiarray produces or outputs a plurality of voltage measurements (e.g., 40 boundary voltage measurements). In some embodiments the hemiarray is configured such that the 1st and 8th electrodes are considered to be adjacent. FIG. 3B is a diagram of exemplary network topology displaying that in some embodiments the hemiarray network, except for its input layer, share the same topology as the full-array configuration. FIG. 3B highlights some of the unique connections of the hemiarray in green.

[0054] In some embodiments, the HA-DNN receives a plurality of boundary voltage inputs (e.g., 40 boundary voltage inputs), wherein a portion or number (e.g., 29) of which are shared with the FA-DNN. In some embodiments, boundary voltage measurements are obtained using the adjacent current injection pattern. In some embodiments, in the hemiarray, the 1st and 8th electrodes are adjacent, resulting in 40 boundary voltage measurements. In some embodiments, an exemplary HA-DNN comprises an architecture with 3-10 layers, varying nodes between 2 and 500, or around 50 nodes per layer, and using or comprising one or more multilayer perceptron (MLP), one or more convolutional neural network (CNN)s, artificial neural network (ANN), or one or more transformer based models. In some embodiments, activation functions such as non-linear activation functions, rectified linear unit (ReLU) activation function, or sigmoid activation functions may be used. In some embodiments, regularization techniques such as dropout (0.2 to 0.5) or L2, and optimizers such as Adam optimization or root mean square propagation (RMSProp) may be used to enhance performance.

[0055] In some embodiments, any disclosed electrode configuration, layout or array can use one or more current injection patterns (e.g., an adjacent current injection pattern), where electrical current is applied between other electrodes in the array (such as between adjacent electrodes 1 and 2 in FIGs. 1A-1B), resulting in voltage differences that can measured between adjacent electrodes (such as 3-4, 5-6,..., 15-16 in FIGs. 1A-1B). In some embodiments, the voltage differences form or produce the boundary voltage vector Vb(as shown in FIGs. 2A-2B & FIG. 3 A). In some embodiments, the injection pattern cycles through all possible pairs of adjacent electrodes, resulting in a plurality of voltage measurements for the full-array (e.g., 16 • 13 = 208 voltage measurements) and a plurality of voltage measurements for the hemiarray (e g., 8 • 5 = 40 voltage measurements). In some embodiments, one or more non-adjacent electrodes are considered or simulated to be adjacent. For example in the hemiarray configuration of FIG. IB, the 1stand 8thelectrodes are considered adjacent. In some embodiments, the hemiarray network shares the same topology as the full array, except for its input layer. In some embodiments, the hemiarray input layer includes the connection between the 1st and 8th electrodes, which is not present in the full array.

[0056] Aspects of the present invention relate to a method for using electrical impedance tomography (EIT) to reconstruct electrical property distributions in a patient with or subjected to an electrode array (in some examples, an anterior region electrode hemiarray), comprising the steps of measuring electrode outputs from the electrode array configured to monitor or measure an anatomical portion, position or region of the patient, mapping the electrical property distributions of the measured electrode outputs with a deep neural network (DNN). In some embodiments, the DNN comprises computing code executed by at least one specialized processor specifically for providing the DNN, the specialized processor being communicatively connected to a providing apparatus of the EIT, and the computing code stored in at least one dedicated computing memory communicatively connected to the at least one specialized processor and being configured to carry out various steps. In some embodiments, the steps comprise receiving by the DNN a plurality or set of boundary voltage inputs (e.g., 40 boundary voltage inputs), weighting at least a subset of the boundary voltage inputs, based on training of the DNN by comparing a reconstruction of the electrical property distributions by the DNN for any number of samples (e.g., 10,000 samples, or 12,000 samples) to reconstructions for the samples (e.g., 10,000 samples) provided by a second neural network (SNN) trained for a full array EIT. In some embodiments, the reconstructed electrical property distributions include randomly placed circular and square anomalies with various conductivities. In some embodiments, the subset of boundary voltage inputs is about 10%, 15%, 20%, 25%, 30%, 35%, 40%, 45%, 50%, 55%, 60%, 65%, 70%, 75%, or about 80% of the plurality or set of boundary voltage inputs. A preferred subset is about 75%. For example, in some embodiments, 29 of the 40 boundary voltage inputs are weighted, or about 72.5% of the boundary voltage inputs. In some embodiments, the plurality of voltage inputs comprises between 5 and 208 voltage inputs, and between 5 and 100 voltage inputs are weighted.

[0057] In some embodiments, the steps of the method further comprise randomly assigning weighting in the training of the DNN for the remaining ones of the set of boundary inputs, finetuning the training of the DNN in epochs (e.g., 80 epochs) of batches of samples (e.g., 100 of the 10,000 samples), checking for data overfitting using finer mesh filtering of outputs of the finetuning, and reconstructing by the DNN of the electrical property distributions received by the anterior region electrode hemiarray based on a pass of the electrode outputs through the DNN after training by the DNN of the receiving step, the weighting step, the assigning step, the finetuning step, and the checking step.

[0058] Aspects of the present invention relate to the training of the DNNs. In some embodiments, the system or method is finetuned for 80 epochs using a batch size of 100 and the MSE loss function on a training set of 10,000 unique samples with randomly placed circular and square anomalies with various conductivities. In some embodiments, the DNN is trained for 300 epochs with mean squared error (MSE) loss, using 100 batch size, but any number of epochs with any batch size may be used. In some embodiments, the plurality of samples comprises at least 12,000 samples and the one or more epochs comprise pretraining epochs (e.g., about 200 epochs) and finetuning epochs (e.g., about 50 epochs). In some embodiments, the step of finetuning the training of the DNN further comprises utilizing one or more evaluation metrics selected from the group consisting of: amplitude response (AR), position error (PE), resolution (RES), shape deformation (SD), ringing (RNG), quality index (QI) and mean squared error (MSE). QI represents the averaged conductivity reconstructed over all or a selected portion of pixels in the training mesh or image.

[0059] The disclosed system and method may utilize various learning techniques. In some embodiments, the techniques include, but not limited to, unsupervised learning techniques, supervised learning techniques, Dropout, data augmentation, weight decay, loss function penalty, Tikhonov regularization, greedy layer-wise pretraining, L2 regularization, noise reduction, and stacked autoencoders (for pretraining) in order to optimize fit. In some embodiments, Dropout involves randomly removing nodes from the hidden and input layers of the DNN during training to prevent the network from becoming too reliant on any particular node. In some embodiments, Weight decay comprises a technique to regularize a neural network by adding a penalty term to the loss function. The penalty term is weight-based and prevents overfitting by encouraging weights with low predictive values to approach zero. In some embodiments, the Weight decay is analogous to Tikhonov regularization. In some embodiments, Greedy layer-wise pretraining comprises an unsupervised learning technique used to identify the weights of a neural network that can optimally encode valuable information from the input data into a lower-dimensional representation while disregarding noise and correlations. In some embodiments, aspects of each network may be compared to or weighted by another network (e.g., transference learning) allowing shared network topology.

[0060] In some embodiments, in order to train a disclosed network (e.g., a DNN), a large dataset of voltage measurements and corresponding conductivity distributions must be provided to the network as training data. In some embodiments, training data can be generated using the forward problem (disclosed in the Examples section), which calculates voltage measurements based on a discretized conductivity distribution. In some embodiments, once a sufficient dataset has been created, the DNN can be trained to predict the conductivity distribution based on the voltage measurements using a process called backpropagation [Paul J Werbos, Proceedings of the IEEE, 78(10): 1550-1560, 1990],

[0061] Computing Device

[0062] In some aspects of the present invention, software executing the instructions provided herein may be stored on a non-transitory computer-readable medium, wherein the software performs some or all of the steps of the present invention when executed on a processor.

[0063] Aspects of the invention relate to algorithms executed in computer software. Though certain embodiments may be described as written in particular programming languages, or executed on particular operating systems or computing platforms, it is understood that the system and method of the present invention is not limited to any particular computing language, platform, or combination thereof. Software executing the algorithms described herein may be written in any programming language known in the art, compiled, or interpreted, including but not limited to C, C++, C#, Objective-C, Java, JavaScript, MATLAB, Python, PHP, Perl, Ruby, or Visual Basic. It is further understood that elements of the present invention may be executed on any acceptable computing platform, including but not limited to a server, a cloud instance, a workstation, a thin client, a mobile device, an embedded microcontroller, a television, or any other suitable computing device known in the art.

[0064] Parts of this invention are described as software running on a computing device. Though software described herein may be disclosed as operating on one particular computing device (e.g. a dedicated server or a workstation), it is understood in the art that software is intrinsically portable and that most software running on a dedicated server may also be run, for the purposes of the present invention, on any of a wide range of devices including desktop or mobile devices, laptops, tablets, smartphones, watches, wearable electronics or other wireless digital / cellular phones, televisions, cloud instances, embedded microcontrollers, thin client devices, or any other suitable computing device known in the art.

[0065] Similarly, parts of this invention are described as communicating over a variety of wireless or wired computer networks. For the purposes of this invention, the words “network”, “networked”, and “networking” are understood to encompass wired Ethernet, fiber optic connections, wireless connections including any of the various 802.11 standards, cellular WAN infrastructures such as 3G, 4G / LTE, or 5G networks, Bluetooth®, Bluetooth® Low Energy (BLE) or Zigbee® communication links, or any other method by which one electronic device is capable of communicating with another. In some embodiments, elements of the networked portion of the invention may be implemented over a Virtual Private Network (VPN).

[0066] FIG. 10 and the following discussion are intended to provide a brief, general description of a suitable computing environment in which the invention may be implemented. While the invention is described above in the general context of program modules that execute in conjunction with an application program that runs on an operating system on a computer, those skilled in the art will recognize that the invention may also be implemented in combination with other program modules.

[0067] Generally, program modules include routines, programs, components, data structures, and other types of structures that perform particular tasks or implement particular abstract data types. Moreover, those skilled in the art will appreciate that the invention may be practiced with other computer system configurations, including handheld devices, multiprocessor systems, microprocessor-based or programmable consumer electronics, minicomputers, mainframe computers, and the like. The invention may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices.

[0068] FIG. 10 depicts an illustrative computer architecture for a computer 1000 for practicing the various embodiments of the invention. The computer architecture shown in FIG. 10 illustrates a conventional personal computer, including a central processing unit 1050 (“CPU”), a system memory 1005, including a random access memory 1010 (“RAM”) and a read-only memory (“ROM”) 1015, and a system bus 1035 that couples the system memory 1005 to the CPU 1050. A basic input / output system containing the basic routines that help to transfer information between elements within the computer, such as during startup, is stored in the ROM 1015. The computer 1000 further includes a storage device 1020 for storing an operating system 1025, application / program 1030, and data.

[0069] The storage device 1020 is connected to the CPU 1050 through a storage controller (not shown) connected to the bus 1035. The storage device 1020 and its associated computer-readable media provide non-volatile storage for the computer 1000. Although the description of computer-readable media contained herein refers to a storage device, such as a hard disk or CD-ROM drive, it should be appreciated by those skilled in the art that computer-readable media can be any available media that can be accessed by the computer 1000.

[0070] By way of example, and not to be limiting, computer-readable media may comprise computer storage media. Computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer-readable instructions, data structures, program modules or other data. Computer storage media includes, but is not limited to, RAM, ROM, EPROM, EEPROM, flash memory or other solid state memory technology, CD-ROM, DVD, or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by the computer.

[0071] According to various embodiments of the invention, the computer 1000 may operate in a networked environment using logical connections to remote computers through a network 1040, such as TCP / IP network such as the Internet or an intranet. The computer 1000 may connect to the network 1040 through a network interface unit 1045 connected to the bus 1035. It should be appreciated that the network interface unit 1045 may also be utilized to connect to other types of networks and remote computer systems.

[0072] The computer 1000 may also include an input / output controller 1055 for receiving and processing input from a number of input / output devices 1060, including a keyboard, a mouse, a touchscreen, a camera, a microphone, a controller, a joystick, or other type of input device. Similarly, the input / output controller 1055 may provide output to a display screen, a printer, a speaker, or other type of output device. The computer 1000 can connect to the input / output device 1060 via a wired connection including, but not limited to, fiber optic, Ethernet, or copper wire or wireless means including, but not limited to, Wi-Fi, Bluetooth, Near-Field Communication (NFC), infrared, or other suitable wired or wireless connections.

[0073] As mentioned briefly above, a number of program modules and data files may be stored in the storage device 1020 and / or RAM 1010 of the computer 1000, including an operating system 1025 suitable for controlling the operation of a networked computer. The storage device 1020 and RAM 1010 may also store one or more applications / programs 1030. In particular, the storage device 1020 and RAM 1010 may store an application / program 1030 for providing a variety of functionalities to a user. For instance, the application / program 1030 may comprise many types of programs such as a word processing application, a spreadsheet application, a desktop publishing application, a database application, a gaming application, internet browsing application, electronic mail application, messaging application, and the like. According to an embodiment of the present invention, the application / program 1030 comprises a multiple functionality software application for providing word processing functionality, slide presentation functionality, spreadsheet functionality, database functionality and the like.

[0074] The computer 1000 in some embodiments can include a variety of sensors 1065 for monitoring the environment surrounding and the environment internal to the computer 1000. These sensors 1065 can include a Global Positioning System (GPS) sensor, a photosensitive sensor, a gyroscope, a magnetometer, thermometer, a proximity sensor, an accelerometer, a microphone, biometric sensor, barometer, humidity sensor, radiation sensor, or any other suitable sensor.

[0075] EXPERIMENTAL EXAMPLES

[0076] The invention is further described in detail by reference to the following experimental examples. These examples are provided for purposes of illustration only, and are not intended to be limiting unless otherwise specified. Thus, the invention should in no way be construed as being limited to the following examples, but rather, should be construed to encompass any and all variations which become evident as a result of the teaching provided herein.

[0077] Without further description, it is believed that one of ordinary skill in the art can, using the preceding description and the following illustrative examples, make and utilize the present invention and practice the claimed methods. The following working examples therefore are not to be construed as limiting in any way the remainder of the disclosure.

[0078] A Deep Neural Network for a Hemiarray EIT System

[0079] Electrical Impedance Tomography (EIT) can map electrical property distributions within the body using a surface electrode array. Standard EIT electrode arrays using a circumferential array applied to the abdomen can be used to monitor acute intraabdominal hemorrhages in trauma patients. Nevertheless, these patients may also have suffered spinal injuries that might be exacerbated by lifting the patient to place the array. Thus, a half array (‘hemiarray’) applied only to the anterior abdomen may be more practical. However, severe reconstruction artifacts result in posterior regions using the standard EIT reconstruction method. This example discloses a novel machine learningbased system and method for standard full and hemiarray EIT reconstructions, demonstrating superior reconstruction characteristics compared to conventional systems and methods. Notably, the disclosed system and method mitigates the challenges of reconstructing anomalies in posterior regions. This performance advantage was consistently observed across reconstructions of phantom data. Based on the findings of the study in this example, it was concluded that the machine learning-based reconstruction system and method holds significant promise for challenging imaging scenarios, particularly when access to the anterior or posterior abdomen is restricted.

[0080] Building upon the success of Li et al. fullarray deep neural network (FA-DNN) [Li et al., Transactions of the Institute of Measurement and Control, 41(14):4035-4049, 2019], a similar framework to tackle the hemiarray problem is disclosed herein. To ensure the consistency of the hemiarray deep neural network (HA-DNN) reconstruction with the FA-DNN, transference learning was implemented by utilizing the learned information from the FA-DNN as the initial starting point for the HA-DNN. The performance of both DNNs were compared against other popular methods, such as truncated singular value decomposition (TSVD) and Tikhonov regularization. The different approaches were assessed using metrics such as the quantity index (the integral or discrete sum of the reconstructed conductivity or resistivity multiplied by pixel area or volume), mean squared error, and qualitative analysis of reconstructions produced with real data. Furthermore, the methods were evaluated using the Graz consensus Reconstruction algorithm for EIT (GREIT) figures of merit, specifically designed to provide a unified approach to assess the consistency and visibility of EIT reconstruction algorithms [Adler et al., Physiological measurement, 30(6): S35, 2009],

[0081] Disclosed herein is an overview of the approach, introducing the FA-DNN and HA-DNN system and method and describing comparison methods and phantom measurements.

[0082] The forward electrical impedance tomography problem aims to construct the voltage pattern V of an object as a function of its internal conductivity distribution a and injected current / :

[0083] V = F(a, r)

[0084] Equation 1

[0085] The forward EIT problem can be solved using the Finite Element Method (FEM) and the Laplace equation:

[0086] V • (o u) = 0

[0087] Equation 2 where u is the electric potential distribution and V • is the divergence operator. This equation relates the electric potential from the electrodes and the conductivity within the body.

[0088] The objective of the EIT inverse problem is to reconstruct the spatial conductivity distribution <J( ) based on boundary voltage measurements Vbc V. Here, we are particularly interested in solving the difference EIT inverse problem; that is, we want to reconstruct the change in the conductivity, de, from the difference of two sets of voltage measurements,

[0089] AV = Vb - Fo

[0090] Equation 3 whereois a reference voltage set. Thus, we want to find the solution to the underdetermined system:

[0091] SAo « AV

[0092] Equation 4 where S represents the sensitivity matrix. This is an ill-posed problem that needs to be solved using regularization methods to obtain a meaningful solution. There two very standard reconstruction approaches were used to compare them against FA- and HA- DNN results: Tikhonov regularization and TSVD. Tikhonov regularization seeks the solution to the minimization problem:

[0093] Equation 5 where A > 0 is a regularization parameter and L is a regularization operator. Typical choices of L include the identity matrix and the discrete first or second derivative operators. In this work, the Tikhonov method implemented in EIDORS was employed with a fixed regularization parameter value of 0.01 for all the numerical experiments presented below [Adler & Lionheart, Physiological measurement, 27(5): S25, 2006],

[0094] On the other hand, the TSVD approximates the solution by retaining the most significant singular values of S and their corresponding singular vectors while limiting the effect of noise in the data. That is, the TSVD solution is defined by:

[0095] Equation 6 represents the Moore-Penrose pseudoinverse of a matrix, retaining only k singular values or singular values smaller than certain tolerance. For testing TSVD, the implementation provided by EIDORS was also used. Because the solutions to both forward and inverse EIT problems depend on the system’s configuration, disclosed herein are the two configurations in detail.

[0096] Full- and hemiarray electrode configurations: the electrodes in the full-array and hemiarray configurations are arranged around a circular boundary, as shown in FIGs. 1A- 1B. The full-array has 16 electrodes spaced by 22.5° each, while the hemiarray has only 8 electrodes with the same spacing except for the 8thand 1stelectrodes, which are separated by 202.5°. The mesh used in the study was a "c2C" pattern, which is a 2D circular model with 576 elements from EIDORS. The test data was generated with a different mesh (EIDORS "d2C" mesh) to avoid an inverse crime.

[0097] Both array types use an adjacent current injection pattern, where electrical current is applied between adjacent electrodes (such as 1 and 2), and resulting voltage differences are measured between adjacent electrodes (such as 3-4, 5-6,..., 15-16). These voltage differences make up the boundary voltage vector Vb(see FIGs. 2A-2B & FIG. 3A). The injection pattern cycles through all possible pairs of adjacent electrodes, resulting in 16 • 13 = 208 voltage measurements for the full-array and 8 • 5 = 40 for the hemiarray. Note that for the hemiarray configuration, the 1stand 8thelectrodes are considered adjacent.

[0098] FIGs. 1A-1B are a set of diagrams depicting exemplary training mesh and electrode layouts for the hemiarray (FIG. IB) and full-array (FIG. 1 A) configurations for a system and method of noninvasively monitoring electrical properties within the body according to aspects of the present invention. It should be noted that in this exemplary hemiarray arrangement, the electrodes cover less than half of the circumference.

[0099] Full-array DNN: deep neural networks (DNNs) can make accurate predictions of the conductivity distribution [Adler et al., Physiological measurement, 30(6): S35, 2009], However, training DNNs can be challenging, as they have complications that are not present in traditional EIT algorithms.

[0100] One issue is the need for large amounts of training data. To train a DNN, it must be provided with a large dataset of voltage measurements and corresponding conductivity distributions. Training data can be generated using the forward problem, which calculates voltage measurements based on a discretized conductivity distribution. Once a sufficient dataset has been created, the DNN can be trained to predict the conductivity distribution based on the voltage measurements using a process called backpropagation [Paul J Werbos, Proceedings of the IEEE, 78(10): 1550-1560, 1990],

[0101] Another complication is the risk of overfitting, which is a common problem with DNNs. To mitigate this risk, methods like dropout, weight decay, and stacked sparse autoencoder-based greedy -lay er- wise pretraining may be employed [Goodfellow et al., Deep learning. MIT press, 2016], Dropout involves randomly removing nodes from the hidden and input layers of the DNN during training to prevent the network from becoming too reliant on any particular node. Weight decay is a technique to regularize a neural network by adding a penalty term to the loss function. The penalty term is weightbased and prevents overfitting by encouraging weights with low predictive values to approach zero. Weight decay is analogous to Tikhonov regularization.

[0102] Greedy layer-wise pretraining is an unsupervised learning technique used to identify the weights of a neural network that can optimally encode valuable information from the input data into a lower-dimensional representation while disregarding noise and correlations [Goodfellow et al., Deep learning. MIT press, 2016; Hinton & Salakhutdinov, Science, 313(5786):504-507, 2006], This is often done using a type of neural network called a stacked autoencoder, which consists of multiple layers of autoencoders stacked on each other. Each autoencoder is trained to reconstruct its input data and consists of an encoder and a decoder [Hinton & Salakhutdinov, Science, 313(5786)504-507, 2006], The encoder maps the input data to a lower-dimensional representation, called the encoding, while the decoder maps the encoding back to the original input data.

[0103] Stacked autoencoders were constructed by stacking several autoencoders sequentially, where the encoding of one autoencoder was fed as input to the next [Hinton & Salakhutdinov, Science, 313(5786)504-507, 2006; Vincent et al., Journal of machine learning research, 11(12), 2010], The first layer of the stacked autoencoder corresponded to the boundary voltage, and subsequent layers encoded increasingly abstract and compressed representations of it. The trained stacked autoencoders provided a method to obtain a lower-dimensional representation of the boundary voltage, which can then be used to initialize the weights of a DNN. Pretraining becomes increasingly necessary as more layers are added to a network because the gradient receives less information from the loss function as the number of layers to backpropagate increases. Consequently, the weights in the first few layers of the network may remain relatively unchanged. Pretraining can provide appropriate initial weights to help address this issue and enable the network to achieve good performance with less training, which reduces the risk of overfitting by preventing the network from becoming too familiar with the training data set.

[0104] FIG. 2A and FIG. 2B are diagrams depicting an exemplary voltage gathering process and exemplary network topology for the full-array configuration according to aspects of the present invention. FIG. 2A is a diagram for an exemplary voltage gathering process displaying how the full-array gathers boundary voltage measurements by injecting adjacent electrodes with current, producing 208 boundary voltage measurements. FIG. 2B is a diagram of exemplary network topology for the full-array showing that as seen from the network’s topology, the boundary voltage measurements are used to reconstruct a discretized internal conductivity distribution with 576 elements.

[0105] Training process, DNN topology: the network comprises three hidden layers with a series of fully connected layers, each containing 50 nodes (see FIGs. 2A-2B). The logistic sigmoid function was used as the activation function for all layers. This activation function was chosen for its ability to produce a smooth gradient and sharp edges that resemble the unit step function, depending on the weights used. These sharp edges can be useful for identifying anomalies’ exact geometries, creating more detailed edge detection. The input layer comprises the 208 boundary voltage measurements, and the output was the conductivity of the 576 pixels in the mesh, as depicted in FIGs. 1A-1B. The loss was calculated using mean squared error throughout the training process.

[0106] Equation 7 where dcr represents the true values, Aa represents the predicted values, and N is the sample size. FIG. 3 A and FIG. 3B are diagrams depicting an exemplary voltage gathering process and exemplary network topology for the hemiarray configuration according to aspects of the present invention. FIG. 3A is a diagram of an exemplary voltage gathering process displaying how the boundary voltage measurements are collected using the adj cent current injection pattern. In the hemiarray, the 1st and 8th electrodes are adjacent, producing 40 boundary voltage measurements. FIG. 3B is a diagram of exemplary network topology displaying that the hemiarray network, except for its input layer, shared the same topology as the full-array configuration. The hemiarray input layer was not a perfect subset of the full-array, as it contained the connection between the 1st and 8th electrode that was not present in the full-array. The diagram highlights some of the unique connections of the hemiarray in green.

[0107] Training data: training data was simulated using the EIDORS forward problem solver. This process involved defining Electrical Impedance Maps (EIMs) or discretized conductivity distributions and then using the forward solver to calculate the corresponding boundary voltages. For an exemplary training set, the conductivity mesh shown in FIGs. 1A-1B was used, and EIMs were generated with one to three disk-shaped or square anomalies of varying size, position, and conductivity within the mesh. Specifically, anomalies with random relative radii between 0.1 and 0.3 were used (boundary has radius 1), and conductivities were randomly chosen between 0 and 2 S / m (in a background of 1 S / m). Each anomaly position was also chosen at random. To accurately represent the problem for training, 12,000 EIM samples were generated.

[0108] Pretraining phase (unsupervised): the stacked autoencoder was trained layer by layer. The first step comprised encoding the input boundary voltages into a smaller latent space. The latent space was then treated as input and encoded again, with this step being repeated twice due to the network having three layers. The training process used 200 epochs in batch sizes of 100 and employed a sparsity proportion of 0.5, which means that only 50% of the neurons on average (including input neurons) were activated during each iteration. This helped ensure that the nodes had independent information and reduced the risk of overfitting. The logistic sigmoid function was used as the activation function, and each layer was a linear combination of the previous layer. To further prevent overfitting, an L2 regularization term (weight decay) was included with a hyperparameter of 0.01. Lastly, the Adam optimization algorithm was employed to improve computational efficiency, using a specified learning rate of 0.001 [Kingma & Ba, arXiv preprint arXiv: 1412.6980, 2014],

[0109] Training phase (supervised): in the first phase of training, called the pretraining phase, the boundary voltage measurements were transformed into a smaller latent representation through an unsupervised process (stacked autoencoding). The second phase of the training process is called the training phase and involves two stages of supervised learning. In the first stage, a mapping was learned between the third hidden layer of the network and the conductivity distribution while keeping the weights learned in the pretraining phase fixed. This stage can be seen as a traditional logistic regression, where the inputs were the latent variables obtained from the third layer of the network, and the output was the conductivity distribution. The hyperparameters for this stage included 50 epochs, 500 batch size, 0.2 sparsity proportion, an L2hyperparameter with a value of 0.01, and a learning rate of 0.001, using the Adam optimizer.

[0110] In the second stage of the supervised phase, all weights in the network were finetuned, allowing them to vary based on the loss function. This stage was implemented to improve the model’s performance if there were any issues in the previous stages. The hyperparameters for this stage included 200 epochs, 100 batch size, 0.2 sparsity proportion, an L2hyperparameter with a value of 0.01, and a learning rate of 0.001, using the Adam optimizer.

[0111] Hemiarray training phase: the full-array EIT inverse problem is already highly ill- posed, and using a hemiarray configuration exacerbates this by reducing the amount of boundary data information. This makes pattern recognition more challenging and increases the likelihood of overfitting to idiosyncrasies or patterns in the training data that may not represent the broader problem. To address this issue, the fact that the full-array configuration entirely contained the HA configuration except for the adjacent connection between the first and eighth electrodes (see FIGs. 2A-2B & FIGs. 3A-3B) was used as an advantage. Next, the shared weights of the HA-DNN were initialized with the trained FA-DNN, transferring the knowledge learned from the FA-DNN and giving the HA- DNN a better baseline, making overfitting less likely. Additionally, it was expected that this initialization would help the networks use similar logic to solve the problem. However, as the HADNN has measurements not present in the FA-DNN, specifically the measurements produced by the connection between the first and eighth electrodes (FIGs. 3A-3B), another fine-tuning process was required. This process was expected to primarily affect the weights corresponding to the new connections the first and eighth electrodes created. However, all weights in the network may have experienced some change due to the FA-DNN’ s weights likely bias toward its training data. This fine-tuning process had a sparsity proportion of 0.2, an L2 hyperparameter of 0.01, a learning rate of 0.001, and a batch size of 100, and it was run for 75 epochs using the Adam optimizer.

[0112] Simulated Test Data: to ensure that the DNN was not overfitted and to avoid the possibility of the goodness of fit being the result of an inverse crime, all test data was generated using a different mesh ("d2C") provided by EIDORS, distinct from the one used for training ("c2C"). The data was generated for small anomalies with a relative radius of 0.2 and an anomaly conductivity of 2 S / m in a background medium of 1 S / m.

[0113] The anomalies were placed at 100 x 100 radial and angular locations for both full- and hemiarrays, using the d2c EIDORS mesh basis. Specifically, the region was divided into 100 sectors with an angle of 2TI / 100 radians. Within each sector, samples (e.g., 100 samples) were collected at various radial positions of the anomaly, ranging from 0 to 1 (the radius of the boundary), with increments of 0.01.

[0114] Phantom Tank Measurements: full- and hemiarray data was collected using a plastic or aluminum cylindrical anomaly placed inside a polycarbonate phantom tank. The tank had an elliptical cross-section and an approximate major / minor axis ratio of 30 cm / 26 cm). Electrodes were long stainless-steel strips (width 10 mm) that rested on the tank’s base, creating an approximately two-dimensional field pattern. The tank was filled to a height of around 2 cm with a ~ 1 S / m saline background solution. Data were acquired using a KHU2.5 16-electrode EIT system [Oh et al., Physiological measurement, 32(7):835, 2011], For full-array data, a frequency of 50 kHz and 16 averages was used for each sample. To obtain hemiarray data, the control sequence used for full-array data was modified to eliminate adjacent measurements made beyond the eighth electrode and added an extra measurement where the current was injected between electrodes 8 and 1. All voltage data was still obtained using adjacent measurements, which meant that voltage measurements between electrodes 8 and 1 were constructed by summing all adjacent differential voltages measured between electrodes 8 and 16 and 16-1 . The cylindrical metal and plastic anomalies had 27 and 29 mm diameters, respectively. Each data set consisted of 100 samples, approximately 50 before anomaly placement and 50 afterward. The first 40 samples in each data set were averaged to provide the reference measurements, and these were subtracted from the average of the last 40 samples in the data set to form dF for each case.

[0115] To estimate the position of each anomaly, photographs of each anomaly taken from above were used and employed simple image processing techniques. By applying edge detection matrices, the precise location of the anomalies were able to be identified. The distances (dx, dy) from the center of each anomaly to the origin were then calculated, considering the scale of the phantom tank. This provided the coordinates (x,y) for each anomaly, with an approximate error margin of ±1 cm.

[0116] Furthermore, due to the elliptical shape of the phantom tank, reconstructions onto the circular mesh were defined with a diameter equal to the major diameter of the ellipse (30 cm). The major diameter was chosen to ensure the circular mesh encompasses the entire ellipse. As a result, any anomaly placement within the phantom tank was guaranteed to fall within the boundaries of the circular mesh (see FIGs. 6A-6D).

[0117] GREIT Figure of Merit Evaluation: the GREIT figures of merit were calculated to evaluate and compare two-dimensional image reconstructions produced by the disclosed DNN against Tikhonov regularization and TSVD methods [Adler et al., Physiological measurement, 30(6):S35, 2009], The GREIT figures of merit were developed as a standard metric to evaluate 2D EIT reconstructions and are widely accepted by experts in the field [Adler et al., Physiological measurement, 30(6): S35, 2009], These figures of merit were chosen to evaluate key performance elements that experts agree should be included in a strong and effective EIT algorithm. These parameters were computed for each algorithm’s reconstructions of the test data using the GREIT performance metric algorithms available in the EIDORS software. Apart from using the GREIT figures of merit, using the quantity index (QI) was also considered to evaluate the performance of the disclosed algorithm. In this instance, QI measured the average conductivity (or resistivity) in the reconstructed image, calculated by summing the reconstructed conductivity or resistivity values multiplied by each pixel’s area or volume and dividing by the total reconstruction area. The difference between the QI in the reconstructed image and the true conductivity distribution should ideally be minimal, indicating an accurate representation of the reconstructed image’s total conductivity (or resistivity).

[0118] The GREIT figures of merit are summarized and defined herein. Amplitude response (AR) measures the ratio of image pixel amplitudes in the target to that in the reconstructed image. The AR of a reconstructed image should be constant for any target position. A constant AR is considered the most important figure of merit and directly relates to QI integrity. Position error (PE) measures the extent to which reconstructed images faithfully represent the position of the image target. The PE of a reconstructed image should be small and show minimal variability for targets at different radial positions. A small and constant PE is considered the second most important figure of merit. Ringing (RNG) measures whether reconstructed images show areas of opposite signs surrounding the main reconstructed target area. The RNG of a reconstructed image should be low and uniform. RNG is considered the third most important figure of merit. Shape deformation (SD) measures the fraction of the reconstructed one-fourth amplitude set, which does not fit within a circle of an equal area. The SD of a reconstructed image should be low and uniform. SD is considered the fifth most important figure of merit. Resolution (RES) measures the size of reconstructed targets as a fraction of the medium. The RES of a reconstructed image should be uniform and small to represent the shape of the target conductivity distribution more accurately. Uniformity of RES is considered the fourth most important figure of merit, while a small RES is considered less important (sixth most important figure of merit).

[0119] Disclosed herein is a discussion of how the models trained on simulated data performed in reconstructing simulated data and phantom data acquired using a tank with an elliptic cross section. GREIT metrics were used to assess results [Adler et al., Physiological measurement, 30(6):S35, 2009],

[0120] Each GREIT metric was calculated for reconstructions on disk-shaped meshes for simulated and phantom data. GREIT measures were calculated as a function of both radial and angular location, and the variance of each measure was indicated by shading a region of two standard errors about each average curve. Exact QI measures were overlaid on each QI plot. Phantom data was also reconstructed on circular and elliptic boundary meshes without adjusting training weights.

[0121] Full-array GREIT evaluation: all methods could reliably reconstruct the conductivity distribution using full-array data. FIG. 4 demonstrates that even when simulated data was calculated using a finer mesh, reconstructions accurately predicted the anomaly placement and contrast. However, both TSVD and Tikhonov reconstructions exhibited distinctive ringing patterns around each anomaly absent in the true conductivity and FA-DNN reconstructions.

[0122] FIG. 4 is a set of plots arranged in columns displaying the results of full- and hemiarray reconstructions of simulated data. The first column shows the true internal conductivity. The second, third, and fourth columns show the reconstructions produced by Tikhonov (TK), truncated singular value decomposition (TSVD), and the full-array deep neural network (FA-DNN), respectively, using the full-array configuration. Further, the fifth, sixth, and seventh columns show reconstructions produced by TK, TSVD, and the half-array deep neural network (HA-DNN), respectively, using the hemiarray configuration.

[0123] While visual inspection of the model’s predictions is useful, the GREIT figures of merit provided quantitative methods for better assessing and comparing model performance. The results of placing simulated conductive anomalies at multiple radial and angular locations and reconstructing them using each full array method are summarized in FIGs. 5A-5F and described herein.

[0124] AR: The reconstructions produced by all methods were consistent in terms of AR values. The FA-DNN reconstructions exhibited slightly higher variation for different DNN for hemiarray EIT reconstruction 13 angular and radial positions than Tikhonov and TSVD. FA-DNN AR values were slightly more variable than for TSVD. All AR values were close to one, independent of anomaly angle and radial position. However, Tikhonov reconstructions had AR values closer to 1 than TSVD and FA-DNN reconstructions.

[0125] PE: The FA-DNN outperformed both TSVD and Tikhonov, exhibiting values close to zero regardless of the angle of the anomaly or its radial position. TSVD PE values were most variable as a function of angular location, while variation as a function of angle was similar for both Tikhonov and FA-DNN methods.

[0126] RES: Again, the FA-DNN outperformed TSVD and Tikhonov, producing the smallest and most uniform output with an average value of 0.21 over all angular positions, compared to 0.25 for TSVD and 0.34 for Tikhonov. Variation of both Tikhonov and TSVD RES metrics as a function of angular position was similar, while FA-DNN variation was lowest.

[0127] SD: The FA-DNN had the smallest and most uniform SD, followed closely by Tikhonov, while TSVD performed significantly worse, with both larger SD and angular variability.

[0128] RNG: The FA-DNN prediction exhibited no ringing artifacts, while the Tikhonov method averaged around 0.25, and TSVD RNG values were close to 1, with TSVD RNG values being more variable as a function of angle.

[0129] QI: FA-DNN and Tikhonov provided consistent predictions of the total change in conductivity, as indicated by the black dotted line on the QI plot. At the same time, TSVD tended to underestimate actual QI values slightly. The variability of QI measures were similar for each reconstruction method.

[0130] Hemiarray GREIT evaluation: as expected, performance metrics for all reconstruction methods were inferior for the hemiarray configuration compared to the full-array. However, HA-DNN reconstructions outperformed both TSVD and Tikhonov reconstructions significantly, as evidenced in FIG. 4 showing GREIT figures of merit. Herein each figure of merit is summarized for hemiarray reconstructions:

[0131] AR: Compared to TSVD and Tikhonov, the HA-DNN demonstrated greater robustness to changes in anomaly placement, maintaining consistent AR values across all radial and angular positions. In contrast, TSVD and Tikhonov only yielded satisfactory results when anomalies were positioned on the same side as the hemiarray electrodes, resulting in subpar performance between [ ~]

[0132] PE: The HA-DNN prediction had low position error as the angle varied, and position error was uniformly low as the angle changed compared to TSVD and Tikhonov, RES: The resolution of TSVD and Tikhonov predictions were non-uniform and relatively large as the angle changed, whereas the HA-DNN prediction had some variability but was relatively small and uniform (see FIGs. 5A-5F), clearly outperforming TSVD and Tikhonov.

[0133] SD: The HA-DNN prediction was ideal, with small and uniform values, while TSVD and Tikhonov produced large variations and means.

[0134] RNG: The HA-DNN prediction had no ringing, while the TSVD and Tikhonov were both non-uniform and significant.

[0135] QI: TSVD and Tikhonov approximately predicted QI for the half of the interior where electrodes were present but underestimated it on the half where electrodes were absent ( )• Incontrast, HA-DNN produced accurate predictions for QI across all angular positions.

[0136] FIGs. 5A-5F are a set of plots displaying the average values of each figure of merit for reconstructing small conductive anomalies. FIGs. 5A-5C shows the results for a fullarray configuration. FIGs. 5D-5F shows the results for a hemiarray configuration. Bold lines indicate the mean value of each figure of merit for all radial positions at a given angle. Shaded regions show two standard errors (one-fifth standard deviation) above and below the mean value, indicating the models’ robustness to changes in anomaly radial positions. Quantity Index (QI) subplots have a black dashed line representing the normalized true QI at each angle. QI values are averages over the entire mesh in units of S / m.

[0137] Phantom data: tank data reconstructions were generated using the HA-DNN network weights found using simulated data from a disk-shaped mesh. Results for a set of both metal (top) and plastic (bottom) anomalies placed at a distance 0.5 of the radius towards the boundary at different angular (electrode) locations are shown in FIGs. 6A- 6D. The images show that reconstructions of the metal cylinder were similar to its actual size, and reconstructed amplitude was consistent across all locations regardless of whether they were in the right-hand half of the phantom containing the hemiarray electrodes. Reconstructions of plastic cylinder images were not as consistent as for the metal cylinder. FIGs. 6A-6D are a set of plots arranged in rows displaying the hemiarray reconstructions of internal conductivity based on actual voltage measurements, with the true placement of cylindrical anomalies superimposed. FIGs. 6A-6B show plots depicting metal anomalies. FIGs. 6C-6D show plots depicting plastic anomalies. Note that anomaly locations are described in terms of the electrode or angular location, i.e., anomaly ‘ 1 ’ is at the same angle as electrode 1, or 90°, and ‘7’ is at the angle of electrode 7 (225°). FIG. 6D further shows an exemplary electrical impedance tomography (EIT) device utilized to collect the data and a depiction of all anomalies within an elliptical boundary.

[0138] The GREIT parameters for HA-DNN reconstructions on the circular mesh are shown in FIGs. 7A-7B. As indicated by the reconstructed images, metal anomaly reconstructions generally performed better than plastic anomalies. However, AR was not uniform for the metal anomaly. Specifically, when the anomaly was positioned at the 14th electrode, the AR was higher than the other anomaly placements. The PE and RES values were higher than expected for the plastic anomalies.

[0139] The HA data was also reconstructed on an HA-DNN trained using weights derived using training data from an elliptic mesh with the same major / minor axis ratio as the real phantom. This produced more stable reconstructions than those found for the original disk-shaped mesh, as shown in FIGs. 8A-8D. Moreover, as expected, the QI response for the elliptical reconstructions was consistent as a function of angular position.

[0140] FIGs. 7A-7B are a set of plots showing a Graz consensus Reconstruction algorithm for EIT (GREIT) figure of merit metrics for DNN phantom data reconstructed on disk mesh. FIG. 7A is a plot corresponding to metal anomaly measures. FIG. 7B is a plot showing plastic anomaly values. QI values are averages over entire mesh in S / m.

[0141] FIGs. 8A-8D are a set of plots arranged in rows displaying the hemiarray reconstructions of internal conductivity based on phantom data, with the true placement of cylindrical anomalies superimposed. FIGs. 8A-8B are plots depicting metal anomalies. FIGs. 8C-8D are plots depicting plastic anomalies. FIG. 8D is an exemplary EIT device utilized to collect the data and a depiction of all anomalies within an elliptical boundary.

[0142] FIG. 9 is a plot displaying the QI expressed as average conductivity over mesh for elliptical reconstructions for each anomaly type. Disclosed herein is a summary of the findings addressing prospects for using these methods in vivo.

[0143] Li et al. (2019) demonstrated the effectiveness of deep neural networks in mapping boundary voltage to internal conductivity distribution using a full-array configuration [Li et al., Transactions of the Institute of Measurement and Control, 41(14):4035-4049, 2019], Their study compared DNN reconstructions with other models and found that DNN produced more accurate results with sharper separation, as measured by mean squared error. The disclosed findings support their conclusions and provide additional evidence.

[0144] It was observed that the full-array reconstructions across all algorithms allowed straightforward visual detection of the anomalies’ placement. However, the FA-DNN algorithm outperformed or achieved comparable results to FA-Tikhonov and FATSVD in all GREIT figures of merit, producing visually cleaner reconstructions with sharper separation between steep conductivity gradients. Importantly, unlike the other algorithms, the FA-DNN algorithm displayed less performance variability for different anomaly placements and did not exhibit ringing patterns around the anomalies. Thus, if only the anomaly’s location is important, all reconstruction methods are suitable. Nonetheless, the FA-DNN overall qualitatively outperformed the other reconstruction methods in representing the region surrounding the anomaly.

[0145] Although hemiarray reconstructions were expected to be worse than full-array counterparts due to the lower amount of available information and weaker signal -to-noise ratio, the HA-DNN algorithm demonstrated similar performance to full-array algorithms such as FA-Tikhonov and FA-TSVD, outperforming other hemiarray algorithms like HA-Tikhonov and HA-TSVD. The strength of HA-DNN lies in its ability to accurately reconstruct conductivity distributions throughout the entire system, as opposed to just near the electrodes like HA-Tikhonov and HA-TSVD.

[0146] However, despite its proficiency compared to other hemiarray algorithms, the HA-DNN’ s reconstruction quality fell short of the FA-DNN’ s. This is particularly evident when comparing the figures of merit of the two models, as the HA-DNN produces similar means to the FA-DNN but with greater stochasticity. This stochasticity is expected to some extent since the HA-DNN uses less information, making it more challenging for the network to differentiate between signal and noise.

[0147] Nonetheless, the HA-DNN showed impressive performance with synthetic data, particularly in reconstructing conductivity distributions that were not part of its training set and generated using a different mesh. However, it is crucial to emphasize that synthetic data is not the same as real-world data, and the true value of the DNN lies in its ability to reconstruct conductivity distributions found in actual scenarios. To address this, disclosed herein is the HA-DNN’ s reconstruction of conductivity data collected in a laboratory setting (FIGs. 6A-6D). In this experiment, the DNN’s performance was tested on two anomalies: a 29 mm diameter plastic object and a 27 mm diameter metal object. These anomalies were placed in seven locations within an elliptical boundary measuring 26 cm by 30 cm.

[0148] Although the reconstructions in FIGs. 6A-6D were not as accurate as those with synthetic data in FIGs. 4A-4C, they still provided a relatively clear indication of the anomaly’s location when placed on the side of the boundary with electrodes, with minimal blurring. That said, the HA-DNN’ s performance suffered when the anomaly was not positioned on the electrode side, resulting in increased blurring, particularly for the plastic anomaly, which has lower conductivity than the surrounding material (saltwater). The GREIT figures of merit for the plastic anomaly reconstructions exhibited higher PE and RES values than ideal but showed good AR, RNG, and SD. For the metal reconstructions, all metrics were decent, although the AR was less uniform than ideal.

[0149] Despite these shortcomings, the HA-DNN’ s performance was still remarkable, considering that it was trained with a circular boundary instead of the actual elliptical boundary used in data collection. As a result, perfect accuracy was not attainable for the DNN, given its assumption of a circular boundary. However, since the EIT phantom only slightly deviated from an ellipse, the minor discrepancies observed in the HA-DNN reconstructions were promising, further suggesting that the DNN was not overfitted. The impact of the misshapen boundary can be observed in FIGs. 8A-8D, which displays the reconstruction of a separate HA-DNN trained specifically on the elliptical boundary. This elliptical-trained HA-DNN showed reduced blurring and improved anomaly placement. Further research could explore the development of a DNN that takes the boundary shape as an input, making it more suitable for real-world applications where the boundary shape may vary.

[0150] Overall, the HA-DNN reconstructions demonstrated favorable characteristics such as good amplitude response, low position error, uniform resolution, minimal shape deformation, absence of ringing, and accurate total conductivity. However, it was not explicitly optimized for these specific GREIT figures of merit but rather for minimizing the mean squared error between the true and reconstructed data. Therefore, in some embodiments, the GREIT figures of merit may be incorporated into the neural network’s loss function, allowing the DNN to optimize for these desirable qualities. This could pose various challenges since the equations defining the figures of merit contain many discontinuities, whereas backpropagation, the learning optimization technique, requires differentiable loss functions. Nevertheless, there may be opportunities to create continuous approximations of these figures of merit for use in the loss function. The hemiarray configuration provides an example of an electrode topology that may be of use in measuring conductivity perturbations in conditions where a complete circumferential array cannot be conveniently applied; this has applications in trauma as well as applications in areas such as monitoring post-surgical bleeding or lung monitoring.

[0151] The disclosures of each and every patent, patent application, and publication cited herein are hereby each incorporated herein by reference in their entirety. While this invention has been disclosed with reference to specific embodiments, it is apparent that other embodiments and variations of this invention may be devised by others skilled in the art without departing from the true spirit and scope of the invention. The appended claims are intended to be construed to include all such embodiments and equivalent variations.

Claims

CLAIMSWhat is claimed is:

1. A method for using electrical impedance tomography (EIT) to reconstruct electrical property distributions in a patient with an electrode array, comprising: measuring electrode outputs from the electrode array configured to monitor an anatomical portion of the patient; mapping the electrical property distributions of the measured electrode outputs with a deep neural network (DNN), the DNN comprising computing code executed by at least one processor for providing the DNN, the processor communicatively connected to a providing apparatus of the EIT, and the computing code stored in at least one dedicated computing memory communicatively connected to the at least one processor and being configured to carry out the steps of: receiving, by the DNN, a plurality of boundary voltage inputs; weighting at least a portion of the plurality of boundary voltage inputs based on training of the DNN by comparing reconstructions of the electrical property distributions by the DNN for a plurality of samples, ones of which have randomly placed circular and square anomalies with various conductivities in the reconstructed electrical property distributions, to reconstructions for the plurality of samples provided by a second neural network (SNN) trained for a full array EIT; randomly assigning weighting in the training of the DNN for the remaining boundary voltage inputs of the plurality of boundary voltage inputs; reconstructing, by the DNN, the electrical property distributions received by the electrode array based on a pass of the electrode outputs through the DNN after training by the DNN of the receiving step, the weighting step, and the assigning step.

2. The method of claim 1, wherein the electrode array is selected from the group consisting of: a reduced-number electrode array, a standard-number electrode array, an electrode full-array, an electrode hemiarray, and an anterior region electrode hemiarray.

3. The method of claim 2, wherein the anatomical position is selected from the groupconsisting of: anterior, posterior, superior, inferior, lateral, medial, and combinations thereof.

4. The method of claim 3, wherein the electrode array is configured to any of a transverse configuration, a coronal configuration, a sagittal configuration, or combinations thereof.

5. The method of claim 4, further comprising applying current patterns to the electrode array.

6. The method of claim 5, wherein the current pattern comprises applying current between other electrodes in the array.

7. The method of claim 6, where the current pattern comprises an adjacent current injection pattern, wherein current is applied between adjacent electrodes in the array.

8. The method of claim 1, further comprising the step of finetuning the training of the DNN in one or more epochs of batches of 100 of the plurality of samples.

9. The method of claim 8, further comprising the step of checking for data overfitting using finer mesh filtering of outputs of the finetuning.

10. The method of claim 9, wherein the DNN and SNN each comprise a series of connected layers with one or more nodes in each layer, wherein the layers comprise input, hidden and output layers.

11. The method of claim 10, wherein the hidden layers comprise between 10 and 500 nodes.

12. The method of claim 10, wherein the hidden and output layers utilize one or more activation functions.

13. The method of claim 12, wherein the one or more activation functions are selected from: non-linear activation function, rectified linear unit (ReLU) activation function, hyperbolictangent (tanh) activation function, and logistic sigmoid activation function.

14. The method of claim 10, wherein the finetuning step comprises randomly removing nodes from at least one of the layers.

15. The method of claim 14, wherein the nodes are removed from the input and hidden layers.

16. The method of claim 1, wherein one or more learning techniques are applied to the networks selected from the group consisting of: unsupervised learning techniques, supervised learning techniques, L2 regularization, loss function penalty, weight decay, Tikhonov regularization, Greedy layer-wise pretraining, noise reduction, autoencoder stacking, data augmentation, dropout, and any combinations thereof.

17. The method of claim 1, wherein a portion of the plurality of voltage inputs are weighted.

18. The method of claim 17, wherein the plurality of voltage inputs comprises between 5 and 208 voltage inputs, and wherein between 5 and 100 voltage inputs are weighted.

19. The method of claim 8, wherein the step of finetuning the training of the DNN further comprises utilizing one or more evaluation metrics selected from the group consisting of: amplitude response (AR), position error (PE), resolution (RES), shape deformation (SD), ringing (RNG), quality index (QI), mean squared error (MSE), and any combinations thereof.

20. The method of claim 8, wherein the plurality of samples comprises at least 12,000 samples and the one or more epochs comprise 200 pretraining epochs and 50 finetuning epochs.

21. The method of claim 8, wherein the plurality of samples comprises between 100 and 100,000 samples, and the one or more epochs comprise between 8 and 800 epochs.

22. The method of claim 1, wherein the electrode array is an electrode hemiarray, and theSNN is configured to simulate an electrode full-array representation of the electrode hemiarray.

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