Five degrees-of-freedom mechanical arm with remote center of motion (RCM) device for volumetric optical coherence tomography (OCT) retinal imaging

Handheld optical coherence tomography (HH-OCT) is gaining popularity for diagnosing retinal diseases in neonates (e.g. retinopathy of prematurity). Diagnosis accuracy is degraded by hand tremor and patient motion when using commercially available handheld retinal OCT probes. This work presents a low-cost arm designed to address ergonomic challenges of holding a commercial OCT probe and alleviating hand tremor. Experiments with a phantom eye show enhanced geometric uniformity and volumetric accuracy when obtaining OCT scans with our device compared to handheld imaging approaches. An in-vivo porcine volumetric image was also obtained with the mechanical arm demonstrating clinical deployability.


Introduction
Handheld Optical Coherence Tomography (HH-OCT) has proven to be effective in clinical diagnostics [1] and is gaining attention for bedside diagnostics of infant ophthalmic diseases [2][3][4][5][6][7][8][9][10].Although an effective diagnostic tool, HH-OCT has limitations associated with OCT probe ergonomics and physiological tremor [11][12][13][14][15][16].The imaging process requires careful aiming of the OCT's imaging plane through the pupil and keeping the probe steady for several seconds.For large high-definition images, the imaging process can take 1.4 to 6 seconds [12] during which the imager needs to maintain a fixed and steady position.Macular imaging requires orienting the OCT probe to aim the imaging plane directly at the macula, which, for supine subjects is a relatively easy-to-maintain position.For imaging the retinal periphery, however, the probe isn't aimed directly at the macula and the effect of gravity on the probe is multiplied due to the location of the probe's center of mass.The gravitational moment (torque) felt by the user when imaging the periphery makes these probe orientations more difficult to maintain and exacerbates the effects of tremor and user fatigue on C-mode (three-dimensional) OCT image quality [11].
C-mode images are generated by stacking evenly spaced B-mode (two-dimensional) OCT images.During handheld imaging, the user's tremor perturbs the OCT probe which may disrupt the spacing of the B-mode images or alter the origin position of each subsequent B-mode image.When the B-mode image spacing becomes non-uniform, or the image's origin position is moved, the generated image in 3D space is a distortion of reality.Imperfect geometric reconstruction may complicate accurate clinical diagnostics and increase the error in numeric estimations [17].
In addition to the challenges presented by physiological tremor, manually orienting and positioning the image plane with precision are difficult tasks in a clinical setting.Aiming the OCT probe to target specific retinal regions requires high precision of scan orientation (a fraction of a degree) which increases operational difficulty for clinicians or technicians.Simultaneously, an imager repositions the probe on a submillimetric scale.OCT resolution, as a function of light wavelength, is typically around 10 µm [18] and with a 14 mm field of view on the video monitor, targeting can only realistically be achieved using submillimetric adjustments, which is also at the boundary of tremor-limited human capabilities [19].
In the case of infant imaging in the neonatal intensive care unit (NICU) the user holds the probe above a baby's head while resting a palm on the patient's forehead for probe stability and bracing the baby's head.The simultaneous consideration of patient safety and comfort, as well as probe positioning, makes for a laborious procedure as demonstrated in [2].The challenges in obtaining HH-OCT images posed by physiological tremor and probe manipulation on submillimetric scales in addition to patient safety concerns, yield a process demanding high skill levels costing a heavy cognitive burden.
Prior works have proposed improved ergonomics in OCT probe designs for high-quality OCT-angiography and high-frequency engines to decrease imaging time [12].Others have proposed a statically balanced mechanical apparatus to carry an OCT probe for supine retinal imaging [20] which carries the mass of the probe freeing the practitioner to focus solely on probe positioning.Increasing the field of view of a single image captures a larger area of the retina which limits the need for complex mosaicing algorithms to generate comprehensive diagnostic images [16,21].These approaches have been shown to improve the image quality and clinical usability of OCT by reducing required imaging times, however, fine motion manipulation of the OCT probe is not available for repositioning the image plane and physiological tremor may still plague image quality.There are image segmentation techniques that correct for image aberrations introduced by tremor, however, rely on computational techniques and require registration as well as demand robust validation [22][23][24].
The literature also presents automated pupil tracking and actuated mirrors to precisely modulate the entry point of the OCT image beam without reliance on the user to manually control probe orientation [25].There are also works developing robotically-controlled systems for OCT that employ pupil and retinal tracking to autonomously aim an OCT probe for retinal imaging [26,27].Additionally, microscope-integrated intraoperative OCT (iOCT) systems are being used in surgical settings that allow for synchronous visualization of tissue and tools with stereoscopic color microscopic views and cross-sectional and volumetric OCT [28][29][30].Integrated iOCT takes advantage of the microscope's mechatronic micro-control enabling precision OCT positioning and these state-of-the-art surgical microscope systems have been shown to impact surgical decision making [31,32].Although robotically guided OCT systems and microcope iOCT offer unprecedented image quality and control, this work aims to supplement OCT imaging technology with a practical low-cost solution for controlling an OCT probe's position and orientation in the clinical setting.
In Section 2.1 we present a mechanical linkage with a statically balanced remote center of motion (RCM) device designed to carry a traditional handheld retinal OCT probe (Bioptigen Spectral Domain Optical Coherence Tomography System -SDOCT).While offloading the mass of the probe from the user, fine motion control of the OCT probe's pitch orientation around one axis is enabled with a parallelogram mechanism.There is also a rotary stage that enables roll orientation adjustment and both orientational adjustments obey an RCM constraint.There is an additional three degrees of freedom of cartesian adjustment of the OCT probe.
Section 3 presents our experimental results and shows the advantages afforded by the RCM device when imaging retinal phantoms.This work demonstrates that an RCM device is a viable tool to aid with OCT-based diagnostics by improving manipulation ergonomics, providing precision control of the OCT probe, and reducing the effects of physiological tremor during imaging.This device can simplify clinical OCT diagnosis for supine imaging by reducing the stress on imagers, particularly with uncooperative subjects (e.g.neonates) as well as improve the safety of the imaging procedure.Additionally, to support our group's work in validating a cooperative robotic retinal injection system [33], this device minimizes instrument error of retinal bleb volumes by reducing three-dimensional image aberrations.

Mechanical design
Figure 1 shows the device used in this study.It is a passive mechanical linkage comprised of an RCM device that is formally a Watt type I six-bar linkage [34] enabling pitch orientation control of the OCT probe.Use of this RCM mechanism was initially made for minimally invasive surgery [35] and adapted for robot-assisted retinal surgery [36,37].The RCM device is actuated by a Velmex A2509 linear slide with a 1mm pitch lead screw.Figure 1 demonstrates the RCM's range of motion defined by the motion constraints of the linear slide.The device is shown in its retracted configuration in Fig. 1 (a) and in the half extended configuration in Fig. 1 (b).Fig. 1 (a) also highlights the lever controlling the linear slide's rapid and fine advancement capabilities for gross probe orientation control, and fine micro-angular control when near a targeting region.The rapid advance acts by disengaging the nut on the linear carriage from the lead screw leaving the carriage to move freely.Shown in Fig. 2 is a torsional spring that acts on the primary base joint of the RCM device accounting for a percentage of the torque applied by the probe's mass.Without this spring, when disengaging the carriage nut for rapid advance the RCM device would be incapable of holding its orientation due to the mass of the OCT probe.Therefore, quick drooping when in the rapid advance mode is prevented by the torsional spring.The stiffness of the spring was estimated using virtual work simulated in CAD with the Creo Parametric 4.0 mechanism environment.
Displayed in Fig. 2 is the remote center of motion point, the virtual point in space around which the OCT image plane rotates and is determined based on the geometric dimensions of the six-bar linkage.The point is chosen, in this case, to be roughly aligned with the centroid of an Fig. 2. RCM device with ① the virtual remote center of motion point, defined by the RCM geometry, is also coincident with the rotary stage's rotational axis.The magnified detail depicts the static balancing spring that compensates for a portion of the OCT probe's mass to reduce the force on the linear slide nut and prevent complete extension due to the force of gravity acting on the probe.eyeball when the OCT image's focal point is the retina.With the RCM point at the centroid of the eye, the scan point can be carefully swept on the retina to locate anatomy more easily.
In addition to the pitch angle control of the OCT probe discussed above, there is a rotational platform that enables control of the probe's roll angle.The axis around which the platform rotates, its central axis, is coincident with the remote center of motion point encircled in Fig. 2. The coincidence of the RCM point and the roll axis allows simultaneous pitch angle and roll angle adjustment of the probe without disrupting the position of the RCM point in space.This allows for simultaneous multi-axis micro-angular orientational control of the OCT image plane, demonstrated in the film strip in Fig. 3, enabling precise targeting of retinal tissue and maintaining probe position and orientation without continued user input.
Attached to the distal end of the RCM linkage are three mutually orthogonal linear stages enabling three additional degrees of freedom of the OCT probe: Cartesian position in the x-axis (±16mm), y-axis (±25mm), and z-axis (±20mm) of the OCT probe frame and enables general compatibility with a wide range of OCT probes as well as lenses by allowing adjustments to align visual axis and desired focal point with the RCM point.The linear stage assembly is linked subsequently to the manually-actuated linear/angular stages that enable pitch and roll angle control, therefore, when manipulating the probe's Cartesian position, the alignment between the image plane and the RCM point degrades.Please refer to the attached visualizations for additional demonstration of the device's motion capabilities.This misalignment is not detrimental to the practical application of the device, however, as a larger search area of retinal tissue is facilitated when manipulating the probe with all the available degrees of freedom.It should be noted that the RCM device may not be compatible with every probe-lens combination available, in which case, the geometry of the device may be adjusted using the open-source CAD found on [38].We note the mechanism is easy to produce using 3D printing technology.

Experimental evaluation
The RCM device was evaluated using a Bioptigen 870nm SDOCT system with a Bioptigen general retinal bore lens to image metal spheres adhered to the retina of a Bioniko OPHT-FDS phantom eye (22mm equatorial diameter and 24mm anteroposterior diameter).C-Mode OCT images were taken of two 1mm diameter hardened bearing-quality steel balls fixed within a phantom eye at 0 • , 90 • , and 125 • from the vertical meridian (defined by a line intersecting a point on the pupil and the retina) as shown in Fig. 4.These angles were chosen to represent the macula, the equator of the eye, and the greatest angle that the RCM device permitted for imaging.With our RCM device, it would be possible to image select areas in the far periphery of the retina as discussed in [39].
The OCT handpiece is connected via a 1.3m flexible fiberoptic cable to a wheeled cart housing the SD-OCT system with a computer and viewing screen.The Bioptigen system was placed in the Free Run mode to locate the spheres with the handheld or the RCM-mounted approach.Then a rectangular 10 x 10 mm volumetric scan (1000 B-scans/volume of 1000 A-scans/ B-scan) was obtained when the examiner indicated locating the spheres.Three users attempted imaging the spheres in each of the angular positions within the phantom eye, and then the RCM device was used to image the spheres (operated by one expert user).The users included one highly experienced handheld OCT user, one user with some past experience with the handheld probe, and one who was inexperienced and received training prior to the study.All had practice training  runs before the experimental collection.We did not display the results of the 3D scans to the users and an independent analyst was responsible for analyzing the 3D volumes without labeling the data and the conditions.This provided blinding of the user and experimental conditions in the data analysis.
Figure 5 shows how the phantom eye was rigidly mounted to a surface at a height for the users to comfortably hold the probe.All users attempted three trials for each of the angular positions of the metal spheres and restarted their targeting approach at the beginning of each trial.A ClaroNAV MicronTracker Hx40 optical tracker (ClaroNav Toronto, Ontario, Canada) tracked the position of the OCT probe via attached markers [Fig.5(b)] throughout each trial.Once the metal spheres were located on OCT, a separate marker was used to indicate in the optical tracker data when OCT-image acquisition began.The image quality was compared between images from the traditional handheld and RCM device approaches by reconstructing the images and calculating volume and sphericity using Imaris 9.9, Oxford Instruments.Our quantitative analysis is based on the half-sphere images captured as OCT is only capable of capturing half of a sphere due to the inability of the imaging beam to penetrate metallic surfaces.The diameter of a ball in pixel numbers was measured from the en face view [40] of the OCT data.The known diameter of the ball was used to calculate the size of one lateral pixel.In the A-scan direction, the number of axial pixels in a cellophane tape layer was measured.A 50µm thick cellophane tape was used to calibrate one pixel.Using the pixel dimensions measured above, the boundary of a semicircle was manually traced in a B-scan image of the volume data.For each OCT volume data, several boundary traces were made in B-scan slices.The surface of a hemisphere was rendered in Imaris from the B-scan traces using the contour tracing method.The pixel dimensions in Imaris were set to the pixel sizes calculated above and the volume and sphericity of the hemisphere were measured using surface statistics.
In addition to quantifying image improvement by the reduced volumetric calculation error and sphericity uniformity afforded by the RCM device, we tracked the motion of the OCT probe during the imaging process using a ClaroNav MicronTracker Hx40 Optical Tracker.It should be noted that the Hx40 specifications state a 0.015 mm RMS jitter of stationary targets; probe movements during image acquisition are small enough that a stationary target assumption is reasonable.The probe's motion was then quantified by maximum positional variance, i.e. the Cartesianal displacement that is greatest along one of the probe's axes during the imaging process once the spheres were located on OCT.
To define positional variance, the probe's positions during imaging are stored in a matrix where i = [1, 2, 3, . . ., N] for N number of probe positions recorded.The centroids of the probe positions are then calculated Equation ( 1) is subtracted from Eq. ( 2) in another matrix, The singular values of ∆ in Eq. ( 3) indicate the positional variance in each Cartesianal direction, the largest being the maximum positional variance.We calculate the singular values via singular User 2 User 3 RCM [mm] ≤ 0.001 Fig. 6.The average maximum positional variance of OCT probe position for each user and for the RCM, for each angle placement of metal spheres within a phantom eye during an imaging procedure.Note the variance of the RCM is ≤ 0.001 using a ClaroNav MicronTracker model Hx40 which reports a jitter of 0.015mm RMS of static targets.We assume the motions of the probe during imaging are nearly static, as this is required for clear images.
value decomposition, UΣV = svd(∆), where U and V are the left and right singular vectors, respectively.The maximum positional variance of the OCT probe is given by the largest singular value, i.e. σ m = max(Σ), the averages of which are plotted in Fig. 6 for all the users for each experimental condition.
Finally, an example of a post-injection OCT image using the RCM device was performed in vivo on a pig.The SD-OCT 870nm system used in this study, according to the manufacturer, met the ANSI standards for ocular exposure to light of <700µW of continuous-wave power in the 800-900nm spectral region).This allows continuous exposure for up to 8 hours [41][42][43][44].The animal was handled in accordance with all applicable international, national, and institutional guidelines for the care and use of animals, including the National Institutes of Health Guide for the Care and Use of Laboratory Animals and the ARVO Statement for the Use of Animals in Ophthalmic and Vision Research.All procedures were approved by the Vanderbilt University Medical Center Institutional Animal Care and Use Committee (IACUC) # M1800009-01.
Anesthesia was induced with an injectable combination of Telazol (4.4mg/kg), Ketamine (2.2 mg/kg), and Xylazine (2.2 mg/kg) given intramuscularly.Following the induction, the animal was placed on Isoflurane inhalation anesthesia to establish a maintenance plane of anesthesia with intubation and mechanical ventilation.After a subretinal injection of 15µl balanced salt solution was administered, the RCM-mounted OCT handpiece connected via a 1.3-m flexible fiberoptic cable to a wheeled cart housing the SD-OCT system with computer and viewing screen was positioned over the eye.The Bioptigen system was placed in the Free Run Mode to locate the bleb with the RCM-mounted approach.Then a rectangular 10 x 10 mm volumetric scan was obtained.The time to place the RCM-mounted probe over the eye, find this bleb, and obtain the rectangular volumetric scan image was two minutes.

Results
The sphere volumes were calculated from acquired C-Mode OCT images using the previously described methods with example renderings from each imaging scenario shown in Figure 7.The results from images acquired using the handheld approach and RCM device are summarized in Table 1 and Table 2, respectively.Although other groups have shown smaller calculated volume error, our OCT system's resolution gives a 14µm uncertainty which propagates in our volumetric calculation.However, from a comparative standpoint, since the same probe is used in both the handheld and RCM approaches, it is clear the effects of tremor during handheld imaging are virtually eliminated when using the RCM device.Tables 1 and 2 follow the error reporting and formatting in [28].Volumetric error is calculated using a ground truth established from diameter measurements of the spheres.The calculated volume is the volume obtained from the procedure using Imaris presented as the mean ± standard deviation.The mean absolute error is the average of the absolute value of the difference between the calculated and nominal volume.The mean absolute percent error is the ratio of the mean absolute volume error and the nominal volume.
Additionally, the handheld and RCM approaches had 29.6% and 5.6% overall failure rates of sphere imaging, respectively, indicating an improved ability to acquire images when using the RCM device.Of note, higher imaging failure rates were recorded as the spheres approached the retinal periphery (i.e.larger angles from the vertical meridian).
The average maximum positional variance of the OCT probe across all imaging scenarios for each user is plotted in Fig. 6.The largest positional variance using the handheld approach was 0.248 mm and 0.001 mm when imaging with the RCM device.The significant decrease in probe motion during imaging with our device is a major contributor to uniform sphere reconstruction discussed below and suggests aiding in decreasing the error in calculated volume.As a measure of geometric accuracy of acquired images of the spheres, we used the sphericity measure as defined by [45].Given a sphere with the same volume as the particle, the sphericity is the ratio of the sphere's surface area to the particle's surface area: Since the OCT is only capturing a half sphere, A and V in Eq. ( 4) are the area and volume of the half spheres as measured in Imaris from the OCT images.A is therefore defined as A = 3  4 πd 2 (surface area of a sphere half including its base) and V = 1 12 πd 3 .For half a sphere, the maximum theoretical sphericity is 0.84.The appearance of the spheres in Fig. 7 visually depicts Eq. ( 4) with a ψ value departing from 0.84 in Fig. 7 (a),(b),(c) and approaching 0.84 in Fig. 7 (d),(e),(f).
The sphericity results from the handheld approach are summarized in Table 3 and from the RCM device in Table 4.The tables present the mean ± standard deviation of sphericity and the mean absolute error as well as the mean absolute percentage error of the calculated sphericity, defined the same as for the volume above.The tables show that the sphericity percent error when using the RCM is less than 3% and it is up to 10 times larger when using the OCT as a handheld device.Additionally, imaging with the RCM device yielded uniformity in sphericity between imaging angles in contrast to the handheld approach which yielded non-uniform sphericity at steep imaging angles.Images taken with the RCM device are characterized by ψ values approaching 0.84 demonstrating spherical reconstruction with less distortion compared to the handheld approach.A Mann-Whitney rank sum test showed significant differences in the measured sphericity between approaches across all trials (p≤ 0.002) (SigmaPlot, SPSS, Inc., Palo Alto, CA).
Finally, as a demonstration of in vivo use, an example post-injection OCT image using the RCM device performed in vivo on an anesthetized pig after a subretinal injection of 15 µl balanced salt solution is presented in Fig. 8.The same Bioptigen general retinal bore lens was used as described above for imaging the metal spheres.The in vivo porcine imaging was a demonstration that the RCM device could be used to image an in vivo retinal structure.There was no probe tracking conducted during this imaging and no comparison to the handheld approach was made.Selected B-mode images on either side of the retinal injection are shown alongside the corresponding en face image in Fig. 8

Discussion and conclusion
We designed and fabricated a practical rigid mechanical linkage with five degrees of freedom with an RCM device for stable C-Mode retinal OCT imaging.The device demonstrated a profound image quality improvement when compared to traditional manual imaging techniques by significantly decreasing the probe's positional variance during an imaging process.The improved image quality yielded decreased volume estimation error and improved preservation of sphere geometry.In addition to improved image quality, this device enables fine OCT image plane manipulability without compromising the image.
The presented RCM device offers five degrees of freedom of orientational and positional control of the OCT probe.The roll and pitch degrees of freedom maintain alignment of the imaging plane and RCM point.The three cartesian degrees of freedom are attached distally to the RCM device which, when manipulated, yield RCM point misalignment.On initial setup of the device with a particular probe, the home position is marked on each of the cartesian actuators for easy realignment after an imaging procedure.In addition to offering fine positional control of the imaging plane with respect to the eye, these 3 degrees of freedom make the device compatible with a wide range of possible OCT probes.If other probes need accommodation that does not fit with this design, the device may be easily printed using rapid manufacturing techniques as we have demonstrated in this work.
The literature (e.g.[28,32]) presents a similar experimental evaluation of OCT systems reporting lower volumetric estimation error than we report in this work.Our OCT system's experimentally obtained resolution along with our experimental setup using a metallic bearing ball limit our minimum achievable volumetric calculation.The surface of the metal ball scatters light thereby creating a larger boundary around the outer surface in the acquired OCT image than another imaging target with a smaller refractive index.Given that we are manually drawing boundaries for volume calculations in each of the B-Mode images, it is reasonable to expect an error on the magnitude we have presented.In the most ideal imaging scenarios in our experiments, we find an absolute percent error in volume calculation within the expected range when factoring system resolution.Further, our sphericity results indicate optimal geometric reconstruction of the imaged hemispheres when using our device in comparison to the less-than-ideal images from the handheld approach.
Our work proves to address the challenges in obtaining clear C-Mode images and can aid in continued research requiring high-fidelity OCT images.Our device can also potentially be adopted as a clinical aid for acquiring more stable images during bedside imaging in the NICU.Disclosures.The authors declare no conflicts of interest.

Fig. 1 .
Fig. 1.CAD model demonstrating the pitch degree of freedom of the RCM device in its a) retracted and b) half extended configurations, respectively.The device is comprised of an ① RCM component which is categorized as a Watt type I six-bar linkage that is actuated by a ② Velmex A2509 linear slide with ③ rapid advance lock shown in the rapid advance configuration and fine motion configuration.

Fig. 3 .
Fig. 3.A demonstration of the degrees of freedom of the device which obeys the RCM constraint with RCM point identified as the black dot and image beam depicted as a red cone (see Visualization 1).a) The reference, or home position of the device with the linear slide completely retracted.b) The rotary stage with a negative rotation angle and, c) a positive rotation angle, both with the linear slide retracted.d) An alternative reference position of the device with the linear slide partially extended.e) The rotary stage with a negative rotation angle and, d) a positive rotation angle with the extended linear slide.

Fig. 4 .
Fig. 4. A phantom eye used for experimental validation of the RCM device to capture C-Mode OCT images of two 1mm spheres fixed to the phantom retina at three different angles from the vertical meridian a) 0 • , b) 90 • , and c) 125 • .The phantom eye is equipped with a cornea through which imaging is performed that is assembled in d) once the spheres have been placed masking the exact position of the spheres from the imager's naked eye.

Fig. 5 .
Fig. 5. Experimental setup for C-Mode OCT imaging of two 1mm sphere balls fixed within a phantom eye.a) Demonstration of the experimental setup for handheld imaging and b) imaging using the RCM device.① The computer monitor displaying the real-time OCT image, ② Bioptigen SDOCT probe, ③ phantom eye with metal spheres mounted within, ④ marker for ClaroNav MicronTracker Hx40 positional tracking and, ⑤ six-bar Watt Type I RCM mechanism with attached OCT probe.

Fig. 7 .
Fig. 7. Examples of C-Mode image reconstructions of two 1 mm spheres fixed in a phantom eye with the handheld approach at a) 0 • b) 90 • and c) 125 • from the vertical meridian demonstrating increased image distortions at steeper angles.C-Mode images from images using the RCM device at d) 0 • e) 90 • and f) 125 • from the vertical meridian demonstrating the improved image quality when using the RCM approach.

Fig. 8 .
Fig. 8.An in vivo image of a subretinal injection of 15 µl balanced salt solution in an anesthetized pig.Selected B-mode images used in acquiring the 3D reconstruction in (a) and (c) with position their positions identified with a green line in the corresponding enface image in (b) and (d).The 3D reconstruction of the formed bleb beneath the retina from Imaris is shown in (e).

Funding.
National Institutes of Health (CA68485, DK20593, DK58404, DK59637, EY08126); National Eye Institute (R01EY028133).Infection, Immunology, and Inflammation (VI4).We thank the assistance of Anthony Daniels, M.D., Jamie Adcock, and M. Susan Fultz as well as the Light Surgical Research and Training Laboratory.The animal was handled in accordance with all applicable international, national, and institutional guidelines for the care and use of animals, including the National Institutes of Health Guide for the Care and Use of Laboratory Animals and the ARVO Statement for the Use of Animals in Ophthalmic and Vision Research.All procedures were approved by the Vanderbilt University Medical Center Institutional Animal Care and Use Committee (IACUC) # M1800009-01.