Digital X-ray stereophotogrammetry for cochlear implantation

1120 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 47, NO. 8, AUGUST 2000

Digital X-Ray Stereophotogrammetry for CochlearImplantation

Ge Wang*, Senior Member, IEEE, Margaret W. Skinner, Jay T. Rubinstein, Member, IEEE, Matthew A. Howard, III,and Michael W. Vannier, Member, IEEE

Abstract—Multielectrode, intracochlear implant systems are ef-fective treatment for profound sensorineural hearing loss. In somecases, these systems do not perform well, which may be partiallydue to variations in implant location within the cochlea. Deter-mination of each electrode’s position in a patient’s inner ear pro-vides an in vivo basis for both the cochlear modeling of electricalfields and the future design of electrode arrays that deliver elec-trical stimulation to surviving auditory neurons, and may improvespeech processor programming for better speech recognition. Wedeveloped an X-ray stereophotogrammetric approach to localizeimplanted electrodes in three dimensions. Stereophotogrammetryof implanted electrodes is formulated in weak perspective geom-etry, with knowledge of a three-dimensional (3-D) reference struc-ture and electrode positions in each of two digital stereo-images.The localization error is theoretically, numerically, and experimen-tally quantified. Both numerical and experimental results demon-strate the feasibility of the technique.

Index Terms—Cochlear implantation, weak perspective, X-raystereophotogrammetry.

I. INTRODUCTION

A PPROXIMATELY 600 000 to 1 000 000 Americans withprofound sensorineural hearing loss receive little or no

benefit from acoustic hearing aids [2], [18], [27]. Since 1989,cochlear implantation has been recognized as medically safetreatment for this population by the American Medical Asso-ciation and the American Academy of Otolaryngology-Headand Neck Surgery [1]. Over the past years, there have been dra-matic improvements in the benefit provided by multielectrode,intracochlear implants. When implant sound processors are suit-ably programmed, average sentence recognition scores withoutlipreading are between 74% and 84% for adults who becamedeaf after learning language [12], [6], [20].

To date, Nucleus, Clarion and MED-EL systems have beenimplanted worldwide in more than 22 000 patients. In the United

Manuscript received August 13, 1999; revised March 14, 2000. This workis supported by NIH/NIDCD (R01 03590).Asterisk indicates correspondingauthor.

*G. Wang is with the Department of Radiology, University of Iowa, 200Hawkins Drive, Iowa City, IA 52242 USA (e-mail: [email protected]).

M. W. Skinner is with the Department of Otolaryngology-Head & NeckSurgery, Washington University School of Medicine, St. Louis, MO 63110USA.

J. T. Rubinstein is with the Department of Otolaryngology, University ofIowa, Iowa City, IA 52242 USA.

M. A. Howard is with the Department of Surgery, University of Iowa, IowaCity, IA 52242 USA.

M. W. Vannier is with the Department of Radiology, University of Iowa, IowaCity, IA 52242 USA.

Publisher Item Identifier S 0018-9294(00)06412-0.

States, these systems have been approved by FDA for clinicaluse (Nucleus-22 and Clarion in adults and children) or clinicalinvestigation (Nucleus-24 in adults and children; MED-EL inadults). External parts of these systems include a directional mi-crophone, a sound processor that encodes signals, and a trans-mitter that sends the coded signals. Internal components includean antenna that detects the coded signals, a receiver/stimulatorthat decodes them, and an electrode array that stimulates thesurviving auditory nerve fibers. The Nucleus-24, Clarion, andMED-EL devices can transmit information from the electrodesback to the sound processor via telemetry. The intracochlearelectrode array of the Nucleus CI22M and CI24M devices has22 insulated platinum-iridium (90:10) wires that run throughthe middle of 32 round platinum bands (the distal 22 of whichare electrodes) over a distance of 25 mm [16]. The Clarion in-tracochlear array consists of 16 platinum-iridium (90:10) stim-ulating electrodes with mushroom-shaped contact surfaces ar-ranged in eight near-radial pairs [19] over 25 mm. The insu-lated platinum-iridium wires from the electrodes form a doublerib configuration that together with the molded silicone rubbercarrier is designed to follow the curvature of the modiolus inthe cochlea. The intracochlear array of the MED-EL COMBI40 systems has either 16 or 24 insulated platinum/iridium wiresthat run through the middle of eight or 12 ellipse-shaped, plat-inum electrodes over 26 mm [29], [12].

Temporal bone imaging demands submillimeter image reso-lution in three-dimensions, and especially so for cochlear im-plantation, because the anatomy of the inner ear is intricatelythree-dimensional (3-D), the dimensions of both the inner earfeatures and the intracochlear electrodes are very small, typicallyin the submillimeter domain. Knowledge of implanted electrodepositions is important to describe the local electrical field theyproduce in individual patients [3], [4]. This information may beused to improvespeech processorprogramming forbetter speechrecognition [21], [28] and improve the future design of the elec-trode array for better delivery of electrical stimuli.

The 3-D trajectory of an electrode array implanted in anindividual’s inner ear and its relation to adjacent anatomicstructures are well-characterized by 3-D reconstruction fromvolumetric spiral computed-tomography (CT) data [22],[24]–[26], [13]. However, maximum resolution with commer-cial spiral CT scanners is insufficient to define the position ofeach electrode within this trajectory because of the platinumelectrodes’ small size (for Nucleus electrodes, the diameteris 0.4-0.6 mm, and the length 0.3 mm), close spacing (inter-electrode center-to-center distance: 0.75 mm), attachment toplatinum/iridium wires, and high density [raw absorption value:

0018–9294/00$10.00 © 2000 IEEE

WANG et al.: DIGITAL X-RAY STEREOPHOTOGRAMMETRY FOR COCHLEAR IMPLANTATION 1121

Fig. 1. Coordinate systems in X-ray stereophotogrammetry. The camerasystemX-Y -Z and the object systemx-y-z are related by a matrix that rotatesthe camera systemX-Y -Z aroundX , Y; andZ axes by angles�; �; and ,respectively. The imaging plane isX-Y .

approximately 20 000 Hounsfield units (HU)] in relation toanatomic structures (3000 HU). In contrast, two-dimensional(2-D) X-ray radiographs provide high-resolution images ofimplanted electrodes but suppress 3-D information in theprojection process. This suppression eliminates much ofthe anatomic detail so that only rough approximation of theposition of the electrode array in the inner ear can be made[14]. Recently, 2-D X-ray radiographs of patients’ implantedelectrode arrays were overlaid on appropriately rotated 3-Dreconstructions of their conventional CT scan images to studythe proximity of electrodes to the facial nerve [11]. However,this approach only permits approximation of thein vivo, 3-Dposition of each electrode in an individual’s inner ear and itsproximity to other anatomic structures of interest (e.g., facialand vestibular nerves).

In this paper, we report a digital X-ray stereophotogrammetryapproach to determine the 3-D distribution of implanted elec-trodesin vivo from radiographs. This information can then befitted into a corresponding volumetric spiral CT image to gainthe advantages of both spiral CT and digital radiography. In Sec-tion II, coordinate systems and notations are introduced, thenthe weak perspective approximation is discussed. In Section III,in the weak perspective framework, scaling factor estimation,3-D localization, and space resection techniques are developedusing a precisely designed 3-D reference structure, then erroranalyses performed theoretically. In Section IV, numerical sim-ulation and experiments with phantom and human data are de-scribed. In Section V, further research topics are discussed.

II. PRELIMINARIES

A. Orthogonal Geometry

We first define the camera and object coordinate systems thatare respectively associated with the X-ray imaging system and

an object to be imaged, as shown in Fig. 1. An orthogonal pro-jection is obtained along the opposite direction of theaxis.The projection is recorded on the- plane. The directionsof the , and axes of the camera system generally differfrom the , and axes of the object system, both of whichform right-hand systems.

Without loss of generality, the relationship between the twosystems can be expressed as a general rotation transform thatconverts a point in camera system coordinatesinto the corresponding point in object systemcoordinates. This general rotation can be decomposed into threesimple rotations. The first is around the axis of the camerasystem, the second around theaxis of the once-rotated camerasystem, and the third around the axis of the twice-rotatedsystem. In the photogrammetric literature, these three angles aredenoted as , which are also called the tilt, pan andswing angles, respectively. As shown in Fig. 1, a generalrotation matrix can be expressed as ,where

(1)

(2)

(3)

that is, (4), shown at the bottom of the page. Therefore,the basicimaging equationis

(5)

or in an alternative form,

(6)

B. Weak Perspective Geometry

When the depth of the structure is small compared to its rangefrom the camera, its perspective projection can be modeled as ascaled orthographic projection, also known as aweak perspec-tive projection[10], [23]. Up to a scaling factor, weak perspec-tive geometry is equivalent to orthogonal geometry. In this work,weak perspective geometry is used for three reasons. First, as itis shown in the following, weak perspective geometry approxi-mates the problem very well, and produces satisfactory results,which is a 3-D localization accuracy of less than 0.05 mm, ac-cording to our clinical collaborators. Second, weak perspective

(4)


Fig. 2. Perspective geometry of X-ray radiography. Weak perspective modelapproximates perspective geometry as scaled orthographic projection.

geometry simplifies X-ray stereo-imaging formulation, and fa-cilitates studies on relationships between the imaging accuracyand the parameters about the imaging geometry and the datacharacteristics. Third, results with weak perspective establishesthe feasibility of the approach, and provides a basis for subse-quent generalization and optimization.

Theoretically, the radiographic imaging geometry is perspec-tive, as shown in Fig. 2. Any point in the camerasystem - - can be mapped on the imaging plane- asfollows:

(7)

where the X-ray source is located at .Without loss of generality, the validity of the weak perspec-

tive approximation can be analyzed by assuming a point to beimaged being in the - plane with coordinates , asshown in Fig. 2. Let denote the angle from the source

to the point , and the magnificationfactor defined as , we have

(8)

(9)

(10)

(11)

(12)

Practically, we can make 100 cm, 20 cm, and20–30 cm. Also, the radius of the object of interest in this

application is less than 1 cm, that is, 1 cm and1 cm. As a result, for 20 cm, 14.0 , 0.84 ,

Fig. 3. Stereo-images of an arbitrary pointp and the unit axial vectorsa, b,c of the reference system.

1.3, 1.6%; for 30 cm, 15.9 , 0.97 ,1.4, 2.0%. These data can be interpreted as the followingstatement:the weak perspective geometry is quite accurate evenin the worst case.

Note that in our stereo-imaging approach, a reference struc-ture is used for determination of the X-ray source orientation,which will be explained in Section IV-C. An interesting andimportant aspect of this scheme is that the reference object andthe implanted electrode array of interestdo not have the sameheight . The stereo angle determined using the reference objectmay differ up to 2 from the stereo angle extended by the X-raysource relative to the implanted electrode array. The implicationand compensation of this discrepancy will be discussed in Sec-tion III-F. For sake of convenience, we assume that these twoangles are the same until Section III-F.

III. M ETHODS

Stereo-imaging under the weak perspective geometry re-quires knowledge of the scaling factor, and the orientation ofpatient’s head with respect to the X-ray beam. A device fordirectly measuring the scaling factor and the orientation isunavailable. The design and manufacture of such a device isexpensive, and also complicates the imaging procedure.Wepropose to provide this information implicitly in the form ofthe image of a 3-D reference structure.If scaling factors andorientations used in stereo-imaging can be determined, soshould the 3-D coordinates of any point, given correspondingpositions of the point in the paired images, as illustrated inFig. 3. In the following subsections, these issues are describedin detail.

A. Scaling Factor Estimation

We attach a 3-D reference structure to the object system, de-fine the three axes of the system, and obtain coordinates of theorigin , the extremes of and unitaxial vectors, and , ina projection view. Suppose that the origin and the two unit axialvectors of the object system have coordinates ,

and , which are not collinear,we can then compute the scaling factor.


Fig. 4. Cross-ratios related to the unit axesa andb of the reference objectsystem. If the line through the tipp of a and the midpointq of b intersectsthe circleC at t , thenp q =q t = 5. Similarly, p q =q t = 5, andp q =q t = 1.

As shown in Fig. 4, we denote the circle passing through theorigin and the extremes of theand unit axial vectors as .The weak perspective projection ofis generally an ellipse .Clearly, the ratio between the longer axis of E and the radiusof is the scaling factor. Hence, the problem is to determineE from , and . This can be done using the techniquesuggested by Huanget al. [10]. The key fact is that ratios ofsegment lengths along a straight line are preserved under weakperspective assumption. Let, , and be the midpoints of

, and , extend , , and to intersectat , , and . As shown in Fig. 4, we have ,

. Because the projections,, and are the midpoints , , and of , ,

and , , and , which are the projections of , ,and , can be found based on the cross-ratios

, . Finally, the ellipse E is determined vialeast-square fitting relative to , , and , , , and .

B. Localization Method

With the 3-D reference structure, we measure coordinates ofthe orthogonal unit vectors of the object system and an arbi-trary object point in two independent projection views. As aresult, the three unit vectors of the object system have coor-dinates , , and in one projectionview, , , and in the other projec-tion view ( Fig. 3), the point gives coordinates and

in the two views, respectively. Then, we apply thebasic imaging equation to these quantities measured from theleft and right views, respectively, and discardand

(13)

The least square solution can be found by satisfying thenormal condition

(14)

where

(15)

and

(16)

That is

(17)

where is nonsingular.

C. Localization Error Analysis

First, we briefly review basic knowledge on perturbationanalysis. For a given vector norm , the correspondingmatrix norm can be defined as

(18)

The stability of the solution to is dictated by the con-dition number of , defined as

(19)

Among various vector norms, the norm is popular and usedin this study

(20)

We consider the exact system

(21)

and a perturbed system

(22)

Again, we assume that be nonsingular. The relative error canbe expressed as

(23)

The error analysis can be greatly simplified by introducingthe regular object and camera systems. As illustrated in Fig. 5,for any two stereo-imaging directions along and axesrespectively, the axis of the regular object system is con-structed along the average of and directions; theaxis is taken as the one perpendicular to, closer to theaxis, and in the - plane; finally, the axis is selectedto form a right-hand system. Also, the regular camera system

- - is initially superimposed upon the regular objectsystem - - , and then rotated to align the axis withthe and axes respectively for stereo-imaging. Becausethe regular object system is related to the original object systemvia orthogonal transformation, the regularization will not affectthe stability of the solution. Similar comments apply to the reg-ular camera system.


Fig. 5. Regular camera and object systems. For any two stereo-imagingdirections,v andv , thez axis of the regular object system is the averageof v andv , thex axis is in thev –v plane and closer tov , y isoriented to form a right-hand system. The regular camera systemX -Y -Zis initially superimposed upon the regular object system, then rotated to alignrespectively withv andv for stereo-imaging.

Using the regular object and camera systems, images of thethree unit axial vectors are measured on the regular imagingplane – along and directions. Readings are

, and with the direction,, and with the direction,

where the angle between and are assumed to be .Consequently, can be expressed as

(24)

Therefore

.(25)

Clearly, the condition number reaches the minimum 2when the stereo-imaging angle 90 .

D. Resection Method

As described in the preceding subsection, the relative error in3-D localization is proportional to the condition number ,which is directly related to the stereo angle. Therefore, thestereo angle must be estimated to assess the relative error. Thiscan be achieved via resection. In the photogrammetry literature,resection refers to the process in which the position and orien-tation of a photograph is determined based on images of groundcontrol points appearing on the photograph. The conventionalresection algorithm requires linearization of the involved equa-tions, and iteration for solution refinement [5], [15], [23]. In thissubsection, we present an alternative method that does not re-quire the equation linearization.

Suppose that the three unit axial vectors of the object systemare identified in an orthogonal projection with coordinates

, , and respectively, according tothe basic imaging equation there holds

(26)

In the case of exact data, can be uniquelydetermined as follows:

arctan (27)

arcsin (28)

and

arctan (29)

In the case of noisy data, the least square error between real read-ings and model-based prediction can be iteratively minimized toobtain the solution using the Powell method [17], starting fromthe analytic solution derived in the noiseless case.

E. Resection Error Analysis

Because of the fitting nature, the least square resection algo-rithm described in the preceding subsection is not sensitive toperturbation. Before presenting a simplified error analysis of thestability of the resection algorithm, we point out that if two or-thogonal unit vectors are projected on an imaging plane, at leastone of the projected lengths is greater than or equal to .Hence, if three orthogonal unit vectors are projected, at leasttwo of the projected lengths are greater than or equal to .This fact will be used below.

First, let us evaluate the change of the rotation anglearound the axis when data are perturbed with a maximummagnitude . As shown in Fig. 6(a)

(30)

because is controlled by the two projected axes whoselengths are both greater than , and clearly the shortestprojected vector cannot introduce an angular error doubling theone defined by arc incrementand radius .

Second, for sake of simplicity let us consider the change ofthe tilting angle of the axis from the axis toward theaxis, assuming that perturbation occurs along theaxis, andthe unit axial vector projected on the – plane is greaterthan in length, as shown in Fig. 6(b). Let us fit withrespect to and by minimizing the least square error

(31)

where . We must have

(32)


Fig. 6. Estimation errors in (a) the rotational angle! around theZ axis and (b) the tilting angle� out of theX–Y plane, both of which are due to measurementerror.

Since

and

we have

(33)

Also, we have

(34)

and

(35)

Therefore

(36)

F. Bias Correction

For the purpose of cochlear implantation, the interelectrodecenter-to-center distance is sufficient for identification of 3-Dlocations of individual implanted electrodes in the cochlearcanal, because the 3-D central path of an implanted electrodearray can be accurately computed using an unwrapping algo-rithm, which was designed to digitally track and uncoil theimplant array in a CT image volume [26]. This unwrappingalgorithm was validated with demonstration electrode arrays,physical wire phantoms, and 20 implanted patients, whichwere scanned and reconstructed into image volumes of 0.1-mmcubic voxels. The unwrapping technique was validated with

Fig. 7. Depth component of the 3-D localization error from perturbation to thestereo angle.

a 0.1–mm accuracy against microscopic and manualin vivomeasures [13].

In the preceding stereo-imaging analyses, we have assumedthat perturbation to imaging parameters and noise in data do nothave any systematic bias. In fact, there is indeed such a bias dueto the weak perspective approximation, and this bias can be cor-rected for more accurate estimation of interelectrode distances,as explained as follows.

A unique feature of our stereo-imaging scheme is use of areference structure for determination of the X-ray source ori-entation (see Section IV-C). This reference structure generallydoes not have the same height as implanted electrodes to be lo-calized in 3-D. The discrepancy between the stereo-angle as-sociated with the reference object and that with the implantedelectrode array is the primary cause for the stereo-imaging bias.

As illustrated in Fig. 7, we have an arbitrary point ex-tending a stereo-angle , its projected coordinates and

corresponding to two viewing angles respectively, and

(37)


Fig. 8. Stereophotogrammetry testing phantom that consists of a reference object which contains precisely made three orthogonal axial arms of length 20 mm, anelectrode array phantom which is precisely measured using reflex microscopy, and fixed in a cylindrical container, as well as a phantom stage which can be rotatedaround three orthogonal axes. (a) Overall picture of the testing phantom. (b) and (c) Top and side views of the electrode array attached to a plexiglasscone-shapedbase with an open spiral path.

Therefore

(38)

Consequently,

(39)

As discussed in Section II-B, can be about 2. If we set10 , then 20%. The effect of this near constant

scaling in is to consistently increase/decrease therange ofrecovered 3-D locations of implanted electrodes, hence, sys-tematically increase/decrease interelectrode distances. Actually,this increment/decrement in the total length of the electrodearray can be identified by comparing the computed length ofthe electrode array to its known length before cochlear implan-tation. Therefore, this bias can be corrected by normalizing thecomputed length of the electrode array to the known length.Specifically, the bias correction is done in the following steps: 1)The total length from the first to the last electrode is computedby a) summing up the interelectrode center-to-center distancesmeasured microscopically, then b) summing up these distancesmeasured stereophotogrammetrically; 2) The correction factoris obtained as the ratio of the microscopic total length versus thestereophotogrammetric total length; 3) This ratio is multipliedwith each of the interelectrode center-to-center distances mea-sured stereophotogrammetrically. The effectiveness of this biascorrection method will be demonstrated in the following section.

IV. RESULTS

A. Testing Phantoms

Two testing phantoms were constructed according to the av-erage parameters of the human cochlea and the implant array.The first testing phantom consists of a plexiglas cone-shapedbase with an open spiral path, a demonstration electrode arrayattached to the spiral path, and a plexiglas platform that canbe rotated around three axes on which the plastic cube wasmounted. Fig. 8 shows the first testing phantom. The secondtesting phantom consists of a plexiglas cube; a demonstrationelectrode array, which is inserted into the cube; and the sameplexiglas platform.

The electrode array of the first testing phantom was mea-sured in situ using Reflex microscopy (Prior S2000 Reflex Mi-croscope), which involves optical stereoscopy to pinpoint land-marks on a surface with a positioning accuracy of 1in 3-D,and provide precise 3-D locations of electrodes. We first placedthe red dot on a boundary point of an electrode so that an imag-inary horizontal plane through that point contains the center ofthe electrode. We then moved the red dot onto the center of theelectrode without changing the focusing lens (dimension) tomeasure 3–D coordinates of the electrode center. Although thecoordinates of the first electrode are arbitrary, all coordinatesthereafter were registered relative to that first reference point.The electrode array of the second phantom was measured earlierusing optical microscopy before its insertion into the plexiglascube.

The second testing phantom is used to provide additionaldata, but we recognize that interelectrode distances before andafter insertion may not be the same. Because the very limitedsupply of the demonstration arrays and the nature of this


feasibility study, in our work we only used these two testingphantoms, however, we performed multiple tests using the firstphantom.

A 3-D reference structure was fabricated using a BridgeportMilling Machine. The rotational axis of the tool is perpendic-ular to the machine table, which can be moved along the twoin-plane axes accurately. The machining tolerance is less than

mm. The reference object consists of a radio-opaquemetal structure that represents three orthogonal axes of the ob-ject system and is supported by a 2.5-cm Plexiglas cube. Themetal structure is formed of two parts. The first part is a 90L-shaped angle made of 0.254-mm (0.010-in)-thick stainlesssteel. Each leg of this angle was machined 0.4 cm in width and2.4 cm in length outside, that is, 2.0 cm long inside. A smallhole was drilled near the end of one leg for labeling. Two edgesof the top surface of the cube were relieved to locate and pro-tect the L-shaped metal angle. The second part is a steel rod of0.5 mm in diameter. A hole for the rod was drilled perpendic-ular to the plane of the L-shaped angle. The rod was then placedwith its center axis at the inside corner of the L-shaped angle.The length of the rod is 2 cm.

B. Numerical Simulation

A software simulator was developed in the IDL language (Re-search Systems, Boulder, CO) to evaluate the characteristics ofthe stereophotogrammetric technique. We noticed that the meanerror (by “mean error,” we mean the average ofabsoluteerrors)in the 3-D localization of cochlear implant electrodes generallydepends on several factors, including the stereo-imaging angle,relative position of a point to be localized, the norm of the point,the nature of the random interference. We consistently foundthat the closer to the stereo-imaging angle is, the more ac-curate the 3-D localization results are.

The first simulation test is for true 3-D localization. In thistest, a point to be localized was placed at mm.The first imaging angle was set to , and the secondimaging angle increased from , , ,until . Then, 500 sets of noisy readings were gen-erated for each stereo-angle with additive uniform noise of onepixel of 0.15 mm in range length. The rationale for selectionof this noise interval is that the feature points are manuallypicked up in an enhanced and magnified region of interet in aradiograph, hence, their coordinates are rounded to those of thenearest neighbors, giving a uniform error distribution with aninterval of one pixel. It was found that when the stereo angleis in [40 , 140 ], a mean error of 3-D localization is less than0.1 mm.

The second simulation test is for interelectrode distanceestimation. In this test, an ideal electrode pair was designedbased on an independent optical microscopic measurement ofa demonstration electrode array. Based on this measurement,average interelectrode center-to-center distance was 0.749 mm;therefore, this separation length was assumed for the idealelectrode pair. The first electrode of the ideal electrode pairwas placed at mm, and the pair arranged along

and axes of the camera system, respectively, withother conditions being the same as in the first simulation test.It was found that interelectrode center-to-center distance can

Fig. 9. Average errors in estimation of interelectrode distances of the electrodearray phantom as function of the stereo angle, relative to the Reflex microscopemeasurement.

be estimated with a mean error of less than 0.1 mm, whenthe stereo-angle is sufficiently large, that is, [40, 140 ]. Thisobservation is consistent to the results obtained in the thefirst simulation test. Furthermore, if an electrode pair is fairlyparallel to the imaging plane, an even larger range of thestereo-angle, [20, 160 ], can be used with an interelectrodedistance estimation accuracy of less 0.05 mm.

The third simulation test is for bias correction due to theweak perspective approximation. In the previous two tests, boththe reference structure and the electrode array were centered onthe same horizontal plane. In the third test, while the referencestructure was centered on the– plane, the electrode arraycan be centered on a different horizontal plane. Furthermore,the 3-D electrode distribution model established using Reflexmicroscopy from the first testing phantom was used hereas a testing object. This realistic array model was alignedalong the axis and centered at mm,mm, mm, mm, mm,

mm, and mm, respectively. Foreach of these positions, the mean error in estimation of in-terelectrode distances was computed from 500 sets of noisyreadings as function of the stereo angle. In the case of thearray model being centered at mm, the averageerrors in estimation of interelectrode distances were computedwith and without bias correction respectively, and plotted, asshown in Fig. 9. All of our simulation results demonstratethat when the stereo angle is in [20–160 , the mean error ininterelectrode distance estimation is about 0.04 mm with thebias correction, and the standard deviation is about 0.004 mm.The effect of the bias correction is insignificant when thereference structure and the electrode array are on the sameplane, but it is quite substantial when these two objects havequite different heights.

C. Phantom Tests

An X-ray imaging system (Super 80CP, Philips MedicalSystems, Shelton, CT) was used to expose storage phosphorplates, giving a digital output of 0.1- or 0.15-mm pixels. Thisdevice allows a 116-cm source-to-film distance. The two testing


Fig. 10. Human volunteer and stereo-images. (a) A human subject biting the banana bar to which the electrode array phantom and the 3-D reference objectareattached. (b) Stereo images of the volunteer’s head where some regions of interest are digitally enhanced.

phantoms with the 3-D reference structure were X-rayed forstereophotogrammetry. The first testing phantom was X-rayedfrom multiple orientations. Images were enhanced via simpleadjustment of brightness and contrast using the image editingsoftware Adobe Photoshop.

Coordinates of points of interest in X-ray images were man-ually identified using NIH Image (National Institutes of Health,Bethesda, MD). Then, the interelectrode center-to-center dis-tances were computed using our stereo-imaging method. Whencompared to independent microscopic measures of the inter-electrode center-to-center distances, stereo measures were quiteaccurate with the mean error consistently less than 0.05 mm.The mean errors with the first and second testing phantoms areabout 0.04 and 0.045 mm, respectively. The stereo-angle in bothcases was about 40. Note that the errors in the two cases are pri-marily due to noise in the data. In the case of the second testingphantom, the error may be partially from manipulation of thearray during its insertion into the cube.

D. Human Study

After several tests with a dry human skull, a volunteer study(the first author) was performed (the protocol was approvedby the IRB of his University) to demonstrate the feasibility ofthe stereo-imaging technique. This human study is importantbecause the subject simulates more realistically what is en-countered in X-ray radiography than a dry human skull for thetwo reasons. First, this test includes soft tissue, fluid containingspaces, as well as the bone. Second, the subject can only bepositioned in certain ways to be imaged just as is true forpatients.

An important issue in clinical application of thestereo-imaging technique is how to firmly attach the 3-Dreference structure to the patient. One solution is to use a light-weight banana bar developed for a noninvasive, reattachableskull fiducial marker system [9]. Rigid fixation to the skull isachieved via a custom-molded mouthpiece. Vinyl Polysiloxanebite registration paste (Dentsply International Inc., Milford,DE) is extruded onto an aluminum mouthpiece. A precise

dental impression of both the maxillary and mandibular teethis created when the patient bites down on the mouthpiece. Theprimary region of fixation is the maxillary teeth. By gentlyclosing the jaw, adequate force is exerted on the mouthpiece.Because the mandibular teeth are positioned matching a preci-sion-molded surface, an optimally balanced and reproducibleforce distribution is generated. A broad, flat portion of thealuminum mouthpiece extends outwardly from the patient’smouth and serves as the site of attachment to the banana bar.Two screws rigidly secure the custom mouthpiece to a reusable,curved aluminum bar that sweeps backward along both thelateral sides of the head. Fig. 10(a) shows that the humansubject biting the banana bar, to which the optically measuredelectrode array and the 3-D reference structure are attached ina position near the right ear.

X-ray head imaging equipment Elema-Schonander (SiemensMedical Systems, Erlangen, Germany) was used to image thehuman subject at the University of Iowa (Iowa City, IA). Thisdevice has a 91.44-cm source-to-film distance, measures the ro-tation angle of the X-ray tube, and also uses the same storagephosphor film. Modified Stenver’s view and the view plus 15were used with 74 kVp, 40 mA, and 1–s exposure. We purposelymade the stereo angle to 15to give our stereo-imaging tech-nique a tough test. In clinical settings, a stereo angle of 20–40can be easily achieved. Images were similarly processed withAdobe Photoshop. Fig. 10(b) includes stereo images of the elec-trode array phantom and the 3-D reference structure, both at-tached to the human subject.

Some regions of interest in Fig. 10(b) were digitally enhancedto ease identification of points of interest. Coordinates of pointsof interest in X-ray radiographs were measured. Then, the inter-electrode center-to-center distances were computed and com-pared to the microscopic measures. It was found that the stere-ographical measures are in agreement with the microscopicalmeasures with a mean error of about 0.047 mm. It is informa-tive to note that without the bias correction step the mean errorwould be about 0.0865 mm. In other words, the bias correctionreduced the error by about 46% in this particular case.


V. DISCUSSIONS ANDCONCLUSION

Although the feasibility of X-ray stereophotogrammetry hasbeen established in this paper, further evaluation, refinement andoptimization are needed. First, X-ray imaging resolution maybe improved, which will lead to higher accuracy in both 3-D lo-calization and interelectrode distance estimation. Second, spec-ification of electrode centers and reference axial extremes inradiographs can be automated for better accuracy and repeata-bility. Third, the 3-D reference structure may be better designedto improve the accuracy and stability of the 3-D localizationalgorithm. Fourth, the clinical stereo-imaging protocol needsbeing designed, involving the location and orientation of thereference structure, the orientations of the patient’s head, andthe X-ray imaging parameters. Before performing more humanstudies, data from the visible human project, dry human skullsand cadaver heads can be utilized to adjust relevant variablesof the stereo-imaging procedure. Fifth, weak perspective resultsmay be compared with strong perspective results, in light of theextensive literature in stereotactic and image-guided surgery,such as [8] and [7]. Actually, we found in numerical simula-tion that even with truly orthogonal projections the mean errorin estimation of interelectrode distances would be still about0.04 mm, given the same data noise level. Therefore, we hypoth-esize that in our specific application there is no significant dif-ference between weak and strong perspective treatment. Sixth,algorithms should be developed to map thein vivo distributionof implanted electrodes onto the 3-D trajectory of the electrodearray in the corresponding CT volume using our unwrapping al-gorithms [26], [13].

In development of a mechanism for registration of stereo-imaging results and CT data, two key issues are 1) determinationof the trajectory of the implanted array, and 2) specification ofthe starting electrode of the array. It has been demonstrated thatthese two problems can be solved within an accuracy of about0.2 mm [13]. In the specification of the starting electrode, anexpected CT number of the central voxel can be utilized, whichcan be derived in experiments with phantoms. The registrationaccuracy is primarily determined by how precisely the startingelectrode can be specified. We estimate that the total registra-tion error would be about 0.25 mm, which should be useful inclinical research. Since a registration study is beyond the scopeof this paper, it will be performed later.

In conclusion, an X-ray stereo-photogrammetric approachhas been developed for 3-D localization of cochlear elec-trodes. The feasibility of the technique has been theoreticallyestablished via perturbation analysis, numerically quantifiedvia computer simulation, and experimentally validated usingphysical phantom and human data. We will further developthe technique and the protocol, produce the implanted arraymodel, and place it in the post-operative spiral CT imagevolume, so that both volumetric anatomy of the cochlea andaccurate positions of electrodes are presented in a unifiedframework. This geometric knowledge would allow modelingof electromagnetic fields about the implanted electrodes, andcorrelation between image-based features and post-implanta-tion performance parameters.

ACKNOWLEDGMENT

The authors would like to thank the following colleaguesat University of Iowa: B. Gantz with Department of Otolaryn-gology for advice and collaboration, J. Dyson with Medical In-strument Facility for construction of the array phantom, S. Wal-lace and A. Budd with Department of Geology, T. Moningerand K. Moore with Central Microscopy Research Facility for re-flex microscopic measurement of the array phantom, B. Mullan,C. Garrell, J. Pitcher, J. Beckler, L. Brunsting, and S. Yang fortechnical assistance in stereo-imaging; as well as E. Muka andG. Harding at Washington University for technical assistancein stereo-imaging. The demonstration array was provided byCochlear Inc. (Englewood, CO).

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Ge Wang (S’90–M’92–SM’00) is Associate Pro-fessor with Department of Radiology, Universityof Iowa, Iowa City. His interests are computedtomography (CT) and image analysis, with emphasison spiral/helical CT. He has 73 journal papers andnumerous other publications.

Dr. Wang serves as Associate Editor ofMedicalPhysics and Guest Editor for a special issue ofIEEE TRANSACTIONS ON MEDICAL IMAGING

(multi-row-detector spiral CT). His honors includethe 1996 Hounsfield Award from the Society of

Computed Body Tomography and Magnetic Resonance, the 1997 GiovanniDiChiro Award for Outstanding Scientific Research from theJournal ofComputer Assisted Tomography, and the 1999 Medical Physics Travel Awardfrom the American Association of Physicists in Medicine (AAPM) and theInstitute of Physics and Engineering in Medicine (IPEM). For detail, seehttp://dolphin.radiology.uiowa.edu/ge.

Margaret Skinner is Professor of Audiology inthe Department of Otolaryngology-Head & NeckSurgery at Washington University, St. Louis, MO,where she is Director of the Cochlear ImplantProgram. In her research, she investigates whatspeech-coding strategies and speech-processingparameters will provide recipients of multielectrode,intracochlear implants the best opportunity to recog-nize speech. Knowledge of electrode position in theinner ear is essential for understanding the relationbetween electrode array design, current required for

a hearing response, and patterning of stimulation that will maximize speechrecognition. She has authored a classic book on hearing aids and 47 otherpublications in peer-reviewed journals or books.

In recognition of her significant and lifelong contributions to understandingof human hearing, Dr. Skinner gave the 1998 Carhart Memoral Lecture to theAmerican Auditory Society; she received the Jerger Award for Research in Au-diology from the American Academy of Audiology in 2000.

Jay T. Rubinstein (S’80–M’82) received the Sc.B.and Sc.M. degrees in electrical engineering at BrownUniversity, Providence, RI, in 1981 and 1983,respectively. He subsequently attended the MedicalScientist Training Program at the University ofWashington, Seattle, where he received the M.D.and Ph.D. degrees in bioengineering in 1988.

He completed a surgical internship at Beth IsraelHospital, and otolaryngology residency at the Mass-achusetts Eye and Ear Infirmary with postdoctoralresearch training in the Department of Otology and

Laryngology, Harvard Medical School, Cambridge, MA. In 1995, he completeda clinical fellowship in Otology/Neurotology at The University of Iowa Hospi-tals and Clinics. Since then he has been an Assistant Professor of Otolaryn-gology, hysiology and Biophysics at The University of Iowa. His clinical in-terests encompass disease of the ear and temporal bone. His research interestsinclude physiological modeling of the electrically stimulated auditory system,and determinants of speech perception with cochlear implants.

Matthew A. Howard, III was born in Manchester,CT, in 1959. He received the B.A. degree in physicsand biology from Tufts University, Medford, MA, in1981 and the M.D. degree from the University of Vir-ginia School of Medicine, Charlottesville, in 1985.

Following his residency and neurosurgical trainingat the University of Washington, Seattle, he accepteda position as Assistant Professor of NeurologicalSurgery at the University of Iowa, Iowa City, wherehe specializes in epilepsy surgery. He is now anAssociate Professor of Neurosurgery. His research

interests include studies of hearing impairment, clinical research in epilepsytreatments, clinical models of Alzheimer’s disease, magnetic stereotaxis for thetreatment of focal neurological disorders, and investigations of the mechanicalproperties of the brain.

While a student at the University of Virginia, Dr. Howard received the JosephCollins Scholarship and was elected to Alpha Omega Alpha.

Michael W. Vannier (S’67–M’71) graduated fromthe University of Kentucky School of Medicine,Lexington, and completed a diagnostic radiologyresidency at the Mallinckrodt Institute of Radiology,St. Louis, MO. He holds degrees in engineeringfrom University of Kentucky and Colorado StateUniversity, Fort Collins, and was a student atHarvard University and the Massachusetts Instituteof Technology, Cambridge, MA.

He is Professor and Head of the Department of Ra-diology, University of Iowa School of Medicine. His

primary research interests are morphometry and anthropometry based on volu-metric imaging modalities, especially CT, MR, and PET/SPECT. He has morethan 250 scientific publications.

Dr. Vannier serves as Editor-in-Chief of the IEEE TRANSACTIONS ON

MEDICAL IMAGING. In 1994, he was inducted into the U.S. Space FoundationHall of Fame for work on digital medical imaging.

Digital X-ray stereophotogrammetry for cochlear implantation

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