purpose. To develop new test procedures for frequency-doubling technology (FDT) perimetry that improve performance beyond those currently used.

methods. Two novel threshold estimation procedures were evaluated: a rapid,
efficient binary search technique (REBS) and a
maximum-likelihood estimation (ZEST) procedure. A computerized
visual field simulation model was developed to determine the accuracy
and efficiency of these procedures. This model was constructed using
previously derived characteristics of FDT perimetry from both normal
observers (*n* = 506) and those with glaucomatous
visual field loss (*n* = 352). The computer
simulation program was used to determine the best parameters for the
two new procedures and the effect of variability and response errors on
algorithm performance. Comparisons were made to the performance of the
modified binary search (MOBS) procedure used in the current commercial
implementation of the FDT perimeter.

results. Both the optimized REBS and ZEST procedures approximately halved the time required for FDT threshold testing without loss of accuracy or reproducibility.

conclusions. With suitable parameter choices, comparable performance was achieved using either ZEST or REBS. Simulation results indicate that accurate thresholds can be measured with an optimized ZEST or REBS procedure in approximately half the time required by traditional estimation methods.

^{ 1 }

^{ 2 }The frequency-doubling effect occurs when a low-spatial-frequency (<4 cyc/deg) grating is counterphased at a high temporal rate (>15 Hz), resulting in the grating’s appearing to have twice its original spatial frequency.

^{ 3 }

^{ 4 }The physiological substrate for the frequency-doubling percept has been postulated to be a subset of magnocellular ganglion cells (M-cells) with nonlinear response properties,

^{ 2 }approximately 15% of the M-cell population (2% of all ganglion cells).

^{ 5 }FDT perimetry generates a frequency-doubling stimulus, and contrast thresholds are measured for detection of the FDT stimulus. FDT perimetry is a reliable method of detecting glaucomatous visual field loss,

^{ 6 }and its reproducibility compares favorably with conventional perimetry.

^{ 1 }

^{ 7 }

^{ 8 }with an average test time of approximately 5 minutes. This compares favorably with the average test time of 15 minutes for a conventional 24-2 full-threshold or 8 minutes for a Swedish interactive threshold algorithm (SITA) standard strategy (Humphrey Systems).

^{ 9 }

^{ 10 }

^{ 11 }

^{ 12 }

^{ 13 }because similar procedures (SITA) have been applied successfully to conventional perimetry.

^{ 14 }

^{ 15 }

^{ 16 }We also optimized the MOBS procedure for use with FDT perimetry to produce a rapid, efficient binary search (REBS).

^{ 11 }

^{ 16 }

^{ 17 }We used simulation to optimize the input parameters and termination criteria of the algorithms and to evaluate the relative importance of these parameters. We compared performance of these algorithms with the MOBS procedure used in the proprietary FDT perimeter. More than 1000 test procedures were assessed. A limited number of these procedures are presented in this report. The full results are available at http://www.computing.edu.au/∼andrew/Barramundi/fdp.html.

^{ 17 }

^{ 18 }The SD of the Gaussian was varied as 0, 1, and 2 dB to simulate patient variability.

^{ 7 }Figure 1 shows an example of an input threshold of 14 dB and a Gaussian distribution with an SD of 1 dB. The threshold used to determine a response is 14 dB with probability 0.40, 13 or 15 dB with probability 0.24, and so on. False-positive and false-negative rates were incorporated as a probability that the subject would respond yes or no, respectively, regardless of the stimulus presented. False-positive and -negative rates of 0%, 10%, and 30% were used within the simulation.

^{ 11 }a variant of QUEST,

^{ 13 }is based on a maximum-likelihood threshold determination. For each stimulus location, an initial probability density function (pdf) is defined for all possible thresholds, which states for each possible threshold (0–20 dB for FDT perimetry) the probability that any patient will have a threshold at that location. The first stimulus is presented with a contrast equal to the mean of this pdf. The subject’s response to that stimulus is used to modify the pdf for the next presentation.

*P*= 0.001). The mean of this pdf is 12 dB, which is presented to the subject. If the subject responds no, then the pdf is modified to give more probability to lower decibel levels (Fig. 2a , bottom). The mean of this new pdf determines the next stimulus presentation at this location (9 dB in this case). If the subject responds yes, then the pdf is modified to give a pdf as shown in the bottom panel of Figure 2b , with more weight on higher decibel levels. A stimulus of 15 dB, the mean of this new pdf, is presented next.

^{ 10 }have noted, the initial pdf can be derived from demographic studies and can be biased by an examiner’s intuition about the subject’s likely thresholds. The likelihood function should reflect the variability inherent in the detection task as well as subjective false error rates. Finally, the termination rule should be chosen with realistic clinical outcomes in mind. One approach is to finish the procedure when the SD (ς) of the pdf declines below a fixed value, which assures a level of confidence about the determined threshold. For example, if ς is chosen to be 1 dB, then there is a 95% chance that the real threshold lies within a ±2-dB range of the measured threshold. One disadvantage of this approach is that unreliable observers may require many presentations. An alternative is to terminate the procedure after a fixed number of presentations, and the 95% confidence interval of the final estimate can be determined from the final pdf.

*pdfu*); pdfs equal to the normalized histogram of sensitivity from the normal eyes in Table 1 (

*pdfn*); pdfs equal to the normalized histogram of sensitivity from the eyes with glaucomatous visual field loss in Table 1 (

*pdfg*); and pdfs formed by combining the normal and glaucomatous pdfs (

*pdfc*). The combined pdfs added the bottom 5% of

*pdfg*to

*pdfn.*

^{ 10 }Before the addition, the bottom 5% of

*pdfg*was reduced by a weighting factor so that it did not dominate the normal portion of the pdf. Twelve different weighting factors were evaluated. The results presented herein are for a weighting factor of 0.6. Each class of pdf contained a single pdf for each of the 17 visual field locations. There was little difference in the form of the 17 pdfs in each class; however, the means of the peripheral pdfs were generally lower than those for the central five locations. The resultant

*pdfc*pdfs were trimodal (Fig. 2 , top panels), unlike the bimodal pdf of Vingrys and Pianta,

^{ 10 }which was derived from advanced glaucomatous deficits.

^{ 7 }this rounding is unlikely to be clinically significant.

^{ 19 }requires selecting the middle number of a range and then adjustment of the range according to the response. For example, to find a number between 0 and 100, the first selection would be 50. If 50 is too high, the target number falls in the range 1 to 49, and the next selection would be 25, and so on. Binary search is a special case of a maximum-likelihood procedure where the initial pdf considers all thresholds equally likely, and the likelihood function is equal to 100% for thresholds one side of the middle and 0% for other thresholds.

^{ 8 }introduced MOBS. MOBS follows the binary-search strategy but also checks the range end points if two yes or no responses occur in succession. If the end point is not consistent—for example, the subject could not see the intensity at the bottom of the range—then the range is widened to the previous end point. A reversal occurs when the previous response differs from the current response. MOBS terminates when the range reaches a minimum width and a fixed number of reversals have occurred.

*pdfn*,

*pdfg*,

*pdfc*, and

*pdfu*respectively. The leftmost four bars are for ZEST procedures terminating with ς = 2 dB, the middle four bars terminating with ς = 1 dB. The final two bars represent the best of the procedures, stopping after three and four presentations, respectively. The best procedure was that with the lowest absolute value of mean error ± SD.

*pdfn*or

*pdfc*on unreliable glaucomatous subjects. In most cases, the magnitude of the mean error is unlikely to affect clinical outcomes, (between −1 and 1 dB, except when using

*pdfg*on normal subjects or

*pdfn*on subjects with glaucoma).

*pdfn*were fastest in normal subjects, and the ZEST based on

*pdfg*was fastest in ideal subjects with glaucoma. A surprising finding was that ZEST using

*pdfn*was the fastest in unreliable subjects with glaucoma. The method based on the uniform pdf class (

*pdfu*, fourth bar) was slower than the other three pdf classes, requiring two to three extra presentations, and showed greater errors than the method using

*pdfc*. The combined pdf was approximately one presentation slower than the best method in each case. If it is known which population the patient is from, then a ZEST procedure using an appropriate pdf can achieve an accurate threshold using three to four presentations. A combined pdf requires approximately five presentations.

*pdfn*and

*pdfc*are as described earlier, whereas

*pdfd*, is the difference between

*pdfc*and

*pdfn*, thus reflecting a pdf for damaged locations only.

*pdfd*requires many presentations once thresholds exceed 5 dB, which is expected of a pdf customized for damaged locations. ZEST using

*pdfn*uses less presentations on average at most threshold values than ZEST with

*pdfc*in the unreliable patients, but at the cost of an increase in mean error. The lower panels of Figure 5 demonstrate that

*pdfc*has the most consistent SD of error, with

*pdfn*and

*pdfd*showing large variability in error response for damaged locations and normal locations, respectively.

*pdfc*appears a good compromise between the two extremes, supporting our simulation results over the entire visual field. The number of presentations is consistent across all threshold values, particularly in patients with some erroneous responses. It sacrifices some speed to ZEST with

*pdfd*in areas of damage (0–5 dB), and to ZEST with

*pdfn*in the range 8 to 16 dB. Unless it is known in advance that a patient’s threshold will fall into one of these two ranges, there is no way of knowing which of these pdfs to use. The error behavior of

*pdfc*is as expected, more variable than

*pdfn*in the normal-threshold range, but less in the damaged range. Similarly the measurements made with

*pdfc*are more erroneous in damaged locations than those made with

*pdfd*, but provide better estimates than pdf in other threshold ranges.

*x*-axis of the bottom panel. MOBS is labeled M.

*pdfc*and a stopping criterion of ς = 1. Figure 7 compares the number of presentations, the mean error, and the SD of the error in each of the six subject groups.

*P*< 0.001), the difference in mean error is minimal for clinical outcomes (≤1.0 dB) in all cases but ZEST in unreliable normal patients (−1.96 dB). Figure 7b shows that the new procedures are twice as fast as the existing MOBS, with ZEST being faster than REBS in unreliable patients.

^{ 10 }Alternately, REBS can be modified to choose a stimulus other than the midpoint of the current range, guided by a pdf of likely thresholds within the range.

*pdfc*, provided the best overall performance of the ZEST procedure. The possibility for further improvements in efficiency at follow-up visits may be realized by choosing the pdf for each location of the visual field on a point-wise basis, depending on the threshold at the last examination. Additional benefits in efficiency may also be possible through the incorporation of neighborhood logic to the thresholding algorithm, in that the threshold at any particular location is not independent of that of its immediate neighbors. We chose not to include such methodology in this study, because the benefits when testing only 17 locations are likely to be small. This may not be the case when greater numbers of locations are tested.

^{ 7 }The variability of FDT perimetry thresholds increases only modestly (20%–30%),

^{ 20 }in contrast to the large changes observed in achromatic perimetry (300%–400%).

^{ 7 }In any patient, responses may vary from typical to unreliable at different locations within the visual field, depending on the deficit depth. In this case, the simulation predicts a different number of presentations and range of errors at these locations. A prediction of performance can be determined for each location from the data shown in Figure 5 , however overall performance will differ from that presented in Figures 3 and 4 .

**Figure 1.**

**Figure 1.**

Group | n | Age (y) | Threshold (dB) | ||||
---|---|---|---|---|---|---|---|

Minimum | Maximum | Mean | |||||

Normal | 506 | 47 ± 16 | 0 | 20 | 13.52 ± 2.03 | ||

Glaucoma | 352 | 67 ± 12 | 0 | 20 | 8.96 ± 4.15 |

**Figure 2.**

**Figure 2.**

**Figure 3.**

**Figure 3.**

**Figure 4.**

**Figure 4.**

**Figure 5.**

**Figure 5.**

**Figure 6.**

**Figure 6.**

**Figure 7.**

**Figure 7.**

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