The geometrical relationship between the human esophagus and left ventricle: Implications for three-dimensional ultrasonic scanning

Ultrasound in Med. & Biol., Vol. 20, No. 1, pp. I 1-20, 1994 Copyright © 1994 Elsevier Science Ltd Printed in the USA. All rights reserved 0301-5629/94 $6.00 + .00

Pergamon 0301-5629(94)E0002-T

OOriginal Contribution THE GEOMETRICAL RELATIONSHIP BETWEEN THE HUMAN ESOPHAGUS AND LEFT VENTRICLE: IMPLICATIONS FOR THREE-DIMENSIONAL ULTRASONIC SCANNING RAM B. HATANGADI, t G. BASHEIN, t$ J. DAVID GODWIN* and RoY W. MARTIN t$ ~Center for Bioengineering, *Department of Anesthesiology,and *Department of Radiology, University of Washington, Seattle, WA, USA (Received 24 February 1993; in final form 18 May 1993)

Abstract--To establish design parameters for a transesophageal ultrasonic probe to image the left ventricle (LV) in three dimensions, the geometrical relationship between the esophagus and the heart was studied in computed tomographic sections of ten humans. Points describing the esophageal centerpoint and the left-ventricular endocardium were digitized. Algorithms were developed to determine from any esophageal viewpoint the ranges of motion required to cover the LV with four modes of scanning; transverse oblique, longitudinal oblique, rotary and linear. Longitudinal oblique scanning was the only single-degree-of-freedom method that allowed complete imaging of the LV in all patients. However, for both conventional and threedimensional LV imaging, the most promising probe design appears to be a rotary scanning probe with an added degree of freedom to tilt the axis of rotation _+ 29 ° away from an axis perpendicular to the local esophageal axis.

Key Words: Esophagus, Heart-ventricle, Endocardium, Geometry, Algorithms, Ultrasonic scanning, Human, Adult, Models--theoretical, Three-dimensional imaging. adapted from flexible fiberoptic gastroscopes, and thus their design has not been optimized for TEE scanning. While the gastroscope-type controls can be used to maneuver the transducer and obtain different imaging planes, the hysteresis in the control cables prevents the operator from having precise information about the orientation of one plane relative to another. To overcome this limitation, we modified a TEE probe by adding a precision micromanipulator at the tip, allowing acquisition of images in a series of transversely oriented oblique planes having a known geometrical relationship between them (Martin et al. 1986). We have demonstrated the method of outlining the frames of images recorded with this probe and making three-dimensional numerical reconstructions of the left ventricular (LV) endocardium in vitro (Martin et al. 1990). Also, by selecting frames occurring at the same phase of the cardiac and respiratory cycles, we have successfully used these reconstructions to estimate LV stroke volume (Martin and Bashein 1989) and ejection fraction in dogs (Martin et al. 1989), and wall motion abnormalities in humans (Bashein et al. 1993).

INTRODUCTION AND LITERATURE

Since the invention in 1982 of a phased-array probe for ultrasonic imaging from the esophagus (Souquet et al. 1982), transesophageal echocardiography (TEE), has rapidly become an important imaging modality in clinical cardiology (Seward et al. 1992), patient monitoring (Shively and Schiller 1988) and clinical research (Clements and de-Bruijn 1987; Leung et al. 1990; London et al~ 1990). The advantages of TEE over its precordial counterpart include superior image quality, the ability to perform imaging readily during surgery and the availability of acoustical windows and viewpoints not obtainable from the chest wall. A less appreciated advantage of TEE is that the esophageal wall tends to hold the transducer probe in a stable position, allowing for images to be compared over time and giving rise to the possibility of acquiring spatially referenced images for numerically generating three-dimensional reconstructions of cardiac structures. The TEE probes in common use today have been Address correspondence to: Ram B. Hatangadi, Department of Anesthesiology, RN-10, University of Washington, Seattle, WA 98195, USA. 11

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Ultrasound in Medicineand Biology

These studies also revealed some limitations of this probe design. While we had been able to scan the entire LV consistently in dogs (once a surgical preparation had been made to eliminate the interference from the accessory lobe of the right lung (Bashein and Martin 1991), we could obtain complete short-axis scans in only about half of the humans studied. Two factors appear to be responsible: the limited range of motion of our probe and the 84 ° sector scan of the phased array. The micromanipulator was designed to have a range of motion of approximately 30 ° cephalic or caudal in reference to a plane perpendicular to the local axis of the esophagus (Martin et al. 1986). These specifications were based upon measurements made from lateral oblique x-ray images of patients whose esophagi were opacified by barium. However, our subsequent experience has shown that the _+ 30 ° range of motion is often not realized in practice, because acoustical contact with the esophageal wall is lost when the micromanipulator is nearly fully deflected. In addition, having only a transversely oriented imaging plane limits the available viewpoints and Doppler crossing angles that can be obtained. Other probe configurations have been reported that could provide a series of spatially referenced images for three-dimensional reconstruction. One of these uses a phased array that can be rotated continuously from transverse, through longitudinal, to a reversed transverse orientation, while maintaining the position of the tip of the probe (Flachskampf et al. 1991). This scanning method (hereafter designated as "rotary") will insonate a conical region of tissue with its apex located at the tip of the probe (see Fig 1C). Versions of this design have been made by at least two commercial manufacturers (Harui and Souquet 1985; Flachskampf et al. 1991) and one university research group (Roelandt et al. 1992). However, in these probes, the angular orientation of the phased array cannot be precisely determined due to backlash errors in the cables that rotate the array. This problem could be eliminated if the rotation sensor were located at the distal end of the probe rather than at the proximal end, and thereby allow for a direct recording of the array rotation. Another design that could be used for three-dimensional reconstruction uses a mechanism to stiffen the distal 20 cm of the probe and to move the transducer in an axial direction along the stiff segment, while acquiring a series of images in parallel planes (Wollschlager et al. 1989). While the acquisition of parallel-plane images is intuitively appealing for 3-D reconstruction, questions remain about the safety of this approach. Seeking an improved design for a probe to permit scanning the entire LV from the esophagi of patients

Volume20, Number 1, 1994 having differing cardiac size, orientation and body habitus, we needed to make calculations of the distances and angles over which these scanning methods would have to range in order to accomplish our objective. The limited literature on the geometrical relationship between the heart and esophagus (Crawfgrd et al. 1986; Drexler et al. 1990; Fujimoto et al. 1984; Jacobs et al. 1978) comes mostly from normal subjects and may not be representative of patients with heart disease. Furthermore, the cross sections shown in anatomic atlases may have been altered by postmortem changes. We therefore sought data obtained from x-ray computed tomography (CT). MATERIALS AND METHODS

Patient selection and data acquisition With institutional approval, we studied previously acquired CT images of ten adult patients. We chose patients having a range of body habitus and cardiac diseases. Coronal CT imaging planes separated by 0.8 cm and covering the entire heart were selected for analysis. The CT scans were not ECG gated. The images were assumed to represent an average chamber volume biased towards diastole. An experienced chest radiologist (JDG) marked the location of the LV endocardial border and the esophagus on each image. For each section, the planar coordinates of the center of the esophagus and approximately sixteen points representing the outline of the LV endocardium were located and entered into a personal computer with a digitizing tablet. The location of the planes containing the carina and the gastroesophageal junction were also noted. The locations of the carina and the gastroesophageal junctions were determined because they reflect the general range of esophageal locations from which LV imaging is possible. Scanning modalities To keep the probe design simple and reliable, it was considered desirable to try to make the precision scanning mechanism have only a single degree of freedom. Because the probe is confined by the esophageal wall, the number of possible single-degree-of-freedom scanning modalities is limited. Translational motion can occur only in the cephalic-caudal direction, while rotary motion can occur about the axis of the esophagus or in directions perpendicular to it. As in our earlier design, we planned to retain the lockable, but otherwise imprecise, gastroscope controls in order to facilitate maneuvering the probe into the optimal scanning position. Given the constraints imposed by the esophagus, the possible modes of scanning are: 1. Transverse oblique (Fig. 1A). Successive imaging

Esophagus/heartgeometry• R. B. HATANGADI et aL Ultrasoundfan

TEE probe

~/%'~PhasedArray ~" ,

TEE probe ,~ _L___ Y

~

13

Ultrasound fan PhasedArrav

! J

Axisof Longitudinalangle0 rotation (A)

Transverseangle

(B)

Axisof rotation TEE,probe

~

,

~

TEE probe

...Ultrasoundfan

g

Ultrasound fan

~ D

(c)

(D)

Fig. 1. Four modes of single-degree-of-freedom multiplanar scanning from the esophagus: (A) Transverse oblique, (B) Longitudinal oblique, (C) Rotary and (D) Linear. planes are acquired by rotating the ultrasonic fan about a fixed line passing through the origin of the ultrasonic sector, lying in the imaging plane, and being perpendicular to the midline of the sector. The axis also passes through and is oriented perpendicular to the local esophageal axis. This geometric configuration is similar to that used in our earlier probe (Martin et al. 1986). 2. Longitudinal oblique (Fig. IB). The transducer array was considered to be swept in a series of longitudinal planes with the local esophageal axis lying in the plane of the ultrasonic fan. Greenleaf et al. (1991) used a crude version of this approach by twisting the handle of a conventional biplane probe while imaging with its longitudinal array. 3. Rotary (Fig. 1C). The midline of the ultrasonic sector is considered to be fixed and oriented perpendicular to the local esophageal axis. The ultrasonic sector is then rotated about its own midline. Thus, the scan will insonate a conical volume of tissue (Flachskampf et al. 1991; Harui and Souquet 1985; Roelandt et al. 1992). 4. Linear (Fig. 1D). In this mode of imaging, the scanning is done in a series of coronal planes passing through each esophageal point. This geometry approximates the scanning method employed by Wollschlager et al. (1989) in that the scanning planes are mutually parallel.

Data analysis All of the digitized points were referenced with respect to a global Cartesian coordinate system whose

origin was located at the sternal notch of each subject, with the x-axis pointing toward the right shoulder, the z-axis toward the head, and the y-axis pointing anteriorly (see inset, Fig. 2). The hypothetical transducer probe was then considered to be moved in the esophagus so that the phased array was centered successively at the points representing the center of the esophagus in each CT section. For each of these positions in the esophagus, the geometrical relationship between the hypothetical phased array and the points representing the contour of the left ventricular endocardium was described in tenns of two angles, 0 and ~b, and a distance r. In order to compare patients with varying heights, the z-coordinate in each patient was normalized such that the sternal notch corresponded to a value zero and the gastroesophageal junction corresponded to a value one. The longitudinal angle 0 was defined as the angle between a vector M, joining the esophageal point and a discrete heart section point, and a vector parallel to the global z-axis, while the transverse angle 4~ was measured between the projection of vector M in a plane parallel to the x - y plane and a vector parallel to the x-axis (see Fig. 2). The distance r between an esophageal point and each heart section point was given by the magnitude of the vector M. For each of the scanning modes listed above, a simulated sweep of the entire LV cavity was performed in each patient, from all the discrete esophageal points between the carina and the gastroesophageal junction. In each case, the origin of the fan of the ultrasonic

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Ultrasound in Medicineand Biology

Volume20, Number 1, 1994

z ~[

~ ~

discrete points in the esophagus transverse phased array

Z

/ /

J ~

~

l i t h esophageal position e i _ distance r

J ~ ~

Y

~ .........

~

X Vector joining esophageal point and discrete heart section point

x Fig. 2. Global Cartesian coordinate system used to determine the limits of visibility for each mode of scanning. Inset shows the relationship of the coordinate axes to the body.

sector was considered to be located at the center of the esophagus in each CT section. An algorithm was developed to calculate the minimum range of angles 0 and th and distances r necessary to ensonify the entire LV for each type of scan in each patient. Details are given in the Appendix. For the transverse oblique mode of scanning, 0 represents the angle between the global z-axis and the plane of the electronic sector, while ~b represents the angle between the global z-axis and the projection of the path of the simulated ultrasound beam onto the x - y plane. For the longitudinal oblique mode of scanning, the roles of 0 and ~b are reversed. A second algorithm was employed for rotary scanning. For each candidate esophageal viewpoint, the axis of rotation of the hypothetical transducer was chosen to lie in the plane perpendicular to the local axis of the esophagus, and it was oriented in that plane so as to minimize the angle of the cone that was required to be able to sweep out the entire LV. Vectors were then constructed, joining each discrete LV point to the candidate esophageal viewpoint. The angles between these LV vectors and the vector representing the transducer rotation axis were then determined. The maximum angle thus obtained was taken to represent the half-angle of the cone for rotary scanning. The third algorithm, for linear scanning, was particularly simple because the ultrasonic imaging planes were identical to the CT planes. The maximum range and sector angle were determined for each section, and it was noted whether or not the entire LV could be scanned.

RESULTS The characteristics of the ten patients are given in Table 1. There were eight males and two females, ranging in age from 36 to 75 years and in body surface area from 1.35 to 2.17 m 2. Three patients had anatomically normal native hearts, two had mild cardiomegaly, four had dilated cardiomyopathy and one patient had a well-functioning transplanted heart.

Transverse oblique scanning Table 2 gives the results for transverse oblique scanning. For each patient, the optimal esophageal position for scanning was determined as the one from which the range of longitudinal angles 0 (Fig. 2) necessary to scan the LV was maximum, thereby bringing the transducer closer to the heart (for improved image resolution) and enabling acquisition of a larger number of image planes to be acquired for reconstruction (assuming a fixed increment for the angle 0). The position in the esophagus (column 2, Table 2) yielding the maximum longitudinal angle range varied considerably from patient to patient. Columns 3 and 4 in Table 2 show the maximum and minimum longitudinal angles 0 over which the imaging plane would have to be tilted in order to image the most cephalic and caudal parts of the LV from the optimized esophageal viewpoint. The maximum and minimum angles 0 were determined as follows. For a given esophageal viewpoint, each point of the LV endocardial border on each CT section has associated

Esophagus/heart geometry • R. B. HATANGADIet al.

15

Table 1. Patient characteristics. Patient Ht Wt BSA no. Sex Age (cm) (kg) (m2) Carinat

GE junctiont

1 2 3 4

M F M M

60 75 66 54

165 152 185 180

74 43 73 96

1.82 1.35 1.95 2.15

8.0 4.0 7.2 7.0

19.2 16.8 24.0 20.3

5 6 7 8 9 10

M M F M M M

71 64 36 48 72 38

168 170 170 180 178 189

59 77 107 88 70 86

1.67 1.88 2.17 2.07 1.87 2.14

7.2 8.8 5.2 7.0 8.4 8.8

16.8 20.8 21.2 18.0 21.2 23.2

Primarydiagnosis

Cardiac status

Metastaticcolon cancer Rule out aortic dissection Dilatedcardiomyopathy Statuspost cardiac transplant Pulmonaryasbestosis Lung mass Metastaticbreast cancer Lung mass Dilatedcardiomyopathy Ascendingaortic dissection

Normal heart Congestive heart failure Marked cardiomegaly; ejection fraction 15% Normal left and fight ventricular function Normal heart Normal heart Normal heart Mild cardiomegaly Marked cardiomegaly; ejection fraction 24% Cardiomegaly; Aorta 4 cm diameter

t Distance from sternal notch (cm).

with it a longitudinal angle. Therefore, each LV section has a local m a x i m u m and m i n i m u m longitudinal angle. Taking all coronal heart sections into account, the largest m a x i m u m and the smallest minimum longitudinal angle values define the working range of motion that must be designed into a transverse oblique probe in order to successfully scan this patient population. At esophageal positions near the sternal notch or the gastroesophageal junction, the range o f longitudinal angles (Table 2, column 3 minus column 4) for imaging the L V tended to be smaller than at the middle range; thus, the optimal scanning position was located at a mean normalized distance o f 0.72 from the sternal notch to the gastroesophageal junction. The largest required scanning range of 0 was 81 ° (19 ° cephalic and 62 ° caudal, relative to an axis perpendicular to the local esophageal axis). The fifth column in Table 2 gives the m i n i m u m ultrasonic range necessary to scan this population. The largest distance of the L V from the phased array was 15.3 cm. In transverse oblique scanning, the transverse angle th lies in the plane of the hypothetical ultrasonic sector for each cardiac point to be imaged. Therefore,

this mode of scanning will be feasible without rotating the entire probe in the esophagus if there is at least one viewpoint in the esophagus from which the range of ~b values is less than the 90 ° angle of the typical sector scan. As shown in column 6 of Table 2, a 90 ° sector angle was sufficient to image only five of the ten patients. Therefore, in half of the patients studied, the probe would need to have an added degree of freedom (rotation about the esophageal axis) built into it in order to scan the full L V reliably. Table 2, column 6 shows that the m a x i m u m range of transverse angles ~b required is 99 °. This means that the entire probe needs to be rotated by 9 ° (the difference between 99 ° and 90 °) about its axis in order for the ultrasound fan to cover the boundaries of the LV.

Longitudinal oblique scanning For longitudinal oblique scanning, the longitudinal angle 0 lies in the plane of the hypothetical ultrasonic sector scan for each heart point being imaged. Table 3 gives the results for longitudinal oblique scanning. Using reasoning analogous to that for the transverse scans, the optimal esophageal position (column

Table 2. Transverse oblique scanning criteria for the left ventricle.

Patient no.

Optimum location along esophagus Z (normalized)

1 2 3 4 5 6 7 8 9 10

0.54 0.71 0.73 0.85 0.83 0.69 0.44 0.75 0.96 0.72

Maximum longitudinal angle 0 (deg) 90.0 112.5 117.6 125.2 133.5 115.9 90.0 116.5 153.0 109.4

Minimum longitudinal angle 0 (deg) 44.7 53.9 42.0 60.0 84.2 35.8 32.3 56.1 83.3 27.8

Minimum distance r (cm)

Range of transverse angles 4~ at normalized esophageal positions (deg)

13.7 12.4 13.3 14.5 11.9 14.8 15.3 14.5 12.9 11.7

51.8 70.3 97.1 97.7 99.0 79.2 60.7 76.0 94.7 92.0

Ultrasound in Medicine and Biology

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Volume20, Number 1, 1994

Table 3. Longitudinal oblique scanning criteria for the left ventricle.

Patient no.

Optimum location along the esophagus Z (normalized)

Maximum transverse angle q5 (deg)

Minimum transverse angle th (deg)

Minimum distance r (cm)

Range of longitudinal angles 0 at normalized esophageal positions (deg)

1 2 3 4 5 6 7 8 9 10

0.92 0.95 0.97 1.00 0.87 0.92 0.95 0.88 0.99 0.96

191.0 210.0 208.3 234.3 193.7 201.9 184.0 178.6 213.8 212.4

110.9 98.0 76.7 86.7 77.4 90.7 75.7 66.5 80.3 104.8

11.7 10.5 13.9 14.4 11.5 13.6 12.2 12.8 12.4 10.7

32.7 52.5 53.6 30.9 49.0 52.2 41.0 50.2 69.7 68.1

2, Table 3) for longitudinal oblique scanning was chosen as the one for which the range of transverse angles ~b was maximum, i.e., the number of serial longitudinal imaging sections would be maximized, assuming a fixed incremental scanning angle. The optimal esophageal position for longitudinal scanning tended to be lower down in the esophagus (mean normalized distance 0.94) than that for transverse scanning (0.72). The maximum angular range over which multiple longitudinal cross sectional images could be taken was found to be 134 ° (Table 3, patient 9, column 3 minus column 4), at an esophageal position near the gastroesophageal junction (normalized distance 0.99). The largest distance of the LV from the phased array was 13.9 cm (Table 3, column 5). Since the maximum longitudinal angle range was 70 ° (Table 3, column 6), the entire LV cavity always fell within the 90 ° ultrasound sector.

Rotary scanning In this mode of scanning, the axis of the imaging cone was assumed to be perpendicular to the local esophageal axis. Table 4 shows the results for rotary scanning. Column 2 shows the range of esophageal

Table 4. Rotary scanning criteria for the left ventricle. Patient no.

Range of optimized esophageal locations Z (normalized)

Range of cone angles a < 90 ° (deg)

1 2 3 4 5

.58-.71 0.65-0.77 -0.61-0.77 0.45-0.68

73-87 81-85 -76-89 61-89

6 7 8 9 10

-0.49-0.68 0.65-0.70 0.66-0.77 --

-68-90 74-84 72-88 --

viewpoints from which it is possible to image the entire LV with a 90 ° sector scan. Column 3 shows the required imaging cone angle when viewing the LV from these esophageal viewpoints. In three of the patients (3, 6 and 10), complete LV scans were not obtainable from any esophageal position, i.e., the cone angle was larger than could be contained within a 90 ° sector scan. In the patients in whom complete LV scanning from certain esophageal viewpoints was possible, the optimal esophageal positions tended to be towards the caudal half of the esophagus, i.e., between the sternal notch and the gastroesophageal junction (mean normalized range 0.45-0.77). The possibility of an additional degree of freedom was considered, in order to enable imaging of the complete LV in patients 3, 6 and 10. The additional degree of freedom would allow tilting of the transducer rotation axis away from the perpendicular to the local esophageal axis. In order to determine the extent of this tilt, we had to modify our rotary scanning algorithm. As before, the initial orientation of the transducer rotation axis was assumed to be perpendicular to the local esophageal axis and was oriented so as to minimize the angle of the cone required to sweep out the entire LV. Vectors were then constructed joining each discrete LV point to the candidate esophageal viewpoint. The angles 6 between these LV vectors and the transducer rotation axis vector were then determined. The constraint in this case was that the cone angle was restricted to 90 °. For all the angles 6 > 45 °, the difference (6-45) represented the angle through which the rotation axis needed to be tilted away from the local esophageal axis in order for a 90 ° sector to image the entire LV. It was found that all patients could be scanned with a 90 ° ultrasound sector by allowing the axis of rotation of the transducer to deviate away from the perpendicular to the local esophageal axis by _+ 29 °.

Esophagus/heart geometry • R. B. HATANGAD! et al.

Linear Scanning As shown in Table 5, column 2, in eight of the ten patients (all but patients 3 and 10), complete LV scanning could be accomplished within an ultrasonic sector angle of 90 °. The echo range requirements for LV scanning varied from 11.0 to 17.0 cm (Table 5, column 3), and the range over which the transducer would have to move axially in the esophagus varied from 7.2 to 11.9 cm (Table 5, column 4). However, in half of the patients the cardiac apex was found to lie in a transverse plane caudal to the gastroesophageal junction (Table 5, column 5). Because acoustical contact with the tissues would be lost when the transducer entered the stomach, complete LV visualization by linear scanning would not have been possible in these patients. Furthermore, the rigid section required of a probe to perform linear scanning from the esophagus would preclude using this device in the stomach. DISCUSSION The shortcomings of our earlier three-dimensional TEE probe, and the difficulties of determining appropriate parameters for a new design, prompted us to embark on a systematic investigation before writing specifications for a second-generation probe. This study was planned to enable comparison of all possible modes of single-degree-of-freedom transesophageal scanning in the same representative set of patients. Although all of these scanning modes have previously been implemented, at least in prototype form, the implementation has been done by separate groups of investigators, and only our original design has been tested with respect to its ability to scan the entire LV and enable computer reconstruction of a three-dimensional ultrasonic ventriculogram in humans (Bashein et al. 1993). Comparison of the performance of actual transesophageal probes in patients would have been impossible. Having digitized CT data available not

Table 5. Linear scanning criteria for left ventricle.

Patient no.

Minimum sector angle a needed for LV (deg)

Minimum range for LV r (cm)

Distance from heart base to GE junction A Z (cm)

Is apex visible?

1 2 3 4 5 6 7 8 9 10

51.4 79.7 98.1 80.6 58.6 80.9 63.2 77.4 62.7 91.6

12.5 12.0 13.2 17.0 14.1 14.5 13.7 14.6 15.2 11.0

7.2 7.8 11.9 10.2 8.0 9.6 8.8 8.8 10.4 8.8

Yes No No No Yes Yes Yes Yes No No

17

only allowed comparisons to be made, but also afforded us an opportunity to evaluate the improvement that an additional degree of freedom would bring in scanning the same set of patients. An important limitation of this study is that we have considered only transesophageal, and not transgastric, imaging. While the majority of short-axis imaging of the LV for intraoperative monitoring purposes is now performed from within the stomach (Orihashi et al. 1990), we have found that it is not possible to view the entire LV from the transgastric position by adjusting the gastroscope controls of commercially available probes (unpublished data). Whether a transverse, longitudinal or rotary scanning design could view the whole LV from the stomach cannot be answered from this study, as it would be difficult to determine from CT scans which locations within the stomach could be reached by a TEE probe. Furthermore, the linear scanning probe cannot be used at all to image from a transgastric position. Of the possible options for single-degree-of-freedom multiplanar echo scanning from the esophagus, we found that only the longitudinal oblique method could scan the entire LV consistently. However, the longitudinal orientation has two major disadvantages: 1) a probe with only a longitudinal array would have limited usefulness for other diagnostic purposes (Seward et al. 1990); and 2) the long axis of the LV will be cut tangentially by a longitudinally oriented scanning sector, and thus the motion of the septal and lateral walls may not be accurately represented. Alternatively, a transversely oriented array having an added degree of freedom, i.e., calibrated rotation about the esophageal axis, could enable complete visualization of the LV, but the lack of a longitudinal array would also limit the utility of the probe for diagnostic imaging (Seward et al. 1990). An orthogonal mode of precordial scanning has been reported that combines the advantages of transverse and longitudinal scanning by allowing simultaneous imaging in two orthogonal planes, but as yet does not allow for transverse/longitudinal sweeps in known angular increments (Snyder et al. 1986). An ideal probe for 3-D reconstruction could perform both transverse and longitudinal sweeps. However, the engineering design of such a probe having the additional degrees of freedom would be a formidable task. Recently, the rotary method of scanning has been shown to be particularly attractive for diagnostic imaging (Flachskampf et al. 1991; Roelandt et al. 1992). In addition to offering all of the capabilities of a biplane probe, it enables the operator to orient the image and the doppler crossing angles in ways not obtainable with either transverse or longitudinal arrays. Further-

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Ultrasound in Medicine and Biology

more, the smooth transition from one imaging plane to another helps the operator to maintain his or her mental orientation with respect to anatomical landmarks. However, we found that rotary scanning would not image the entire LV in three of our patients, unless an additional degree of freedom were added to enable the axis of rotation to be tilted with respect to the plane perpendicular to the local esophageal axis, while maintaining acoustical contact with the esophageal wall. Therefore, it appears that a rotary scanning probe having the capability to tip its axis of rotation by _ 29 ° from the perpendicular to the local esophageal axis would be nearly ideal for both diagnostic imaging and three-dimensional reconstruction of the LV cavity and, presumably, the mitral valve surface. The rotary scanning method does require that the tip of the probe have a larger diameter than that of a probe with only transversely or longitudinally oriented arrays (i.e., the diameter is determined by the diagonal measurement, rather than the length or width of the phased array). This should be a minor disadvantage, as the available rotary scanning probes have been reported to be relatively easy to swallow. Furthermore, a single-transducer, rotary scanning probe will have fewer wires in its shaft than a biplane probe, so that shaft diameter (which has been reported to determine the limits of patient tolerance) could be reduced. In conclusion, this study has found that the only single-degree-of-freedom TEE probe design that appears to be able to scan the entire LV from a single probe position within the esophagus is the longitudinal one. However, the most appealing probe design for both diagnostic imaging and three-dimensional reconstruction would incorporate rotary scanning and an additional degree of freedom to tilt the axis of rotation _+ 29 ° away from an axis perpendicular to the local esophageal axis. To realize the full range of tilting, the probe would likely need a balloon or another device to maintain acoustical contact with the wall of the esophagus (Bashein et al. 1993). Acknowledgement--Supported by Grant HL41464 from the National Heart, Lung and Blood Institute.

REFERENCES Bashein, G.; Martin, R. W. Transesophageal echocardiography in dogs [letter]. Anesthesiology 74:958-959; 1991. Bashein, G.; Sheehan, F. H.; Nessly, M. L.; Detmer, P. R.; Martin, R. W. Three-dimensional transesophageal echocardiography for depiction of regional left-ventricular performance: Initial results and future directions. Int. J. Cardiac Imaging 9:121-131; 1993 Clements, F. M.; de-Bruijn, N. P. Perioperative evaluation of regional wall motion by transesophageal two-dimensional echocardiography. Anesth. Analg. 66:249-261; 1987. Crawford, T. M.; Dick, M.; Bank, E.; Jenkins, J. M. Transesophageal atrial pacing: Importance of the atrial-esophageal relationship. Med. Instrum. 20:40-44; 1986.

Volume 20, Number 1, 1994 Drexler, M.; Erbel, R.; Mueller, U.; Wittlich, N.; Mohr, K. S. Measurement of intracardiac dimensions and structures in normal young adult subjects by transesophageal echocardiography. Am. J. Cardiol. 65:1491-1496; 1990. Flachskampf, F. A.; Hoffmann, R.; Hanrath, P. Experience with a transesophageal echo-transducer allowing full rotation of the viewing plane: The omniplane probe. J. Am. Coll. Cardiol. 17:34A; 1991. Fujimoto, L. K.; Jacobs, G.; Przybysz, J.; Collins, S.; Meaney, T. Human thoracic anatomy based on computed tomography for development of a totally implantable left ventricular assist system. Artif. Organs 8:436-444; 1984. Greenleaf, J. F.; Kuroda, T.; Seward, J. B. Three-dimensional image analyses of the heart from transesophageal images. J. Ultrasound Med. 10:$28; 1991. Harui, N.; Souquet, J., inventors; Advanced Technology Laboratories Inc., assignee. Transesophageal echocardiography scanhead. U.S. patent 4,543,960. 1985 May 1.2p. Int. cl4 A61B 10/ 00. Jacobs, G. B.; Agishi, T.; Ecker, R.; Meaney, T.; Kiraly, R. J. Human thoracic anatomy relevant to implantable artificial hearts. Artif. Organs 2:64-82; 1978. Leung, J. M.; O'Kelly, B. F.; Mangano, D. T. Relationship of regional wall motion abnormalities to hemodynamic indices of myocardial oxygen supply and demand in patients undergoing CABG surgery. Anesthesiology 73:802-814; 1990. London, M. J.; Tubau, J. F.; Wong, M. G.; Layug, E.; Hollenberg, M. The "natural history" of segmental wall motion abnormalities in patients undergoing noncardiac surgery. Anesthesiology 73:644655; 1990. Martin, R. W.; Bashein, G.; Zimmer, R.; Sutherland, J. An endoscopic micromanipulator for multiplanar transesophageal imaging. Ultrasound Med. Biol. 12:965-975; 1986. Martin, R. W.; Bashein, G. Measurement of stroke volume with three-dimensional transesophageal ultrasonic scanning: Comparison with thermodilution measurement. Anesthesiology 70:470476; 1989. Martin, R. W.; Graham, M. M.; Kao, R.; Bashein, G. Measurement of left ventricular ejection fraction and volumes with three-dimensional reconstructed transesophageal ultrasound scans: Comparison to radionuclide and thermal dilution measurements. J. Cardiothorac. Anesth. 3:260-268; 1989. Martin, R. W.; Bashein, G.; Detmer, P. R.; Moritz, W. E. Ventricular volume measurement from a multiplanar transesophageal ultrasonic imaging system: An in vitro study. IEEE Trans. Biomed. Eng. 37:442-449; 1990. Orihashi, K.; Hong, Y.; Sisto, D. A.; Goldiner, P. L.; Oka, Y. The anatomical location of the transesophageal echocardiographic transducer during a short-axis view of the left ventricle. J. Cardiothorac. Anesth. 4:726-730; 1990. Roelandt, R. T. C.; Thomson, I. R.; Vletter, W. B.; Brommersma, P.; Born, N. Multiplane transesophageal echocardiography: Latest evolution in an imaging revolution. J. Am. Soc. Echocardiogr. 5:361-367; 1992. Seward, J. B.; Khandheria, B. K.; Edwards, W. D.; Oh, J. K.; Freeman, W. K. Biplanar transesophageal echocardiography: Anatomic correlations, image orientation, and clinical applications. Mayo Clin. Proc. 65:1193-1213; 1990. Seward, J. B.; Khandheria, B. K.; Oh, J. K.; Freeman, W. K.; Tajik, A. J. Critical appraisal of transesophageal echocardiography: Limitations, pitfalls, and complications. J. Am. Soc. Echocardiogr. 5:288-305; 1992. Shively, B. K.; Schiller, N. B. Transesophageal echocardiography: Its role in the intraoperative detection of myocardial ischemia and infarction. In: Kerber, R. E., ed. Echocardiography in coronary artery disease. Mount Kisco, New York: Futura; 1988:283304. Snyder, J. E.; Kisslo, J.; vonRamm, O. T. Real-time orthogonal mode scanning of the heart. I. System design. J. Am. Coll. Cardiol. 7:1279-1285; 1986. Souquet, J.; Hanrath, P.; Zitelli, L.; Kremer, P.; Langenstein, B. A.

Esophagus/heart geometry • R. B. HATANGADI et al.

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Transesophageal phased array for imaging the heart. IEEE Trans. Biomed. Eng. 29:707-712; 1982. Wollschlager, H.; Zeiher, A. M.; Klein, H. P.; Kasper, W.; Wollschlager, S. Transesophageal echo computer tomography (ECHO-CT): A new method of dynamic 3-D reconstruction of the heart. Biomed. Tech. (Berlin). 34 suppl.:10-11; 1989.

APPENDIX Algorithm to determine the angles O, 4' and the distance r The line segment connecting the ith esophageal point to the fh discrete point on the kth coronal LV section represents a vector M in space (see Fig. 2). This vector can be described by its cylindrical coordinate components r, 0 and 4,, where: ru, = x/(xjk - x,k)2 + (yj, - Yik)2 + (Zjk -- Zi~)2

(1)

Ouk = cos l(zj~ - zik) I \ rijk /

(2)

4,Uk = tan-~ (Yjk -- Yi__.__----4"). \xjk - x w

(3)

Each discrete point on the LV boundary therefore, has an

associated r, 0 and 4, with respect to each esophageal viewpoint. To find the range of distance r for imaging the LV from a given esophageal viewpoint, we choose the maximum and minimum of r0~ from the entire population of discrete LV points. Similarly, the maximum and minimum longitudinal angle 00k define the range of 0. In order to find the range of transverse angle 4,, we first have to determine the orientation of the narrowest fan beam that covers the entire LV. It is assumed that as the fan beam is scanned in 0, its centerline lies in a plane P defined by the local esophageal axis and the centroid of the LV (Fig. 3A). For example, if the fan beam is scanned in a caudal-cephalic direction, the sector angle a goes through a maximum value. The sector orientation at which this maximum occurs is determined as follows. For each increment in transverse angle 0, the data set is projected onto the plane of the sector. To accomplish this, the entire data set is rotated so as to make the plane of the sector parallel to the coordinate plane x - y . The steps in this process are given below. Step l: The global centroid of the LV cavity is calculated for all the discrete LV points. A plane P containing the local esophageal axis and the LV centroid is then defined (see Fig. 3A). Step 2: The entire data set (esophageal and discrete LV section points) is rotated until the plane P becomes perpendicular to the x - y plane and is parallel to the y - z plane (see Fig. 3B). Step 3: The data set is now rotated about the x axis until the ultrasound fan beam is parallel to the x - y plane. The x, y coordinates of the transformed data set now represent the projection of the data

20

Ultrasound in Medicine and Biology

set onto the plane of the sector. In the x - y plane, line segments are now constructed between each discrete LV point and the esophageal viewpoint. The two extreme left and fight line segments define the left and fight boundaries of the sector. The angle between these line segments is the sector angle a (Fig. 3C). Steps 1, 2 and 3 are repeated for each increment in 0. The optimal location of the sector is where the sector angle a is maxi-

Volume 20, Number 1, 1994 mum. The two discrete LV points (boundary points) that define the left and fight extremes of this optimal sector are now identified. Step 4: We now return to the original data set (before all coordinate transformations) and connect the esophageal viewpoint with the boundary points of the optimal sector. The actual range of transverse angle ~b is now the difference between the transverse angles for the two respective LV boundary points (see Fig. 3D).