AN ASSESSMENT PROCEDURE INVOLVING WAVEFORM SHAPES

FOR PU

PIL LIGHT REFLEX

Minoru Nakayama

CRADLE, Tokyo Institute of Technology, Tokyo 152-8552, Japan

Wioletta Nowak

Institute of Biomedical Engineering and Instrumentation, Wroclaw University of Technology, Wroclaw, Poland

Hitoshi Ishikawa, Ken Asakawa

School of Allied Health Sciences, Kitasato University, Sagamihara 228-8555, Japan

Keywords:

Pupil light reﬂex, Waveforms, Fourier descriptor, Dissimilarity, Multidimensional scaling.

Abstract:

The waveforms of Pupillary Light Reﬂex (PLR) can be analyzed in a diagnostic test that allows for differ-

entiation between disorders affecting photoreceptors and those affecting retinal ganglion cells. This position

paper proposes quantitative comparison metrics for waveform shapes using Discrete Fourier Transform (DFT)

descriptors (FDs), and another procedure for emphasizing stimuli and subject differences using MultiDimen-

sional Scaling (MDS) and clustering, where dissimilarities between stimuli are deﬁned using descriptors as

waveform features. To determine the efﬁciency of the procedures, a set of PLR data from a conventional

experiment for the determination of a melanopsin-associated photoreceptive system was analyzed. Though

the captured data was based on single trial for the stimuli, and the number of samples was small, both char-

acteristics of stimuli and subjects were quantitatively extracted using the proposed procedures. Therefore, the

possibility of applying the procedures to clinical diagnostics using PLR was examined.

1 INTRODUCTION

The Pupillary Light Reﬂex (PLR) is a well-known

phenomenon, and recently its behavior has been

examined in detail because of the existence of a

melanopsin-associated photoreceptive system in the

human retina, in addition to the conventionalrod-cone

system (Gamlin et al., 2007). Many studies have con-

sidered the contributions of this melanopsin to be a

subset of intrinsically photosensitive retinal ganglion

cells (Hattar et al., 2002; Dacey et al., 2005). To

reveal the sensitivity and activity of these cells, the

transient phase of PLR has often been studied using

pupillary responses for low and high stimulus inten-

sities, which were evoked using either short or long

wavelength stimuli (Young and Kimura, 2008). In

particular, the waveforms in the sustained phase of

PLR are often compared across the stimulus condi-

tions. These observations may be useful for clinical

diagnostic procedures (Kawasaki and Kardon, 2007),

though a quantitative index of PLR waveforms has

not yet been established, however. In most cases,

waveform shapes are subjectively compared in pupil-

lograms, therefore quantitative metrics and analytical

procedures for corresponding waveforms have been

desired. Because PLR observations are based on the

response to a light pulse, human subjects cannot be

subjected to repeated measurement. Also, a simpli-

ﬁed procedure is required for clinical diagnostic tests.

Though conventional pupil research has discussed

mean pupil diameters and mean frequency spectra

(Kuhlmann and Bottcher, 1999), these metrics cannot

be applied. Simpliﬁed metrics of single waveforms

are required to reveal the melanopsin-associated pho-

toreceptive system.

In the area of signal processing and pattern

recognition the features of waveforms using Fourier

Descriptors have often been discussed (Zahn and

Roskies, 1971; Pinkowski, 1994; Zhang and Lu,

2002). These waveforms can be compared to each

other. Once the quantitative features are deﬁned, the

metrics of similarity or dissimilarity across the wave-

forms can also be extracted.

This position paper proposes a procedure for cre-

322

Nakayama M., Nowak W., Ishikawa H. and Asakawa K. (2010).

AN ASSESSMENT PROCEDURE INVOLVINGWAVEFORM SHAPES FOR PUPIL LIGHT REFLEX.

In Proceedings of the Third International Conference on Bio-inspired Systems and Signal Processing, pages 322-326

DOI: 10.5220/0002756603220326

 SciTePress

ating quantitative features of PLR waveforms, and

demonstrates comparisons of these waveforms across

stimuli and individuals using the metrics. Therefore,

following topics are addressed:

1. A procedure for extracting feature vectors of PLR

waveforms is created, and the metrics to compare

these waveforms are determined.

2. The dissimilarities across the waveforms are also

deﬁned, and the differences in stimuli condi-

tions and subjects are examined using multidi-

mensional scoring and clustering techniques.

2 METHOD

2.1 Experimental Procedure

The Pupillary Light Reﬂex (PLR) is the constriction

of the pupil elicited by an increase in illumination of

the retina. A conventional experiment used for the de-

termination of a melanopsin-associated photorecep-

tive system was conducted. In the experiment, a

long wavelength (635nm bandwidth) red light and a

short wavelength (470nm bandwidth) blue light were

used at 2 different light intensities (10 cd/m

and 100

cd/m

Both Figure ?? and 2 show the PLR of a 10

sec. light pulse as a constriction phase and a 10 sec.

restoration phase in two normal subjects. In these ﬁg-

ures, red lines show PLRs for long wavelengths, and

blue lines show PLRs for short wavelengths. Also,

solid lines show PLRs for high intensity light, and

dotted lines show low intensity light. In this paper,

the four conditions are deﬁned as follows: r10 (long

wavelength – low light intensity), r100 (long–high),

b10 (short–low), b100 (short–high).

During this experiment, PLRs for these four con-

ditions were observed for each subject.

Pupil light responses were recorded using an iris-

tracker (Hamamatsu Iriscorder Dual). Subjects were

6 healthy individuals with normal vision between the

ages of 20 and 21 years. Subjects were asked to

not blink for 20 sec. while their pupil diameter was

recorded at a sampling rate of 30 Hz. These measure-

ments were taken in a dark room with constant light-

ing conditions. A dark-adaptation period of 5 minutes

was allowed prior to taking all measurements.

2.2 Fourier Descriptors

The feature vectors for PLR waveforms were ex-

tracted using the Discrete Fourier Transform (DFT)

procedure (Pinkowski, 1994; Zhang and Lu, 2002).

0 10 20

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0.5

Stimulus on Stimulus off

Time (sec.)

Diameter (mm)

r10

r100

b10

b100

Figure 1: sub1.

−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0.5

10 20

Stimulus on Stimulus off

Time (sec.)

Diameter (mm)

r10

r100

b10

b100

Figure 2: sub2.

As mentioned above, PLRs were sampled as discrete

signals. Here, the length N of a discrete signal is de-

ﬁned as x(n), which is sampled at time t with spacing

∆. The signal x(n) can be noted as an equation (1)

using DFT (Morishita and Kobatake, 1982).

x(n) = a

N/2

∑

k=1

(a(k)c

os(2πk

t(n)

N∆

)

+ b(k)sin(2πk

t(n)

N∆

)) (1)

= X(1)/N

a(k) = 2 real(X(k+ 1))/N

b(k) = 2 imag(X(k+ 1))/N

This suggests that PLR waveforms can be repre-

sented using coefﬁcients a

, a(k) and b(k) with peri-

odical cosine and sine functions. To present the fea-

tures of the waveform, the magnitude of coefﬁcients

is preferred, because coefﬁcient b(k) is the imagi-

nary part of a value. The magnitudes of coefﬁcients,

AN ASSESSMENT PROCEDURE INVOLVINGWAVEFORM SHAPES FOR PUPIL LIGHT REFLEX

323

including a

, FD

(i = 0,. .. ,N/2 − 1) are used as

Fourier descriptors (FD) as follows in vector (2):

f = [FD

,FD

,...,FD

N/2−1

] (2)

In general, the components FD

, a

in the equa-

tion (1), show the DC components of the signal.

These DC components represent the amplitude, ex-

cept the waveform shape consisting of frequency

components. Also, features are affected by individual

factors, so that a standardized feature is preferred as

follows in vector (3) as follows(Zhang and Lu, 2002):

f = [

,... ,

N/2−1

] (3)

Additionally, an appropriate number of compo-

nents for the feature vector represent the character-

istics of most signals only at the low-order values of

4 or 5 FDs (Pinkowski, 1994).

3 RESULTS

3.1 Feature of PLRs

According to the analytical procedure in the above

section 2.2, the features of PLRs for a subject (Sub1)

were extracted. The actual calculations were con-

ducted using MATLAB (Mathworks, Inc.). First,

are extracted in order to compare the waveform

amplitude as follows:

0,r10

= 319.4, FD

0,r100

= 832.5,

0,b10

= 773.8, FD

0,b100

= 1001.6

For FD

values, the value for the b100 condition

is the largest, and the value for r10 condition is the

smallest. The order of these values coincides with the

pattern in Figure ??. The FD

values are extracted

for all subjects and are illustrated in Figure 3. The or-

der of these values is maintained across most subjects

though individual differences are observed. In com-

paring PLRs between Sub1 and Sub2 in Figure ?? and

2, the relationships between the four conditions are

different between the two subjects, though the orders

of FD

are almost similar to those in Figure 3.

Feature vectors are extracted for every waveform

using the format of vector (3). For example, the set of

vectors for a subject Sub1 is shown as follows:

r10

= [0.408, 0.384,0.197,0.276,0.150]

r100

= [0.253, 0.289,0.122,0.204,0.025]

b10

= [0.177, 0.365,0.071,0.152,0.072]

b100

= [0.160, 0.289,0.104,0.141,0.051]

According to the set of features, the vectors for

b10 and b100 may be similar, but the vector for r10 is

relatively different.

sub1 sub2 sub3 sub4 sub5 sub6

500

1000

1500

2000

r10 r100

b10

b100

DC component

Figure 3: Comparison of DC components.

Table 1: Euclid distance between stimuli (sub1).

r10 r100 b10 b100

r10 0

r100 0.24 0

b10 0.30 0.14 0

b100 0.33 0.12 0.09 0

3.2 Similarity/Dissimilarity

To compare the shape of waveforms quantitatively,

metrics of similarity of dissimilarity should be deﬁned

using waveform feature vectors. This is a very popu-

lar approach for pattern recognitions such as catego-

rization and discrimination (Stork et al., 2001). Here,

the Euclidean distance (or Minkowski’s power met-

ric) can be deﬁned as the Euclidean norm between

two feature vectors. This is the dissimilarity metric.

The distances amongst stimuli conditions for Sub1 are

summarized in Table 1 as a triangular matrix. Accord-

ing to the matrix, the longest distance is between r10

and b100, and the shortest distance is between b10

and b100.

Distance matrices were created for all subjects.

3.3 Conﬁguration of Stimuli and

Subjects

To create an overall structure of relationship be-

tween PLR waveforms, the Multi Dimensional Scal-

ing (MDS) method is applied to the distance ma-

trix. The famous application of MDS is re-creation of

the geographical map of the distance matrix amongst

cities (Takane, 2007). The Individual Difference

MDS procedure has been introduced to extend the

conventional MDS analysis to multiple distance ma-

trices using every subject’s matrix. The actual calcu-

lation was conducted using SAS (Mayekawa, 1997).

BIOSIGNALS 2010 - International Conference on Bio-inspired Systems and Signal Processing

324

-1

-1 0 1 2

r10

r100

b10

b100

Dimension 1

Dimension 2

Figure 4: The stimulus conﬁguration using two-

dimensional scales from MDS.

-1

-1 0 1 2

sub2

sub4

sub5

sub6

sub1

sub3

Dimension 1

Dimension 2

Figure 5: The stimulus for subjects conﬁguration using two-

dimensional scales.

First, the stimulus are conﬁgured on a two-

dimensional space which is created by MDS analy-

sis, as shown in Figure 4. The horizontal axis shows

dimension 1, and the vertical axis shows dimension

2. Both dimensions are created as a result of MDS,

therefore they show distance between stimuli while

the dimensional interpretation is unstable. Both b10

and b100 almost overlap because the distance are the

shortest. Both r10 and r100 are separated from b10

and b100, and the value of dimension 1 for r100 is

almost the same as for b10 and b100. According to

the two-dimensional conﬁguration shown in Figure 4,

the stimulus r10 differs from other conditions in both

dimension 1 and dimension 2. In a sense, dimension

1 extracts r10 conditions while dimension 2 extracts

r100 conditions.

All results for the four conditions and 6 subjects

0.4

0.6

0.8

1.2

0.8 1 1.2 1.4

sub2

sub4

sub5

sub6

sub1

sub3

Dimension 1

Dimension 2

Figure 6: The subjects conﬁguration using two-dimensional

scales.

sub5

sub1

sub4

sub3

sub6

sub2

0 0.1 0.2 0.3 0.4 0.5

Distance

Figure 7: A dendrogram of the cluster for subjects.

are mapped in Figure 5. The stimuli conditions make

clusters in response to the conﬁgurationsof stimuli, as

shown in Figure 4 where all subject’s data is mapped

in a similar style. When subjects’ conﬁguration inside

three clusters are carefully observed, plots of subjects

are shifted regularly in every cluster.

All subjects can be conﬁgured on the same space,

as shown in Figure 6. Subjects are distributed on a

line. Also, three clusters can be observed, conﬁgu-

ration for one subject (Sub2) is separated from the

others. To clarify the relationship between subjects,

cluster analysis was conducted using two dimensional

MDS information for each individual. A dendrogram

is summarized in Figure 7. The horizontal axis shows

averaged distance between subjects. The clustering

process responds to the distribution of subjects in Fig-

ure 6. The distance between Sub1 and Sub4 is the

shortest, and Sub2 is separated from the others.

The number of dimensions which are created by

MDS analysis were extended to three dimension. The

dimensional values are summarized in Table 2. The

contribution of both dimension 1 and dimension 2 to

AN ASSESSMENT PROCEDURE INVOLVINGWAVEFORM SHAPES FOR PUPIL LIGHT REFLEX

325

Table 2: Three dimensional information of MDS for stim-

uli.

Dim1 Dim2 Dim3

r10 1.73 0.39 1.07

r100 -.60 1.46 -.12

b10 -.60 -1.03 0.62

b100 -.55 -.82 -1.57

the discrimination has the same tendency as in the

case of a two-dimensional analysis. However, the

stimuli b10 and b100 are separated from each other

on a scale the same as in dimension 3, therefore di-

mension 3 may be related to the light strength of the

short wavelength.

In this analysis, all subjects are normal individu-

als. This procedure can be used to detect diseases or

as a diagnostic procedure if target patient data is sep-

arated from a cluster of normal subjects. This will be

a subject of our further study.

4 CONCLUSIONS

In this position paper, we propose a quantitative com-

parison metrics of Pupil Light Reﬂex (PLR) wave-

form shapes using the Discrete Fourier Transform

(DFT) descriptors (FDs), and another procedure for

emphasizing stimuli and subject differences using

Multi Dimensional Scaling (MDS) and clustering

when the dissimilarity between stimuli is deﬁned us-

ing the descriptors as waveform features.

The demonstrations were conducted using a

conventional experiment for the determination of

a melanopsin-associated photoreceptive system.

Though the captured data was based on single trial

for the stimuli, and the number of samples was small,

both characteristics of stimuli and subjects were

quantitatively extracted using the proposed proce-

dures. Therefore, the possibility of its application for

clinical diagnostics using PLR was examined.

The interpretation of scales and clinical applica-

tions will be subjects of our further study.

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