Three-dimensional electrical impedance tomography (EIT) to study regional ventilation/perfusion (V/ Q̇ ) ratios in anesthetized pigs

This study aimed to develop a 3D method for assessing V/ Q̇ ratios in a pig model of hemodynamic perturbations using electrical impedance tomography (EIT). In order to evaluate whether the physiological coherence of changes in EIT-derived V/ Q̇ ratios, global EIT-derived V/ Q̇ mismatch were compared with global gold-standards. The study found regional heterogeneity in the distribution of V/ Q̇ ratios in both the ventrodorsal and craniocaudal directions. Although global EIT-derived indices of V/ Q̇ mismatch consistently underestimated both low and high V/ Q̇ mismatch compared to global gold standards, the direction of the change was similar. We have made the software available at no cost for other researchers to use. Future studies should compare regional V/ Q̇ ratios determined by our method against other regional, high-resolution methods such as SPECT or PET scan.


Introduction
Critically ill patients often present with signi cant alterations in gas exchange, which can lead to lifethreatening respiratory failure.Regional matching of ventilation and perfusion (V/Q) is the key physiological event that ensures optimal gas exchange in the lungs 1 .Therefore, longitudinal evaluation of regional V/Q̇ matching to follow up disease progression and therapeutic interventions is clinically relevant.
Recently, electrical impedance tomography (EIT) has emerged as a non-invasive imaging technique for studying regional changes in ventilation and perfusion of the lungs [2][3][4][5][6] .Pulsatility-based methods have been described to evaluate lung perfusion; however, the validity of these methodologies have been challenged 7 .In contrast, the conductivity contrast bolus method, using most commonly a bolus of hypertonic saline during a respiratory hold, has shown good agreement with high-resolution techniques such as single-photon emission computed tomography (SPECT) or positron emission tomography (PET) 7,8 .By evaluating the pixel-wise change in impedance associated with ventilation and perfusion, studies have used 2D EIT to describe regional V/Q̇ ratios in different relevant lung pathologies such as pulmonary embolism or COVID-19 acute respiratory distress syndrome (ARDS) 5,6 .However, given the highly heterogeneous distribution of ventilation and perfusion, especially in pathologic conditions such as ARDS or chronic obstructive pulmonary disease, classical 2D EIT misses potentially key information about regional superior-to-inferior distribution of V/Q̇ ratios across the lungs.In projecting the 3D volume to the plane, single plane EIT introduces several artefacts 9 ; the sensitive region varies across the thorax, and out-of-plane conductivity changes are projected arti cially closer to the volume center.Thus, important information about the spatial distribution of V/Q̇ ratios may be lost.
Therefore, the present study aimed to develop a two-plane, 3D image reconstruction of regional V/Qṙ atios.Building on previous descriptions from our group describing the 3D EIT reconstruction approach, we adapted the current validated rst pass kinetics bolus approach to determine pulmonary blood ow and report the regional V/Q̇ in different regions of the lung in the craniocaudal axis in pigs.The novelty of our study lies in the fact that we report regional V/Q̇ matching in 3D, unlike previous reports that have used 2D EIT.In this article, we describe the methodology, and then evaluate the ability of the technique to track trend changes in global markers of V/Q̇ mismatch such as Q̇S/Q̇T and Bohr dead space (V D /V T,BOHR ).The results of our study may have important clinical implications for the longitudinal evaluation of regional V/Q̇ matching in critically ill patients at the bedside, and for the optimization of therapeutic interventions aimed at improving gas exchange in the lungs.

Methods
This study was conducted at Cornell University with Institutional Animal Care and Use Committee approval (protocol 2021-0016) Animal preparation, instrumentation, and monitoring Eight female, juvenile, purpose-bred Yorkshire cross pigs weighing 55 kg on average, were included in the study.All pigs were housed in group stalls and were acclimated at Institutional facilities for 5 days.
Animals were fasted from solid food overnight but had access to water.The morning of the experiment, pigs were sedated intramuscularly with detomidine 0.1 mg/kg (Orion Corporation, Kalamazoo, MI, USA), ketamine 10 mg/kg (Covetrus North America, Dublin, OH, USA), and midazolam 0.4 mg/kg (Almaject Inc., Morriston, NJ, USA).While providing ow by oxygen supplementation, a 22 G (Cardinal Health, Waukegan, IL, USA) auricular catheter was placed.Animals were shaved circumferentially around the thorax and topical saline solution (Nova-Tech Inc., Grand Island, NE, USA) and electrode gel (Spectra 360, Parker Laboratories, Inc., Fair eld, NJ, USA) were applied to improve electrode contact for the electrical impedance tomography (EIT) belt.A custom-made, 32 electrode EIT belt (2 x16 electrode arrangement) was placed over the shaved region and secured using wrapping material to improve electrode contact.
After anesthesia induction with 2-4 mg/kg propofol IV (Sagent Pharmaceuticals, Schaumburg, IL, USA) pigs were connected to an anesthesia machine with a mechanical ventilator (Fabius® Tiro, Draeger, PA, USA).Anesthesia was maintained with iso urane (Covertus North America, Dublin, OH, USA) in oxygen, targeting an end-tidal iso urane concentration between 1.5-2.0%and using a fraction of inspired oxygen (FiO 2 ) > 0.9 throughout the procedure.All pigs were placed in the supine position and ventilated in volume-controlled mode using the following settings: tidal volume 10 mL/kg, respiratory rate 12-20 bpm, to target an end-tidal partial pressure of CO 2 30-50 mmHg, and positive end-expiratory pressure (PEEP) of 5 cmH 2 O.The patient was connected to a pneumotachometer (NM3, Respironics, Philips, MA, USA) for spirometry monitoring and recording.Expired CO 2 and ow were recorded (KleisTek, for o ine calculation of global V D /V T,BOHR .Standard anesthetic monitoring was provided throughout the experiment.Plasma-Lyte (Baxter Healthcare Corporation, Deer eld, IL, USA) was infused throughout the experiment (2.5-5 mL/kg/hour).
Under ultrasound guidance (brand), a 7F introducer sheath (SafeSheath® II Introducer System, Pressure Products, WV, USA) was placed into the right external jugular vein.An 18 G catheter (Covidien, Mans eld, MA, USA) was placed on each femoral artery.Through the introducer sheath, a 6F Swan-Ganz catheter (Edwards Lifesciences, Irvine, CA, USA) was oated to the level of the pulmonary artery and placement was con rmed via characteristic pressure waveforms.

Study Phases
The study consisted of four phases: a) Baseline; b) Dobutamine infusion; c) Phenylephrine infusion, and; d) Controlled hemorrhage.A 15-minute equilibration period was implemented post-instrumentation to ensure pigs did not display any signi cant changes in physiological status under anesthesia prior to baseline data collection.Pigs were randomized into rst receiving a phenylephrine or dobutamine infusion.For all pigs, a phenylephrine (AuroMedics Pharma LLC, Windsor, NJ, USA) infusion was started at 0.5 mcg/kg/min and dobutamine (Hospira Inc., Lake Forest, IL, USA) infusion started at 2.5 mcg/kg/min IV during their individual study phases.A 30% increase from baseline mean arterial pressure (MAP), maintained for ve minutes, was the goal metric for each drug infusion.If target metric increases were not achieved, continued titration in two minute increments were implemented until target MAP was reached and maintained for ve minutes.If target MAP was reached, measurements were recorded.Between phenylephrine and dobutamine infusions, a 15-minute period of equilibration was instituted to allow drug elimination.All pigs were then hemorrhaged in a controlled fashion from one of the femoral artery catheters at a volume of 20 mL/kg over ve minutes.If the MAP decreased below 30 mmHg, hemorrhage ceased.At the end of the study pigs were humanely euthanized with sodium pentobarbital 15 mg/kg (Euthasol®, Virbac, TX, USA) IV after con rming an adequate plane of anesthesia.

Data Collection
At the end of each study period, data collection consisted of the following: vital and hemodynamic parameters, pneumotachometer parameters, EIT raw signals and cardiac output (CO) measurements.Vital and hemodynamic parameters included the following: heart rate, SpO 2 and invasive systemic and pulmonary arterial pressure.The following pneumotachometer measurements were recorded: V T , PEEP, PIP and ƒ R .Cardiac output (CO) was measured using the thermodilution technique by rapidly injecting 10 mL of chilled saline through the proximal port of the Swan-Ganz catheter.Measurements were done in triplicate and averaged for data analysis.Paired mixed venous and arterial blood samples were anaerobically drawn from the distal port of the pulmonary artery catheter and femoral artery, respectively, for blood gas measurements (iSTAT 1 Analyzer, Abaxis Inc., Union City, CA, USA) at baseline, end of rst drug, and completion of hemorrhage.At the end of the experiment one pig was taken to the CT scan to obtain a full thoracic image.The DICOM data was imported into specialized segmentation software (Mimics Research version 21, Leuven, Belgium) and thresholding masks were applied to segment the skeleton and lung tissue.The 'region grow' tool was used to select the airways.The mask for the lung category was manually split to remove any regions outside of the lung which may have been included based on the threshold values.The split mask tool was further applied to separate the region of interest of the lung from the remainder of the lung.The resulting models were exported in OBJ format, combined into a single le using Blender (www.blender.org)and uploaded to Sketchfab (www.sketchfab.com) for display (custom colors were applied using Sketchfab).EIT data acquisition is described below.

Electrical Impedance Tomography Data Acquisition
A custom-made belt comprised of 32 electrodes in a 2 x 16 electrode arrangement (Analyti.ca,Ottawa, Canada) was placed just caudal to the axillary region.EIT images were acquired using a skip 4 pattern in a square con guration 9 .Ventilation EIT data was recorded (Pioneer Set, SenTec, Therwil, Switzerland) for two minutes at a rate of 47.7 frames/sec for each study time.Pulmonary blood ow was studied by rapidly injecting 10 mL of hypertonic saline 7.2% into the lateral port of the introducer during an endexpiratory maneuver 7 .A dose of cisatracurium (Meitheal Pharmaceuticals, Chicago, IL, USA) was given if spontaneous breathing was observed before the measurement.Assisted ventilation was resumed thereafter.

Image reconstruction
To reconstruct EIT images a 3D model was created based on a full-thoracic CT-scan obtained from the rst pig immediately after euthanasia, at end-expiration (Supplementary Figure)

Data Processing
Ventilation images were generated from a 30 s recording of uninterrupted ventilation.All breaths were identi ed and ensemble averaged together to create a single representative breath representing ventilation over the entire recording.The difference in impedance was reconstructed between the end of expiration and end of inspiration of the representative breath.The ventilated volume was calculated for the 3 layers (Fig. 2).
To obtain perfusion images the technology described by Borges et al. (2012) was adapted to be used on 3D images.The perfusion image was generated by imaging the transit of a bolus through the lungs during apnea.After 10s of apnea, the hypertonic saline bolus was injected (Fig. 3).To isolate the component of the bolus that corresponded to perfusion, the bolus signal that passed through the heart was subtracted from the image.To subtract the change in impedance due to the contract agent passing through the heart, pixels that corresponded to both the heart and the lungs were identi ed manually 11 .
The tool used to aid in manual identi cation of heart and lung pixels can be seen in Fig. 4 and has been made open-access in the following link (https://sourceforge.net/p/eidors3d/code/HEAD/tree/trunk/dev/VQ_analyze/).The 3d_perfusion_tool software was written to work with Octave version 6 and is not tested with Octave version 7.
The heart pixel was used to identify a representative curve corresponding to the passage of blood through the heart.The rate of the bolus injection passing through the heart was approximated using a gamma function.Due to the spatial resolution limitations of EIT, some pixels in the image contained spatial information that corresponded to both the passage of the bolus through the heart and through the lungs 7 .To eliminate the signal related to the bolus travelling through the heart from all voxels in the 3D image, a gamma curve was t to the manually identi ed heart pixel to obtain the rate of ow for the bolus through the heart.This gamma function was then t to each voxel of the 3D image to identify and subtract the component of the signal corresponding to the passage of blood within the heart.The difference between the start of bolus injection and the peak amplitude of the gamma function t to the lung perfusion was reconstructed as the lung perfusion image.As with the ventilation image, three layers corresponding to posterior, intermediate and anterior planes were reconstructed (Fig. 4).

V/Q̇ mismatch calculation
The V/Q̇ mismatch was calculated using the difference between the 3D ventilation and perfusion distributions.To calculate the units of ventilation and perfusion measurements of tidal volume, respiratory rate, cardiac output and dead space were used.Units of ventilation were calculated for each voxel in the image using the following equation 6 : Where ΔZ (voxel) is the impedance change in a single voxel, ΔZ (total) is the total change in impedance, and V T * respiratory rate * (1-V D /V T,BOHR ) represents the total minute ventilation.
The perfusion for each voxel was calculated using the total CO (averaged from the triplicate) in liters per minute as shown in the equation below: The resulting voxel by voxel V/Q̇ was normalized using the total V/Q̇ ratio: Global markers of V/Q̇ mismatch.
Expiratory ow and mainstream capnography waveforms along with other respiratory variables were displayed (NM3 monitor; Respironics, PA, USA) and collected for further analysis on a personal computer at a sampling rate of 200 Hz (ICU Lab; KleisTEK Engineering, Italy).The V D /V T,BOHR was calculated o ine as: where PACO 2 = mean alveolar partial pressure of CO 2 , determined as the value located midpoint on the slope of phase III of the volumetric capnography waveform, and PECO 2 = mixed expired CO 2 12 .PECO 2 was determined as the fraction of mixed expired CO 2 (FECO 2 × barometric pressure) 13 .
Comparison of global EIT-derived V/Q̇ ratios and global markers of V/Q̇ mismatch We compared the global EIT-derived V D /V T and Q̇S/Q̇T against the V D /V T,BOHR calculated with volumetric capnography and the Q̇S/Q̇T calculated with the standard equation, respectively.At each study time, the voxel-wise V D /V T and Q̇S/Q̇T values of all regions were summed, to obtain a global EIT-derived V D /V T and Q̇S/Q̇T containing information about the total lung parenchyma included within the two-electrode planes.
For the dobutamine and phenylephrine phases, arterial and mixed venous blood gases were measured in 4 animals for each treatment, whereas blood gases were obtained during all hemorrhage steps.Therefore, global vs EIT-derived Q̇S/Q̇T was compared for a set of 4 animals during dobutamine and a different set of 4 animals during phenylephrine.Global Q̇S/Q̇T was compared with EIT-derived Q̇S/Q̇T in all animals during hemorrhage.Global EIT-derived V D /V T and V D /V T,BOHR were calculated in all animals at all study times.The performance of global EIT-derived V/Q̇ mismatch indices were evaluated with linear regression, Bland and Altman plots and four-quadrant plots.Differences in global measures of V/Qṁ ismatch indices between baseline and the treatment were analyzed with ANOVA for repeated measures.A p < 0.05 was considered signi cant.

Results
Regional Distribution of V/Q̇ ratios by 3D-EIT Figure 5 illustrates regional changes in V/Q̇ ratios during each study phase as observed in one representative pig.Heterogeneity in the distribution of V/Q̇ ratios is evident both in the ventrodorsal direction as well as the craniocaudal direction.Figure 6 shows the quanti cation of Q̇S/Q T,EIT and V D /V T,EIT .The fraction of Q̇S/Q T,EIT was higher in almost all treatments in dorsal compared to ventral regions, and in caudal compared to cranial regions.Overall, V D /V T,EIT was higher in ventral regions but there were no consistent craniocaudal differences.
Global Changes in V/Q̇ Mismatch using EIT and Gold-standard Methods Figure 7 shows the global Q̇S/Q T,EIT and V D /V T,EIT , and global Q̇S/Q T and V D /V T,BOHR changes during baseline and each of the treatments.Since blood gases for dobutamine were determined for different animals than during phenylephrine, baseline global Q̇S/Q T fractions are different for each treatment.
Global Q̇S/Q T,EIT and V D /V T,EIT consistently underestimated both global Q̇S/Q T and V D /V T,BOHR .Dobutamine signi cantly increased both global Q̇S/Q T,EIT and Q̇S/Q T , whereas hemorrhage reduced global Q̇S/Q T,EIT and Q̇S/Q T .Phenylephrine did not induce signi cant changes in Q̇S/Q T with either method.Hemorrhage signi cantly increased V D /V T with both methods, whereas dobutamine and phenylephrine did not induce signi cant changes.
Comparison Between Global Changes in V/Q̇ Mismatch using EIT and Gold-standard Methods There was a signi cant linear correlation between the global gold-standard Q̇S/Q T and Q̇S/Q T,EIT and between the global V D /V T,BOHR and V D /V T,EIT (Figure 8A and B).Bland and Altman plots showed signi cant underestimation of both extremes of V/Q̇ mismatch by EIT (Figure 8C and D), suggesting that the new method cannot be used interchangeably with the gold standard.However, concordance ratios showed a good trending ability of EIT for both Q̇S/Q T and V D /V T (Figure 8E and F).

Discussion
In this study, we developed a 3D method to assess V/Q̇ ratios in a pig model of hemodynamic perturbations.Our ndings reveal heterogeneity in the distribution of V/Q̇ ratios in both the ventrodorsal and craniocaudal directions.While the EIT-derived indices of V/Q̇ mismatch changed in a similar direction to gold standards, they consistently underestimated both Q̇S/Q̇T and V D /V T .This suggests that EIT cannot be used interchangeably with global gold standards.However, we found that the trending ability of EIT was satisfactory from a clinical perspective.It is worth noting that our study is not intended to replace the use of global gold standards for V/Q̇ mismatch analysis.Rather, we used global gold standards to ensure physiological coherence of our ndings as we were unable to compare regional EIT distribution of V/Q̇ ratios against a gold standard like SPECT.Our results are encouraging, and we suggest further re nement of our methodology for both research and clinical applications of 3D EIT.
Current methods such as SPECT or PET provide high spatiotemporal resolution for the evaluation of V/Qṙ atios mismatch.However, these methods are not applicable at the bedside, and most of them require the use of radiation 2,4,8 .EIT is an emerging, non-invasive bedside technique that has been validated for ventilation studies and more recently, perfusion studies.Borges et al. demonstrated that the rst-pass kinetics method outperformed the impedance pulsatility method for estimating perfusion in a piglet model of lung collapse 7 .Based on this nding, we decided to adapt this method for our algorithm.More recently, Bluth et al., using a swine model showed similar results when comparing the EIT-based perfusion method with positron emission tomography 8 .These studies have looked at ventilation and perfusion as separate entities; however, gas exchange depends on the ne regional balance between ventilation and perfusion 1 .Therefore, the combined relationship between ventilation and perfusion, the regional V/Qṁ atching, is clinically more relevant.The results of a recent study indicate that using EIT to calculate V/Qṁ ismatch can be useful in distinguishing between patients with pulmonary embolism (PE) and those without 5 .Another study in patients with COVID-19 ARDS showed that EIT-derived V/Q̇ ratios were useful to assess e cacy of recruitment strategies 6 .However, using 2D EIT for the study of V/Q̇ may lead to errors by attempting to project a 3D volume onto a 2D image 4 .Therefore, we developed our 3D method in an attempt to improve the methodology and to better describe heterogeneous lung pathologies.
For the present study, we leveraged our previously described methodology for 3D EIT ventilation image reconstruction using the Graz consensus reconstruction algorithm for EIT (GREIT) 9 , and develop recommendations for 3D placement of electrodes aimed at best imaging thoracic volume slices.For this, we built a custom two-electrode plane belt that allowed for inclusion of a signi cant portion of lung parenchyma, as shown on the supplementary le.Our results indicate signi cant heterogeneity of the regional distribution of V/Q̇ ratios, both on the craniocaudal and ventrodorsal axes.
To assess the validity of our 3D method, we examined the overall trend of our V/Q̇ ratios by comparing the total number of voxels with V/Q̇ ratios corresponding to Q̇S/Q̇T and those corresponding to V D /V T and compared them with gold standard measurements of global estimates of V/Q̇ mismatching.As expected, the accuracy of our method was low, as revealed by the Bland and Altman plots for both V/Qṁ ismatching extremes.Likely reasons for the low accuracy may include the use of thresholds to de ne our lung regions, which could have resulted in signi cant underestimation of both V/Q̇ extremes, and the fact that we only study a de ned region of the lung, excluding a portion of cranial and caudal parenchyma.Despite this, there was signi cant correlation between the EIT-method and the gold standards and the concordance rate was good, suggesting that in general our method was able to follow the true global change in V/Q̇ mismatch induced by the different interventions.
A signi cant increase in global Q̇S/Q̇T was detected by both methods during infusion of dobutamine, while hemorrhage resulted in a signi cant decrease in global Q̇S/Q̇T also detected by both methods.
The gamma function representing the passage of blood through the heart was t to each voxel in the image and subtracted to leave only the impedance change due to the bolus passage through the heart.
The perfusion image was reconstructed as the difference in impedance between the time of bolus injection and the maximum of the gamma function t to the lung perfusion.The reconstructed volume was again converted into 3 layers from posterior to anterior.
Perfusion images were generated from data collected during apnea following the injection of a conductive bolus agent.A custom software tool was used to identify pixels corresponding to the heart and lung signals.The identi ed pixels were used to t gamma functions corresponding to the passage of the bolus uid through the heart and lungs.
. The EIT reconstruction was done in EIDORS by extruding a 2D pig thorax boundary into a 3D model10 .The model is shown below in Fig.1.Two rows of electrodes were added to the 3D model according to the spacing from the electrode belt.To reconstruct the EIT images a 3D GREIT model was constructed consisting of 3 layers from cranial to caudal.The most caudal model layer was centered around the lower plane of electrodes (referred to as caudal layer), the central image layer was in the center of the two electrode planes (intermediate layer), and the most cranial model layer was centered on the upper row of electrodes (cranial layer).The resulting reconstructed image yielded 3 image planes corresponding to each of the electrode planes and one central plane.This resulted in a 3D image that was 32 by 32 by 3 pixels large.

Figure 1 A
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Figure 7 Global
Figure 7