Threshold Amplitude and Frequency for Ocular Tissue Release from a Vibrating Instrument: An Experimental Study

Abstract

purpose. During retinal pigment epithelium (RPE) and choroid graft translocation in the treatment of patients with exudative age-related macular degeneration, the adhesion of the graft to the translocation instrument complicated its submacular release. Vibration of the instrument improved the release of the graft. This study was conducted to validate the effectiveness of the principle of vibration and to determine the threshold amplitude and frequency required for development of an optimized instrument.

methods. An experimental in vitro model with fresh porcine RPE-choroid grafts was used. Release of the graft was studied by a masked observer for amplitudes in the range of 0.05 to 1.2 mm and frequencies in the range of 25 to 200 Hz in the horizontal plane.

results. The minimum threshold amplitude required to release the graft was approximately 0.15 mm from a frequency of 100 Hz and higher.

conclusions. This study confirmed the clinical experience that vibration of an instrument induces the release of the RPE-choroid graft. The minimum threshold amplitude and frequency needed for optimum tissue release were estimated.

Aretinal pigment epithelium (RPE)-choroid graft translocation is used as a last treatment option in patients with exudative age-related macular degeneration (AMD). ^{1 2} During this surgery, the neovascular membrane is removed from the subretinal space through a paramacular retinotomy in the temporal raphe. This procedure is preceded by the induction of a posterior vitreous detachment and a complete vitrectomy. After circular heavy diathermia in the midperiphery at the 12 o’clock position, a full-thickness graft of retina, RPE, and choroid of approximately 2 × 3 mm is cut. The graft is grasped from the choroidal side, and the neurosensory retina is removed just before the graft is repositioned under the macula through the existing paramacular retinotomy. The midperipheral donor site is surrounded with laser coagulation followed by a silicone oil tamponade. ^{1 2}  

The most critical step during this surgery was the submacular release of the graft, which was complicated by the adhesion of the graft to the translocation instrument. 

Two kinds of translocation instruments were used—the aspiration-reflux spatula and the fine forceps currently used (both from the Dutch Ophthalmic Research Center [DORC], Zuidland, the Netherlands; Fig. 1 )—but both presented the problem of persistent adhesion. These instruments hold the graft from the choroidal side (by suction and grasping, respectively) to avoid damage to the RPE. 

The injection of perfluorocarbon liquid (PFCL) to hold the graft in place and facilitate release of the graft when retracting the instrument slightly improved the release. However, real improvement was achieved by having the instrument vibrate during the submacular release of the graft. Vibration was transmitted to the translocation instrument by attaching a mobile phone vibration device (which had a frequency of 140 Hz) to the handle of the translocation instrument. 

The rationale for vibrating the instrument was to exceed the maximum friction force between the graft and the instrument by accelerating the instrument. The amplitude and frequency of the vibration of the instrument determine the acceleration. 

Therefore, the present study was performed to validate the principle of tissue release by vibration and to determine the minimum threshold amplitude and frequency needed for optimum tissue release from a vibrating translocation instrument. 

Materials and Methods

Preparation of the Graft

Freshly enucleated porcine eyes were prepared (within 12 hours after death). First, the anterior segment was removed together with the vitreous. The posterior segment was dissected into two parts, and the neural retina was removed. 

Small grafts (∼2 mm²) consisting of the RPE and choroid were cut and separated from the sclera. These grafts were kept in physiologic salt solution (PSS) until use in the experiments. 

Loading of the Graft onto the Instrument

For every experiment, the graft was placed on an aspiration-reflux spatula (DORC), which was connected to a 5-mL syringe by a 10-cm long polyurethane tube (lumen diameter, 2.3 mm) and filled with PSS. Gentle suction was applied by retracting the syringe plunger for 1 mL, as used during the RPE-choroid translocation surgery in patients. Subsequently, the suction was terminated by a slow reflux, and finally the syringe was disconnected from the spatula. This procedure resulted in a graft adhering to the spatula in a manner that mimics the clinical situation. A new graft was used for every measurement. 

Maximum Friction Force of the Graft

First, an experiment was designed to determine the maximum friction force between the graft and the aspiration-reflux spatula (Fig. 2) . The results of this experiment were to be used as input for the mathematical model. 

On one platform of a fine balance, we secured an aspiration spatula connected by a 10-cm long polyurethane tube (lumen diameter, 2.3 mm) to a 10-mL syringe. The RPE-side of a graft was fixated by applying strong suction (exerted by retracting the plunger of a 10-mL syringe for 8 mL) to the aspiration spatula, while the choroidal side of the same graft was aspirated with another aspiration-reflux spatula by gentle 1-mL suction and slow reflux. This aspiration-reflux spatula was fixated into an instrument holder. Weights were added to the other side of the balance until tissue release was achieved from the aspiration-reflux spatula by the choroidal side of the graft (Fig. 2) . The maximum friction force was calculated from the mass and position of the weights. The experiment was repeated eight times. 

Mathematical Model

A straightforward mathematical model was derived. The model assumed release of the graft when its inertial force exceeded the friction force between the graft and the instrument. 

The graft was modeled as a rigid body, and the friction force was assumed to be acting on the graft’s center of mass. No assumptions were made regarding the type of friction between the graft and the spatula. Interactions between the surrounding PSS and the graft were not included in the model. 

We estimated the mass of the graft at 0.8 mg by multiplying the dimensions of the graft by its density (2 mm × 2 mm × 0.2 mm × 1000 kg/m³). 

The x-direction for the adhered graft lies in the plane of the blade of the spatula, parallel to the lateral edges (Fig. 3) . The equation of motion in the x-direction for the graft was defined as  

\[F(t){=}m\frac{d^{2}}{dt^{2}}(x(t)).\]

In this equation, F(t) is the friction force acting on the graft, m is the mass of the graft, and x(t) is the position of the instrument (Fig. 3)and can be written as  

\[x(t){=}\frac{A}{1000}\ \mathrm{sin}\ (2{\pi}ft),\]

where A is the amplitude of the vibration (in millimeters) and f is the frequency (in hertz). 

Acceleration of the graft can then be expressed as  

\[\frac{d^{2}}{dt^{2}}(x(t)){=}\frac{d^{2}}{dt^{2}}\left(\frac{A}{1000}\ \mathrm{sin}\ (2{\pi}ft)\right){=}{-}\frac{A}{1000}\ (2{\pi}f)^{2}\ \mathrm{sin}\ (2{\pi}ft).\]

 

The absolute maximum value of the friction force throughout time is given by  

\[\mathrm{max}\ ({\vert}F(t){\vert}){=}m{\cdot}\frac{A}{1000}(2{\pi}f)^{2}{=}\frac{{\pi}^{2}mAf^{2}}{250}.\]

If this value exceeds the maximum friction force (F _max), the model predicts tissue release. 

The threshold frequency and amplitude are therefore given by:  

\[F_{\mathrm{max}}{=}\frac{{\pi}^{2}mAf^{2}}{250}.\]

 

Experimental Setup

An experimental setup was used to validate the results of the mathematical model (Fig 3) . The experimental setup consisted of an aspiration-reflux spatula fixated into a linear slide. The linear slide consisted of two leaf springs that allowed motion of the instrument holder in the horizontal plane exclusively (i.e., with the spatula moving backward and forward). The tip of the spatula was placed horizontally in a Petri dish filled with PSS to simulate the conditions during surgery (Fig. 3) . 

To make the instrument vibrate, the linear slide was physically attached to a loudspeaker operating as a linear motor. The loudspeaker was connected to one channel of a stereo amplifier. The amplifier was connected to the sound card of a computer. Vibration of the instrument was achieved by supplying a sinusoidal input signal generated by the computer. 

The position of the instrument (x(t)) was measured at 1000 Hz throughout the experiment by a laser displacement sensor (optoNCDT ILD1401-20; Micro-Epsilon Messtechnik GmbH & Co., Ortenburg, Germany). The data were transmitted to the computer by means of a data-acquisition device (LabJack UE9; LabJack Corp., Lakewood, CO). 

Experimental Method

Five seconds after release of the suction, the instrument was vibrated for 1 second. The vibration signal consisted of a sinusoidal waveform starting with a smooth increase to the maximum amplitude (within 250 ms) and ending with smooth decrease to resting position. Special care was taken to have a fast but controlled increase of the amplitude of the input signal to the desired value to avoid an initial peak amplitude overshoot as observed in pilot measurements. 

All experiments were monitored on video and assessed after the experiments by an examiner masked to frequency and amplitude. Release of the graft was defined as a complete loss of contact between graft and spatula. Recordings of a sham procedure were made for each combination of frequency and amplitude. 

To identify the threshold amplitude and frequency, the experiment was performed at eight frequencies and at four amplitudes per frequency. Each combination of frequency and amplitude was tested five times. If the graft was released three out of five times or more, the graft was said to be released at that combination of frequency and amplitude. 

For each frequency, the first amplitude was selected on the basis of the computer simulation model. The sequential amplitudes were chosen with the bisection method: If the graft had been released at the last amplitude, the next amplitude was set to the average of the last amplitude and the highest amplitude at which the graft had not been released and vice versa. 

The data were saved and analyzed and the experimental set up controlled by computer (MatLab; The MathWorks, Natick, MA). 

Measurement of the Mobile Phone Vibration Device

The amplitude and the movement directions of the tip of the vibrating forceps currently used during surgery were determined. 

The instrument was fixated between silicon rubber pads to mimic the surgeon’s hand. Measurements were performed at a frequency of 70 and 140 Hz and were recorded in two planes: (1) straight superior of the instrument (observing the forward-backward and side-to-side movement) and (2) from the side of the instrument (observing the upward and downward movement). Recordings (1250 frames per second) were made with a high-speed camera system (Motion Pro 10000 and associated MiDAS software; Redlake Imaging, Tucson, AZ) attached to a microscope (SZ-PT SZ-40; Olympus, Tokyo, Japan). 

Results

Maximum Friction Force of the Graft

The maximum friction force between the graft and the instrument was 0.32 ± 0.11 mN (mean ± SD). 

Mathematical Model

The value of the maximum friction force, as estimated in the balance model, was used in equation 5of the mathematical model to predict the threshold amplitudes for each vibration frequency (Fig. 4) . 

The predicted threshold amplitudes were higher than the amplitudes determined with the experimental setup. 

Experimental Results

The release of the RPE-choroid graft from the instrument could be easily observed. Contact between graft and instrument was lost immediately after onset of the vibration. The graft remained adherent to the instrument during the sham procedures. 

The modes of the experimental results are shown in Figure 4 . With increasing frequency, the threshold amplitudes remain approximately constant (± 0.15 mm) from ∼100 Hz and higher. 

The initial amplitude that was tested at 200 Hz did not induce tissue release, and this result necessitated a break from the original experimental protocol. The initial amplitude was increased to 0.15 mm, and the protocol was executed again. In addition, experiments were performed at amplitudes below the initial amplitude to determine whether the results of the experiments at the initial amplitude were accurate. 

Measurement of the Mobile Phone Vibration Device

The amplitude (in millimeters) of the tip of the vibrating forceps in different movement directions (i.e., in different planes), is shown in Table 1 . The movements were ellipse-shaped, reflecting the direction of vibration forces caused by the rotating unbalanced motor in the mobile phone vibration device. 

Discussion

To improve the predictability of the submacular release of the RPE-choroid graft during translocation surgery, we empirically had the translocation instrument vibrate. The vibration was achieved by attaching a mobile phone vibration device (frequency, 140 Hz) to the handle of the instrument. The translocation instrument tip moved approximately less than a quarter of the diameter of a 20-gauge cannula, when viewed with standard video camera recordings edited with video software (Pinnacle Studio ver. 9; Pinnacle Systems, Mountain View, CA). 

Vibration of the translocation instrument improved the submacular release of the graft. Because the vibrating instrument was in contact with the choroidal side of the graft, damage to the RPE and retina was unlikely. Potential damage is probably balanced by the advantage gained by having a predictable release with a subsequent decrease of submacular manipulations. Further studies are necessary to exclude an increased release of RPE cells by having the instrument vibrate. However, a smooth graft insertion and less manipulation correlated with better visual outcome. ³  

In this study, a minimum amplitude of ∼0.15 mm was needed to release the graft. This minimum threshold amplitude was effective at a frequency of 100 Hz and higher. At lower frequencies, a higher amplitude was needed for the release. 

High-speed camera observation of the tip of the instrument attached to the mobile phone vibration device revealed that the amplitude in the horizontal plane (forward and backward and side-to-side movement) was already just above the threshold amplitude at a frequency of 140 Hz, as estimated in this study. The vertical amplitude, however, was approximately 0.40 mm. It is uncertain whether release of the graft in the clinical setting was achieved by the amplitude in the horizontal or vertical plane. It is likely, however, that movement in the horizontal plane achieves the safest and most effective instrument tip acceleration to overcome the friction between instrument and tissue. 

For the experimental setup, an aspiration-reflux spatula was used instead of the fine forceps currently used during surgery. The rationale was that the suction force could be very accurately reproduced in all measurements, whereas it would have been difficult to achieve an identical grasping force with the forceps or to grasp an identical amount of tissue for each graft. 

The mathematical model identified the upper boundary of the theoretical threshold curve. The model predicted higher threshold values than were found in our experimental model. This result may be explained by (1) not taking the influence of fluid flow into account; and (2) the estimate of the measured maximum friction force between the graft and the aspiration-reflux spatula was too high in the experimental model, because it was measured in air. However, the shape of the curve of the mathematical model is almost identical, as estimated with the experimental mode, which indicates that the variables used in the mathematical model were correct. 

Backward retraction of the instrument as occurs during surgery was not performed. In our experimental study, the graft was released immediately after onset of the vibration. It is likely that the shearing force caused by vibration is greater than the shearing force of a slowly retracting instrument would be. Therefore, additional retraction may not have influenced the results. 

The present study confirmed the clinical impression that having an instrument vibrate helped the release of the RPE-choroid graft. The principle of vibration-induced release may also be valuable for other surgical techniques in ophthalmology. The threshold amplitudes and frequencies for tissue release as well as the instrument tip movements were determined, to be better able to develop an optimized instrument. 

 Supported by the SWOO-Flieringa Foundation (Foundation for Scientific Research, Eye Hospital, Rotterdam), Rotterdam Eye Hospital, Rotterdam, The Netherlands.

 Submitted for publication September 19, 2007; revised December 1, 2007; accepted February 22, 2008.

 Disclosure: K. Maaijwe, None; T. Koolen, None; D. Rosenbrand, None; E. Jacobs, None; S. Kleinheerenbrink, None; A. Knulst, None; J. Bos, None; W.P. Holland, None; A. Brouwer, None; J.C. van Meurs, P; S. Schutte, None

 The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked “advertisement” in accordance with 18 U.S.C. §1734 solely to indicate this fact.

 

Figure 1.

 

The aspiration-reflux spatula (A) and the translocation forceps (B). The diameter of A 10-eurocent coin is 19.75 mm.

Figure 2.

 

The experimental setup to determine the maximum friction force between the graft and the aspiration-reflux spatula. An RPE-choroid graft was attached on the RPE side to a spatula attached to the tip of the balance (suction, 8 mL) and on the choroidal side to another spatula (suction and reflux, 1 mL). Weights were added to the other side of the balance until tissue release from the choroidal side was achieved.

Figure 3.

 

Experimental setup to determine the threshold amplitudes and frequencies for sinusoidal vibrations that induce tissue release from an instrument.

Figure 4.

 

Frequencies and amplitudes to release the graft as predicted with the mathematical model and as estimated with the experiment. The mathematical model curve divides the graph into grafts released (above the line) and grafts not released (below the line).

Table 1.

 

The Amplitude of the Ellipse-Shaped Movements of the Tip of the Forceps Attached to a Mobile Phone Vibration Device

Frequency (Hz)	Movement
		Forward-Backward	Side-to-Side	Up-Down
70	0.22	0.29	0.45
140	0.18	0.19	0.40

 Data are amplitudes expressed in millimeters.

The authors thank Nico de Jong and Rik Vos (Department of Biomedical Engineering, Erasmus University Medical Center) for assisting us in using their high-speed camera.