IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 64, NO. 4, APRIL 2017 807 High-Resolution Electrogastrogram: A Novel, Noninvasive Method for Determining Gastric Slow-Wave Direction and Speed Armen A. Gharibans∗, Student Member, IEEE, Sanggyun Kim∗, Member, IEEE, David C. Kunkel, and Todd P. Coleman, Senior Member, IEEE

Abstract—Despite its simplicity and noninvasiveness, amplitude of the signal increases after meal ingestion for normal the use of the electrogastrogram (EGG) remains limited subjects, reflecting a postprandial increase in the electromechan- in clinical practice for assessing gastric disorders. Recent ical activity of the [1]. EGG irregularities, including studies have characterized the occurrence of spatial gas- tric myoelectric abnormalities that are ignored by typical bradygastria, tachygastria, and concurrent loss of signal ampli- approaches relying on time-frequency analysis of single tude increase with meal ingestion, have been reported in patients channels. In this paper we present the high-resolution (HR) with and vomiting [2], dyspepsia [3], [4], EGG, which utilizes an array of electrodes to estimate the di- [5], and motion sickness [6]. rection and speed of gastric slow waves. The approach was There have been contradictory reports in the literature about verified on a forward model of the stom- ach, demonstrating that an accurate assessment of slow- the correlation between EGG parameters and abnormalities in wave propagation can be made. Furthermore, we tested the gastric emptying. Some investigations have reported no rela- methodology on eight healthy adults and calculated propa- tion [7], while others have reported a strong positive correlation ◦ ◦ gation directions (181 ± 29 ) and speeds (3.7 ± 0.5 mm/s) [8]. Overall, normal EGG does not assure normal gastric emp- that are consistent with serosal recordings of slow waves tying (sensitivity <50%), but an abnormal EGG may predict de- described in the literature. By overcoming the limitations of current methods, HR-EGG is a fully automated tool that may layed gastric emptying (specificity 78Ð92%) [9]. In other words, unveil new classes of gastric abnormalities. This could lead while subjects with an abnormal EGG typically have delayed to a better diagnosis of diseases and inspire novel drugs gastric emptying, there are patients with a normal EGG who can and therapies, ultimately improving clinical outcomes. still have slow emptying. This limitation is an important reason Index Terms—Electrophysiology, gastric myoelectric ac- why EGG has not been widely adopted clinically. tivity, medical signal processing, multichannel, slow waves, High-resolution electrical mapping during surgery has re- , stomach, wave propagation. cently been carried out to understand normal gastric slow-wave I. INTRODUCTION activity [10]. This technique involves positioning a spatially dense electrode array directly on the surface of the stomach to LECTROGASTROGRAPHY (EGG) is a noninvasive allow for the recording and reconstruction of patterns of electri- E technique for recording the gastric myoelectric activity cal activation [11]. The finding for normal subjects, in brief, was using electrodes placed cutaneously on the abdominal surface that the gastric slow waves originate in the pacemaker region overlaying the stomach. The simplicity and safety of EGG make of the corpus, quickly form circumferential bands around the it attractive for diagnosing abnormalities in gastric motility. stomach, propagate slowly in the axial direction, and eventually Spectral analysis of individual EGG channels have previously terminate in the pylorus. Due to the slow speed of propagation, been used to quantify anomalies. Normal EGG readings have multiple wavefronts typically exist on the stomach surface at traditionally been defined as demonstrating a 2Ð4 cycles/min any given time. frequency for at least 70% of the recording [1]. Moreover, the Using the same technique, the researchers also evaluated the gastric slow waves in subjects with gastroparesis [12] and Manuscript received March 13, 2016; revised May 5, 2016; accepted chronic unexplained nausea and vomiting [13] in order to de- June 7, 2016. Date of publication June 9, 2016; date of current version fine, quantify, and classify abnormalities with spatiotemporal March 17, 2017. This work was supported by the Ruth L. Kirschstein detail. They observed aberrant initiation and conduction of the National Research Service Award NIH/NHLBI T32 HL 105373. Asterisk indicates corresponding authors. slow waves, which occasionally led to premature termination ∗A. A. Gharibans is with the Department of Bioengineering, University and colliding wavefronts. The crucial finding was that half of of California, San Diego, CA 92093 USA (e-mail: [email protected]). the subjects exhibited spatial abnormalities that occurred at the ∗S. Kim is with the Department of Bioengineering, University of Cali- fornia, San Diego, CA 92093 USA (e-mail: [email protected]). normal 3 cpm frequency. This suggests that single channel EGG D. C. Kunkel is with the Department of Medicine, University of Califor- recordings are unable to detect such abnormalities. Results from nia, San Diego. a recent study [14] further emphasize this point by modeling T. P. Coleman is with the Department of Bioengineering, University of California, San Diego. both normal slow-wave propagation and a conduction block re- Digital Object Identifier 10.1109/TBME.2016.2579310 sulting in colliding wavefronts. It revealed that a single channel

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EGG recording on the abdominal surface would be unable to The Nyquist criterion for temporal sampling also applies detect the irregularity. to spatial sampling. The density and measurement area of the There have been attempts at extracting EGG spatial informa- electrodes dictate the highest spatial frequency that can be tion from multiple surface electrodes in the past [15], [16]. By detected without spatial aliasing. The electrode is an analog placing four electrodes along the axis of the stomach, the amount filter that eliminates spatial frequencies with wavelengths of frequency coupling between channels can be evaluated, with shorter than its measurement diameter [22]. This is due to the the notion that coupling between channels reflects normal wave fact that the electrode averages the potentials within the region propagation. This method, however, does not measure true wave that is in contact with the gel or measurement area. Consider propagation and therefore does not accurately estimate propa- an array of electrodes that has uniform center-to-center spacing gation velocity. Moreover, this approach is dependent on the d and electrode diameter D. Applying the Nyquist criterion placement of electrodes, particularly the reference. If the ref- to the edge-to-edge distance between neighboring electrodes erence electrode is positioned in a region with strong gastric results in the following constraint: signal, phase shifts will not be observed. Given the amount of λ d − D< min intersubject variability in stomach anatomy, standardizing elec- 2 (1) trode placement becomes challenging [17], [18]. λ In addition to the potentials recorded by surface electrodes where min is the shortest spatial wavelength of the signal [22]. in the EGG, the gastric electrical currents also produce a mag- The electrode spacing and measurement area is determined netic field that can be measured with a magnetometer, known as by a lower bound for the spatial wavelength of the cutaneous the magnetogastrogram (MGG). The relationship between the wave, which can be estimated by considering its slowest speed and highest frequency (λ = speed ). We assume that the slow- EGG and MGG is analogous to that of the electroencephalo- freq gram (EEG) and magnetoencephalogram utilized for studying est physiological serosal and cutaneous speeds are equivalent. the activity of the brain. The MGG has been used to detect After applying the appropriate values from the literature for gastric slow-wave frequency and propagation with promising healthy subjects (1.5 mm/s, 0.06 Hz) [10], the minimum spa- λ results [19], [20]. A key feasibility distinction between the two tial wavelength ( min) of the cutaneous wave is calculated to be modalities is that the MGG requires measuring the signal with 25 mm. Therefore, to ensure that no spatial aliasing occurs, the edge-to-edge distance between electrodes should be less than large, expensive equipment in a controlled environment, while λ min ) D the EGG has the potential for ambulatory monitoring [21]. 12.5 mm ( 2 . We chose an electrode diameter of 11 mm d Herein, we address the spatial limitations of the EGG by with a center-to-center spacing of 20 mm, which results in an presenting the high-resolution electrogastrogram (HR-EGG), a edge-to-edge distance of 9 mm to satisfy this condition. method for determining gastric slow-wave propagation direction and speed from an array of skin-mounted electrodes. B. Surface Laplacian Typically, biopotentials are recorded with a differential am- plifier, where the desired signal appears as a voltage between II. METHODOLOGY two input terminals. Differential amplifiers are able to reject the common mode signal from various sources of interference yield- A. Spatial Sampling ing improved signal quality. A consequence of this recording In order to accurately map the potentials on the abdominal scheme is that the local potentials are not accurately depicted. surface, the layout and size of the electrodes need to be consid- The surface Laplacian can provide a more realistic representa- ered. The abdominal surface potential is a continuous field that tion of local source distributions compared to conventional bipo- is discretely sampled at each electrode location. The recorded lar recordings by removing the effects of the reference electrode potentials are a smeared version of the current sources gener- and eliminating volume conducted signals from distant regions ated by the interstitial cells of Cajal on the stomach surface. [24]. The surface Laplacian has previously been applied for This is due to the conduction of the signal through the tissue ECG mapping to provide better spatial resolution and resolve (i.e., fat, muscle, and skin) separating the electrodes and the depolarizations in different regions of the [25]. The surface source. While volume conduction limits the spatial resolution Laplacian has also been shown to be more robust to ECG and of HR-EGG compared to serosal recordings, it makes it feasible respiratory interference when recording electri- to discretely sample the abdominal potentials. The separating cal activity [26]. tissue acts as a natural antialiasing spatial filter enabling ac- The surface Laplacian is the second spatial derivative of the curate sampling of the potentials with a reasonable number of surface potential estimated on the surface of a geometry that electrodes [22]. passes through the electrode locations. For a voltage Φ on a The discrete sampling of continuous time-series data has planar surface, it is defined by the expression: been well characterized [23]. The key concept is the Nyquist ∂2 Φ ∂2 Φ criterion, which states that for lossless digitization, the sam- ∇2 (Φ )= + . S S ∂x2 ∂y2 (2) pling rate should be at least twice the maximum frequency (i.e.,fs > 2fmax, where fs is the sampling rate and fmax is the A simple nearest-neighbor method of estimating the surface maximum frequency of the signal). Once a time series has been Laplacian of EEG data was first published in 1975 by Hjorth aliased, there is no signal processing technique that can recover [27]. This approach used a finite-difference approximation for the lost information. the second spatial derivative of the scalp potential by averaging GHARIBANS et al.: HR-EGG: A NOVEL, NONINVASIVE METHOD FOR DETERMINING GASTRIC SLOW-WAVE DIRECTION AND SPEED 809

Fig. 2. False positive rate of white Gaussian noise being classified with PGD greater than 0.5 as a function of minimum sustained wave duration. The different lines indicate independent simulations.

phase ϕ(x, y, t): V (x, y, t)+iHb [V (x, y, t)] = a (x, y, t) eiϕ(x,y,t). (4) Fig. 1. Schematic used to illustrate the eight neighboring electrodes that are used to calculate the finite-difference surface Laplacian. The In biological signals, contours of constant phase provide a P source activity is within a measurement area centered at electrode 0 . better approximation to the motion field compared to those of constant amplitude, since the amplitude of the signal is propor- potential differences between a central and four surrounding tional to the distance of the recording electrode to the source. electrode locations. Although there have been many advances Surfaces of constant phase satisfy the equation: since the first paper, the finite-difference approximation is prac- tical and easy to implement. ϕ (x, y, t)=c, c ∈ R. (5) The original method was improved by including eight elec- By assuming that the constant phase surfaces move along the trodes positioned radially with respect to the central electrode motion field, we can differentiate the phase with respect to time position [28]. Involving a larger number of electrodes improves using the total derivative: the possibility of obtaining a good approximation. Before aver- dϕ ∂ϕ aging, the potential difference is divided by the corresponding = ∇ϕ · v + =0 (6) electrode distance in order to represent the gradient. This is dt ∂t calculated using the following equation: where ∇ϕ is the spatial gradient of the instantaneous phase, dy v =(dx , ) is the wave velocity, and “·” represents the dot v0 = P0 − 0.15 (P1 + P2 + P3 + P4 ) dt dt product operator. Since the phase gradient is parallel to the − 0.1(P5 + P6 + P7 + P8 ) (3) velocity direction, the speed can be calculated as follows:   where, P0 is the potential measured at the central electrode, and ∂ϕ (t)=v (t) =   ∇ϕ P1 to P8 are the potentials measured at the radially neighboring speed  ∂t  (7) electrodes, as seen in Fig. 1. The weighting coefficient for each n of the surrounding electrodes is proportional to the reciprocal where for any z ∈ R , z represents the two-norm and z¯ in- of its distance to the center electrode. The method described by dicates the spatial average (i.e., across all electrodes) at a given (3) was used as a preprocessing step before the estimation of time. The wave direction is then computed by:   wave propagation. direction (t)=ang ∇ϕ (8) C. Wave Estimation where ang(·) is the elementwise arc tangent, choosing the quad- rant correctly. Motivated by a realistic, multiscale model of EGG [29], we A quantity called phase gradient directionality (PGD), is de- expected coherent spatial propagation of the surface potential in fined as a measure of how well the phase gradients align across healthy subjects. We implemented a technique originally devel- the array [31]: oped to compute the two-dimensional (2-D) component velocity   from image sequences [30] to estimate features of stomach wave PGD (t)=∇ϕ ∇ϕ. (9) propagation on the abdominal surface. By using a data-driven approach that evaluates the temporal evolution of constant phase PGD can take on values between 0 and 1, where 0 represents spatial contours, strong underlying assumptions are not made of phase gradients that are randomly distributed and a value of 1 the spatial properties of the cutaneous potentials. signifies perfect spatial alignment. Here, we provide the framework which forms the basis of the Estimates at time points when the PGD is less than 0.5 are algorithm. The Hilbert transform is first applied to the surface typically ignored, since velocity is only well defined when phase Laplacian estimate at each electrode location (x, y), resulting gradients are coherent across the array [31]. With a small num- in a characterization of instantaneous amplitude a(x, y, t) and ber of sensors, it is possible that the PGD can be greater than 0.5 810 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 64, NO. 4, APRIL 2017

Fig. 3. (a) Plot of stomach anatomy and electrode configuration used for the forward model. The black circles represent electrodes (5 × 5ar- ray). The blue line corresponds to the location of the 1-D serosal solution Fig. 4. Depiction of electrode configuration on the abdominal surface. 2 that is expanded to a 2-D mesh to match the stomach geometry. The Electrodes are disposable pregelled AgÐAgCl electrodes with 95 mm pacemaker (P), corpus (C), and antrum (A) regions of the stomach are measurement area and 2 cm center-to-center spacing. The middle of labeled. (b) Time snapshots over a 16 s period for the 1-D serosal solu- the array is selected as the reference and the ground electrode is placed tion are shown. The pulses are generated in the pacemaker (P) region, on the right hip bone. have a decreased speed and amplitude in the corpus (C) followed by an increase of both in the antrum (A), and eventually terminate in the pylorus. ensure the pulses were absorbed into the pylorus rather than by chance, even when a spatial wave does not exist. We gener- being reflected back into the stomach. The CourantÐFriedrichsÐ ated independent, identically distributed (i.i.d.) white Gaussian Lewy condition dictated the temporal step size to guarantee noise on a 3 × 3 sensor array across time (i.e., no spatial wave a converged finite-difference solution. We expanded the 1-D present) and evaluated the false positive rate of the PGD being serosal solution onto a 2-D mesh to match a realistic geometry greater than 0.5 by coincidence. Without an additional minimum of the stomach, using anatomical and physiological parameters duration constraint, up to a 50% of the samples would be con- described previously (see Fig. 3) [32]. sidered to be a wave (see Fig. 2). By further imposing criteria The cutaneous potentials are essentially a weighted summa- that the PGD must be above 0.5 for a certain duration of time, tion of the serosal slow wave at every time point. Due to the the likelihood of false positives can be drastically reduced. We electrical properties of physiological systems, a quasi-static as- defined a sustained wave as one having a PGD greater than 0.5 sumption can be made even though the sources are time varying for at least 2 s, since the false positive rate for noise with this [33]. By further assuming a volume that is linear, homogenous, ϕ (x,y,z) specification is near zero (see Fig. 2). Values of wave propaga- and isotropic, the potential at a field point due to a volume current source density Iv (x, y, z) is given by [34]: tion direction and speed in this paper are reported for instances  that meet these criteria. 1 Iv (x, y, z) ϕ (x,y,z)= dv (11) 4πσ˜ v r III. EXPERIMENTAL METHODS where, σ˜ is the conductivity and r is the Euclidean distance be- A. Model tween the source point and the field point. The primed variables refer to the points on the abdominal skin while the unprimed A forward electrophysiology model of stomach was used to variables correspond to those on the stomach surface. We chose validate the wave estimation methodology. For simplicity, we a conductivity of 0.125 S/m, which is halfway between the mean ignored circumferential propagation of the serosal slow wave conductivities of fat and the human trunk [33], the two primary and solved the following 1-D wave equation using a finite- constituents separating the stomach and skin. The distance r difference approach: depends on the stomach size and abdominal thickness, which 2 2 ∂ u 2 ∂ u was chosen to be 4 cm. The simulated cutaneous potentials were = c (x) (10) ∂t2 ∂x2 computed at locations that matched our experimental electrode layout (5 × 5 grid, 2 cm center-to-center electrode distance, where c(x) is the wave speed that depends on the location on the 2 stomach surface. Gaussian pulses with a width of 35 mm were 95 mm electrode measurement area). Fig. 3 depicts the stom- generated every 20 s (0.05 Hz) in the pacemaker region of the ach anatomy and its relation to the electrode configuration used stomach, as illustrated in Fig. 3. The pulse width, in addition to in the forward model. the modulations of its speed and amplitude along the organoaxial B. Experimental Protocol direction of the stomach, were chosen to be consistent with the most recent description in the literature for healthy subjects [10]. Ethical approval for this work was obtained from the institu- Both the speed and amplitude were highest in the pacemaker tional review board at the University of California, San Diego, region (6.0 mm/s, 0.57 mV), followed by a reduction in the USA. Eight healthy subjects (5 male, 3 female, age = 26 ± corpus (3.0 mm/s, 0.25 mV), and finally increased in the antrum 4 years, BMI = 22 ± 3) without gastrointestinal symptoms or (5.9 mm/s, 0.52 mV). Mur’s boundary condition was used to discomfort participated in the study. Subjects were asked to fast GHARIBANS et al.: HR-EGG: A NOVEL, NONINVASIVE METHOD FOR DETERMINING GASTRIC SLOW-WAVE DIRECTION AND SPEED 811

Fig. 6. Individual time snapshots of the voltages for a 20 s segment from Subject 1. Voltage is presented in whiteÐblue color (blue represent- ing positive voltage) and time (in seconds) is labeled above each plot. The snapshots are interpolated for visualization purposes. This particu- lar wave took approximately 20 s to propagate across the array at about 180◦ relative to the positive x-axis.

IV. RESULTS A. Simulated Data To determine if the surface Laplacian method alters the estimates of direction and speed, we generated signals us- Fig. 5. Results from a 60 s simulation of cutaneous potentials from the forward model on a 5 × 5array.(a) The voltage from three channels with ing a forward model with known parameters, as described in a dotted black line illustrating wave propagation. (b) Estimate of wave Section III. The signals were subtracted from the center elec- ◦ direction (mean: 187 ) and (c) speed (mean: 5.3 mm/s). (d) The PGD is trode to replicate the use of a reference electrode in the exper- above 0.9 throughout the simulation. imental recording. The surface Laplacian was then calculated and the output was used to verify that the wave-estimation al- gorithm can estimate the correct direction and speed. overnight prior to the recording. Any excess abdominal hair The simulation results are shown in Fig. 5. The voltages from was removed and the skin was prepped with NuPrep to reduce three simulated electrode sites from the horizontal axis illustrate electrode contact impedance. Conventional pregelled AgÐAgCl the wave propagation across the array. The wave estimation al- electrodes with a 95 mm2 measurement area were placed on the gorithm outputs direction, speed, and PGD for every time point abdominal surface using anatomical landmarks for consistency in the simulation, which is also displayed in Fig. 5. The aver- between subjects. The array was horizontally centered on the age estimated direction (187◦) and speed (5.3 mm/s) match the subject’s midline and the top row was positioned 5 cm below model parameters. PGD is greater than 0.9 for all the time points, the xiphoid. The electrodes were arranged in a 5 × 5 square indicating phase gradients with near perfect spatial alignment. grid with a 2 cm center-to-center electrode distance, as seen in Fig. 4. The middle electrode of the array was assigned as the B. Experimental Data reference and the ground electrode was placed on the right hip bone. The BrainProducts BrainAmp 32ch EEG amplifier was By generating a series of time snapshots, a sample wave can used to acquire the signals at a sampling rate of 250 Hz. The be visualized (Fig. 6). In the time window shown, the wave test meal was a 250 kcal nutrient bar (CLIF Bar: 5 g fat, 45 g originated on the right side of the array and propagated slowly carbohydrate, 10 g protein, 7 g fiber) along with 8 oz of room to the left at a speed of approximately 4 mm/s. The snapshots temperature water. The duration of the recording was 30 min display local potentials as calculated by the surface Laplacian, preprandial and 60 min postprandial. The subjects sat in a com- which are spatially interpolated for better visualization. The fortable recliner angled at 45◦ and were asked to limit talking amplitude of the signal was about 100 μV , as indicated by the and bodily movement throughout the recording. color bar. A two-minute segment of the surface Laplacian time series from three electrodes parallel to the wave propagation direction C. Data Preprocessing is displayed in Fig. 7. A phase delay between the electrodes Prior to wave estimation, the signals recorded from each elec- that is characteristic of wave propagation is indicated by a black trode were down-sampled to 5 Hz and then bidirectionally fil- dotted line. The output of the wave estimation algorithm is tered to avoid phase distortion using a finite-impulse response also displayed with a shared time axis. The instantaneous wave band-pass filter with pass-band frequencies between 0.015 and direction and speed estimates for sustained waves are displayed 0.15 Hz. The surface Laplacian was then calculated at each in blue, while time points not meeting the sustained wave criteria interior electrode location using (3). are red. Sustained waves are defined as having a PGD greater 812 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 64, NO. 4, APRIL 2017

Fig. 8. PGD as a function of frequency for the band-pass filtered data (bandwidth 0.04 Hz) from Subject 1. The star indicates the maximum PGD, which is at 0.05 Hz.

Fig. 7. (a) Voltages of three channels from a 120 s segment of data from Subject 1 data. Wave propagation observed by the phase delay between the channels is depicted by the black diagonal dotted line. A plot is shown of the (b) direction, (c) speed, and (d) PGD as computed by the wave estimation algorithm at every time point. A PGD threshold is used to detect sustained waves (above 0.5 for at least 2 s). Blue indicates a sustained wave while red is used for points that do not meet the criteria.

than 0.5 for at least two consecutive seconds. The waves in this two-minute window have a bearing of 180◦ relative to the positive x-axis at a speed of about 4 mm/s. Time points between subsequent slow waves typically had lower PGD values and did not meet the sustained wave criteria, indicated by the red dots Fig. 9. (a) Histogram of the PGD values from every time point through- out the recording for Subject 1. (b) The mean phase map, computed approximately every 20 s in Fig. 7. The data used to visualize using the instantaneous phase for time points meeting the sustained the wave propagation in Fig. 6 corresponds to the data from wave criteria. The white arrow indicates the propagation direction of the the 30Ð50 s interval in Fig. 7. Note that the start and end of waves based on the direction of the negative phase gradient. (c) Polar histogram showing the estimated direction of propagation for sustained a representative slow wave is observed at about 30 and 50 s, waves. (d) Histogram of the estimated speed for sustained waves. respectively. To quantitatively confirm that the gastric electrophysiology was the source for the coordinated spatial activity, we com- waves by spatially unwrapping the phase at each time point and puted the mean PGD as a function of frequency, as shown in then subtracting the phase value of a reference electrode at that Fig. 8. The plot was constructed by calculating the average PGD time prior to averaging (see Fig. 9(b)). The white arrow shows for the dataset after applying various band-pass filters (band- the direction of propagation, which is along the negative phase width = 0.04 Hz) that swept through a frequency range from gradient. Fig. 9(c) and (d) captures the variability in the wave 0.02 to 0.17 Hz. The peak PGD value in this case occurred at parameters throughout the recording. 0.05 Hz, which corresponds to the normal stomach slow-wave Wave propagation was observed in all eight of the subjects. frequency [1]. Summary statistics for the various wave parameters are shown in Histograms of wave direction, speed, and PGD reveal overall Table I. The mean wave direction and speed for all the subjects distributions of the wave propagation parameters for the entire were 181◦ ± 29◦ and 3.7 ± 0.5 mm/s, respectively. On average, recording (see Fig. 9). Only time points of direction and speed 41% of the time points met the sustained wave criteria. There during sustained waves were used to generate the histograms. were no statistically significant differences in slow-wave prop- For this particular subject, the waves propagated at 186◦ ± 27◦ agation between male and female subjects. To quantify that the (subject’s left to right) and 3.2 ± 0.9 mm/s throughout the record- observed wave phenomna were not be generated by noise, we ing. An average phase map was also computed for sustained designed the test statistic as the fraction of time that the PGD is GHARIBANS et al.: HR-EGG: A NOVEL, NONINVASIVE METHOD FOR DETERMINING GASTRIC SLOW-WAVE DIRECTION AND SPEED 813

TABLE I the reference electrode. Each current source contributes to the WAVE PROPAGATION AND EGG PARAMETERS ACROSS SUBJECTS signal based on its orientation, strength and electrical distance to the electrode. Two nearby electrodes record similar signals Subject Wave Direction Wave Speed Sustained % 2Ð4 cpm since they record the average activity in overlapping volumes (◦) (mm/s) Waves (%) of tissue. The surface Laplacian effectively reduces the volume 1 - M 186 ± 27 3.2 ± 0.9 53∗ 99.4 that each electrode averages, culminating in improved spatial ∗ 2 - F 156 ± 29 4.8 ± 1.6 57 100 resolution [24]. The surface Laplacian emphasizes superficial 3 - F 185 ± 40 3.4 ± 1.3 43∗ 98.9 4 - M 173 ± 35 3.6 ± 1.4 32∗ 98.9 localized sources, while suppressing deep sources along with 5 - M 182 ± 48 3.8 ± 1.6 34∗ 96.6 shallow sources that are widespread and coherent. This property ∗ 6 - F 131 ± 48 3.2 ± 1.3 33 96.6 allows us to detect accurate gastric slow-wave propagation from 7 - M 224 ± 44 4.0 ± 1.3 36∗ 98.9 8 - M 211 ± 35 3.9 ± 1.4 36∗ 100 the abdominal surface. Average 181 ± 29 3.7 ± 0.5 41 ± 10 98.7 ± 1.4 In this paper, we calculated the surface Laplacian using a finite-difference approach. Other surface Laplacian estimation ∗ < 10−4 . p-value methods have been developed for the brain that fit surface po- tential maps to spline functions [35] and incorporate more real- istic scalp surfaces using MRI [36]. We investigated the use of greater than 0.5 for 2 s or longer. With generation of i.i.d. white more sophisticated surface spline Laplacian derivations, but did Gaussian noise, we used a nonparametric bootstrapping method not observe any significant differences in the wave estimation to develop the distribution of the test statistic under the null parameters. Unlike the scalp, our electrode configuration for hypothesis. Examples of the false positive rate of i.i.d. white the stomach is fairly planar and therefore the finite-difference Gaussian noise are shown in Fig. 2. With this, we calculated a method was chosen for its simplicity. p-value using the histogram from the bootstrap, which was less Although our forward model had simulation parameters such than 10−4 for all subjects. as propagation speed and electrode location chosen to mimic the A commonly reported EGG metric, the percent of 2Ð4 cy- physiology and experimental recordings, it had several simplify- cles/min activity, is also shown in Table I. This value was ing assumptions. In particular, we applied a 2-D approximation calculated by generating a spectrogram (4 min windows, 75% of the stomach geometry and did not incorporate the ionic com- overlap) using the short-time Fourier transform of a single bipo- ponents of smooth muscle cells and the interstitial cells of Cajal. lar channel with the strongest gastric signal for each subject, Nonetheless, our findings verify that the wave speed and direc- and evaluating the percentage of time the dominant frequency tion can be accurately estimated, and that the surface Laplacian was within the 2Ð4 cpm range. A value over 70% is indicative does not distort the estimation of wave parameters. of a normal EGG, and all the subjects were above 95%. It is well established that the normal gastric slow-wave fre- quency in humans is between 0.04 and 0.06 Hz [1]. Selec- tively band-pass filtering the signal to narrow 0.04 Hz bands V. D ISCUSSION and sweeping across frequencies enabled us to confirm that the The optimal number and layout of the electrodes remains an peak wave detection occurred at 0.05 Hz. The average PGD was open question that deserves further attention. We note that strict used as a metric to identify when waves were present, since application of the Nyquist criterion requires aprioriknowledge a higher PGD indicates the presence of waves. The peak of of the spatial spectra along with the source distributions. Such the PGD spectrum occurred near 0.05 Hz for all subjects, con- information is not generally available, in part because knowl- firming that the stomach was the source of the detected wave edge of an adequate number of electrodes for the gastric signal propagation described in this manuscript. would first require oversampling of the potential distribution to Gastric contractions are initiated and coordinated by slow- determine the highest spatial frequencies present in the data. wave activity, and the results from this study generally agree There may be concern that propagation of the potential from with existing descriptions of human gastric motility. MRI the source to the electrode may lead to phase delays that distort studies of contraction wave propagation in healthy stomachs the estimated wave parameters. It has been shown that a quasi- have demonstrated a contractile displacement rate between static assumption can be made to describe the potential field in 1.8Ð2.7 mm/s [37]Ð[39]. Using invasive serosal electrical the human body [33]. Since the capacitive component of the measurements, O’Grady et al. observed a mean slow-wave tissue impedance is negligible in the frequency range of internal propagation speed of 8.0 mm/s in the pacemaker region, a drop bioelectric events, electromagnetic propagation effects can be to 3.0 mm/s in the corpus, followed by an increase to 5.7 mm/s neglected. This allows us to make true gastric slow-wave speed in the antrum for normal subjects [10]. The average speed estimates. recorded in our study was 3.7 ± 0.5 mm/s. The variability for The surface Laplacian is critical in resolving the reference each subject can be seen in Table I, with the distribution for issue and yielding local potentials that can be used to estimate a representative recording shown in Fig. 9(d). These results wave propagation. The signal recorded at an electrode position is suggest that the HR-EGG reflects slow-wave activity in both the a spatial average of the active current sources within the volume. corpus and antrum, which is where most spatial abnormalities The signal depends on several factors, including the volume have been detected during invasive recordings [12], [13]. Higher geometry and conduction properties, as well as the location of gastric slow-wave speeds of 7.4 mm/s were reported in a recent 814 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 64, NO. 4, APRIL 2017

MGG study for normal subjects [20]. Further investigations are with developments in analytical methods such as the HR-EGG, required to resolve the differences between these modalities. will enable improved unobtrusive quantification of the state of An important consideration is that the stomach is a three- the gastrointestinal system in health and disease. dimensional organ, and its angle of elevation relative to the plane of the electrode array may skew the results. Also, no VI. CONCLUSION obese (BMI > 30) subjects participated in this study. It is possible that a significant amount of fat tissue separating the In this manuscript, we outline a methodology for noninva- stomach and electrodes will present a challenge in detecting sive estimation of gastric slow-wave propagation called the HR- wave propagation. A future study that includes imaging and/or EGG. This approach builds on recent findings demonstrating modeling is required to determine how an individual’s stomach that gastric slow-wave spatial abnormalities can go undetected and torso anatomy affects the speed estimated from electrodes by traditional single channel recordings. Our proposed tech- placed on the abdominal surface. nique does not depend on the placement of the reference elec- The slow-wave direction estimates in our study were trode and is fully automated. For the first time, to our knowledge, consistent with the expected stomach orientation. Although we are able to generate estimates of slow-wave propagation di- there is a considerable amount of intersubject variability, the rection and speed at each time point using surface electrodes. stomach typically lies in the left superior quadrant, terminates Improved spatially detailed analysis of propagating gastric myo- across the median line and can descend below the plane of the electrical events will facilitate better understanding of the patho- umbilicus [40]. The average gastric slow-wave direction for our physiology of gastric dysrhythmias among patients with motility subjects was 181◦ ± 29◦, consistent with the aforementioned disorders. This in turn will create opportunity for interventions anatomical description. Nonetheless, a study with stomach to reduce gastric dysrhythmic activity and improve symptoms. localization relative to the electrodes can more quantitatively confirm that our direction estimates align with the principal REFERENCES stomach axis in normal subjects. [1] H.P.Parkmanet al., “Electrogastrography: A document prepared by the The slow-wave propagation was detected in both the fasting gastric section of the American motility society clinical GI motility testing and postprandial states for all the subjects in our study. There task force,” Neurogastroenterology Motility, vol. 15, no. 2, pp. 89Ð102, were no significant differences in the speed and direction of 2003. [2] H. Geldof et al., “Electrogastrographic study of gastric myoelectrical the waves in the two states. We chose a 250 kcal nutrient bar activity in patients with unexplained nausea and vomiting.” Gut, vol. 27, along with eight ounces of water since that is similar to the no. 7, pp. 799Ð808, 1986. standardized meal given with tests of gastric motor function. [3] B. Pfaffenbach et al., “Gastric dysrhythmias and delayed gastric emptying in patients with functional dyspepsia,” Digestive Diseases Sci., vol. 42, Further, investigation is necessary to determine the consequence no. 10, pp. 2094Ð2099, 1997. of test meals with different volume and composition on wave [4] G. Riezzo et al., “Gastric electrical activity and gastrointestinal hormones propagation parameters. in dyspeptic patients,” , vol. 63, no. 1, pp. 20Ð29, 2001. [5] R. J. Brzana et al., “Gastric myoelectrical activity in patients with gastric Traditional EGG spectral analysis relies on using large outlet obstruction and idiopathic gastroparesis,” Am. J. , windows of the recording (typically 4 min), due to the slow vol. 93, no. 10, pp. 1803Ð1809, 1998. nature of the signal. This can be limiting, since gastric electro- [6] S. Hu et al., “Motion sickness severity and physiological correlates dur- ing repeated exposures to a rotating ,” Aviation, Space, physiological abnormalities may occur at a shorter time scale. Environ. Med., 1991. Estimating the wave properties at every time sample, as shown [7]K.L.Kochet al., “Gastric emptying and gastric myoelectrical activity in Fig. 7, allows for the detection of instantaneous episodes in patients with diabetic gastroparesis: Effect of long-term domperidone treatment,” Am. J. Gastroenterology, vol. 84, no. 9, pp. 1069Ð1075, 1989. of abnormalities. Moreover, the methodology described in this [8] T. Abell et al., “Gastric electromechanical function and gastric emptying manuscript is fully automated and not susceptible to human in diabetic gastroparesis,” Eur. J. Gastroenterology Hepatology,vol.3, bias. The summary statistics for wave direction, wave speed no. 2, pp. 163Ð167, 1991. [9] M. Verhagen et al., “Pitfalls in the analysis of electrogastrographic record- and PGD in Table I demonstrate that the HR-EGG can be ings,” Gastroenterology, vol. 117, no. 2, pp. 453Ð460, 1999. used to estimate the gastric slow-waves properties for normal [10] G. O’Grady et al., “Origin and propagation of human gastric slow- subjects. Statistical signal processing, including state space wave activity defined by high-resolution mapping,” Am. J. Physiology- Gastrointestinal Physiology, vol. 299, no. 3, pp. G585ÐG592, 2010. models, can be used in the future to describe the dynamics of [11] P. Du et al., “High-resolution mapping of in vivo gastrointestinal slow wave propagation across time. wave activity using flexible printed circuit board electrodes: Methodology There appears to be a trend towards portable, noninvasive and validation,” Ann. Biomed. Eng., vol. 37, no. 4, pp. 839Ð846, 2009. [12] G. O’Grady et al., “Abnormal initiation and conduction of slow-wave systems that quantify gastrointestinal function, such as tech- activity in gastroparesis, defined by high-resolution electrical mapping,” nology to extract gastric motility information from finger Gastroenterology, vol. 143, no. 3, pp. 589Ð598, 2012. photoplethysmographic signals [41] and ingestible wire- [13] T. R. Angeli et al., “Loss of interstitial cells of cajal and patterns of gastric dysrhythmia in patients with chronic unexplained nausea and vomiting,” less motility capsules that measure whole gut transit times Gastroenterology, vol. 149, no. 1, pp. 6Ð66, 2015. [42]. Synergistic with this theme, there have been recent [14] M. Buist et al., “Multiscale modelling of human gastric electric activity: developments in demonstrating thin, flexible, and stretchable Can the electrogastrogram detect functional electrical uncoupling?” Exp. Physiology, vol. 91, no. 2, pp. 383Ð390, 2006. skin-mounted electronics that can measure a multitude of [15] J. D. Z. Chen et al., “Detection of gastric slow wave propagation from the electrophysiological signals [43], as well as developments in cutaneous electrogastrogram,” Am. J. Physiology-Gastrointestinal Liver improving reliability, latency, and cost associated with the Physiology, vol. 277, no. 2, pp. G424ÐG430, 1999. [16] Z. S. Wang et al., “Detection of gastric slow wave uncoupling from multi- microfabrication procedures needed to build such systems at channel electrogastrogram: Validations and applications,” Neurogastroen- scale [44]. The maturation of these technologies, in parallel terology Motility, vol. 15, no. 5, pp. 457Ð465, 2003. GHARIBANS et al.: HR-EGG: A NOVEL, NONINVASIVE METHOD FOR DETERMINING GASTRIC SLOW-WAVE DIRECTION AND SPEED 815

[17] F. Burdan et al., “Anatomical classification of the shape and topography of Armen A. Gharibans (S’12) received the B.S. the stomach,” Surgical Radiologic Anatomy, vol. 34, no. 2, pp. 171Ð178, and the M.S. degrees both in mechanical en- 2012. gineering from the University of California, San [18] L. K. Cheng et al., “Anatomically realistic multiscale models of normal Diego, CA, USA, and from the University of Illi- and abnormal gastrointestinal electrical activity,” World J. Gastroenterol- nois, Urbana-Champaign, Urbana, IL, USA, in ogy, vol. 13, no. 9, pp. 1378Ð1383, 2007. 2009 and 2011, respectively. [19] L. A. Bradshaw et al., “Surface current density mapping for identification He is currently working toward the Ph.D. de- of gastric slow wave propagation,” IEEE Trans. Biomed. Eng., vol. 56, gree in bioengineering at the University of Cali- no. 8, pp. 2131Ð2139, Aug. 2009. fornia, San Diego. His research interests include [20] L. A. Bradshaw et al., “Diabetic gastroparesis alters the biomagnetic sig- modeling and statistical signal processing of bi- nature of the gastric slow wave,” Neurogastroenterology Motility, vol. 28, ological signals with a focus in gastroenterology. no. 6, pp. 837Ð848, 2016. [21] G. Lindberg et al., “24-hour ambulatory electrogastrography in healthy volunteers,” Scandinavian J. Gastroenterology, vol. 31, no. 7, pp. 658Ð664, 1996. [22] P. L. Nunez and R. Srinivasan, Electric Fields of the Brain: The Neuro- Sanggyun Kim (S.02ÐM.09) received the Ph.D. physics of EEG. New York, NY, USA: Oxford Univ. Press, 2006. degree in electrical engineering and computer [23] J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurement science from the Korea Advanced Institute of Procedures. New York, NY, USA: Wiley, 2011, vol. 729. Science and Technology, Daejeon, Korea, in [24] P. L. Nunez and K. L. Pilgreen, “The spline-Laplacian in clinical neu- 2008. rophysiology: A method to improve EEG spatial resolution.” J. Clinical He joined the Statistical Learning for Sig- Neurophysiology, vol. 8, no. 4, pp. 397Ð413, 1991. nal Processing Laboratory in EECS at KAIST in [25] B. He and R. J. Cohen, “Body surface Laplacian ECG mapping,” IEEE 2001. From January 2009 to June 2010, he was Trans. Biomed. Eng., vol. 39, no. 11, pp. 1179Ð1191, Nov. 1992. a Postdoctoral Researcher in the Department [26] J. Garcia-Casado et al., “Enhancement of noninvasive recording of elec- of Brain and Cognitive Sciences at the Mas- troenterogram by means of a flexible array of concentric ring electrodes,” sachusetts Institute of Technology (MIT), Cam- Ann. Biomed. Eng., vol. 42, no. 3, pp. 651Ð660, 2013. bridge, MA, USA. [27] B. Hjorth, “An on-line transformation of EEG scalp potentials into orthog- Dr. Kim is currently an Assistant Project Scientist in bioengineering onal source derivations,” Clinical Neurophysiol- at the University of California, San Diego. His research interests include ogy, vol. 39, no. 5, pp. 526Ð530, 1975. data science, machine learning, and statistical signal processing with [28] B. Hjorth, “Source derivation simplifies topographical EEG interpreta- applications to neuroscience and healthcare data. tion,” Am. J. EEG Technol., vol. 20, no. 3, pp. 121Ð132, 1980. [29] P. Du et al., “A multiscale model of the electrophysiological basis of the human electrogastrogram,” Biophysical J., vol. 99, no. 9, pp. 2784Ð2792, 2010. [30] D. J. Fleet and A. D. Jepson, “Computation of component image veloc- David C. Kunkel received the B.S. and M.D. ity from local phase information,” Int. J. Comput. Vision, vol. 5, no. 1, degrees from the University of New Mexico in pp. 77Ð104, 1990. Albuquerque, NM, USA, in 2003 and 2008, re- [31] D. Rubino et al., “Propagating waves mediate information transfer in the spectively. motor cortex,” Nature Neuroscience, vol. 9, no. 12, pp. 1549Ð1557, 2006. He completed a one-year research fellowship [32] A. Pal et al., “Gastric flow and mixing studied using computer simula- at the National Institutes of Health. His internal tion,” Proc. Royal Soc. London B: Biological Sci., vol. 271, no. 1557, medicine residency was completed at Cedars- pp. 2587Ð2594, 2004. Sinai Medical Center, followed by a fellowship in [33] R. Plonsey, Bioelectric Phenomena. New York, NY, USA: Wiley, 1969. gastroenterology at the University of California, [34] J. I. E. Liang and J. D. Z. Chen, “What can be measured from surface elec- Los Angeles. trogastrography (computer simulations),” Digestive Diseases Sci., vol. 42, Dr. Kunkel is currently an Assistant Clinical no. 7, pp. 1331Ð1343, 1997. Professor in the Division of Gastroenterology and serves as the Asso- [35] F. Perrin et al., “Scalp current density mapping: Value and estimation from ciate Director of the GI Motility and Physiology Program at the University potential data,” IEEE Trans. Biomed. Eng., no. 4, pp. 283Ð288, Apr. 1987. of California, San Diego. His research interests include gastroparesis, [36] F. Babiloni et al., “Spline Laplacian estimate of EEG potentials over short bowel syndrome, innovations in biofeedback therapy and irritable a realistic magnetic resonance-constructed scalp surface model,” Elec- bowel syndrome. He is a Member of the American Neurogastroenterol- troencephalography Clinical Neurophysiology, vol. 98, no. 4, pp. 363Ð ogy and Motility Society, the American Gastroenterological Association, 373, 1996. and the American College of Gastroenterology. [37] M. A. Kwiatek et al., “Quantification of distal antral contractile motility in healthy human stomach with magnetic resonance imaging,” J. Magn. Resonance Imag., vol. 24, no. 5, pp. 1101Ð1109, 2006. [38] K. Schulze, “Imaging and modelling of digestion in the stomach and the ,” Neurogastroenterology Motility, vol. 18, no. 3, pp. 172Ð183, Todd P. Coleman (S’01–M’05–SM’11) received 2006. the Ph.D. degree in electrical engineering from [39] L. Marciani, “Assessment of gastrointestinal motor functions by MRI: A the Massachusetts Institute of Technology(MIT), comprehensive review,” Neurogastroenterology Motility, vol. 23, no. 5, Cambridge, MA, USA, in 2005. pp. 399Ð407, 2011. He was a Postdoctoral Scholar in neuro- [40] F. H. Netter, Atlas of Human Anatomy. New York, NY, USA: Elsevier science at MIT and Massachusetts General Health Sciences, 2010. Hospital (MGH) during the 2005Ð2006 academic [41] S. M. Yacin et al., “On noninvasive measurement of gastric motility from year. He was an Assistant Professor in Electri- finger photoplethysmographic signal,” Ann. Biomedical Eng., vol. 38, cal and Computer Engineering as well as Neu- no. 12, pp. 3744Ð3755, 2010. roscience at the University of Illinois, Urbana- [42] B. Kuo et al., “Comparison of gastric emptying of a nondigestible capsule Champaign (UIUC) from 2006 to 2011. to a radio-labelled meal in healthy and gastroparetic subjects,” Alimentary Dr. Coleman is currently an Associate Professor in bioengineering, the Pharmacology Therapeutics, vol. 27, no. 2, pp. 186Ð196, 2008. Principal Investigator of the Neural Interaction Laboratory, and the co- [43] D. Kim et al., “Epidermal electronics,” Science, vol. 333, no. 6044, Director of the Center for Perinatal Health at the University of California, pp. 838Ð843, 2011. San Diego. His research is highly interdisciplinary and lies at the inter- [44] D. Y. Kang et al., “Scalable microfabrication procedures for adhesive- section of bio-electronics, neuroscience, medicine, and applied mathe- integrated flexible and stretchable electronic sensors,” Sensors, vol. 15, matics. He was named a Gilbreth Lecturer for the National Academy of no. 9, pp. 23 459Ð23 476, 2015. Engineering in 2015.