Automated screening of Parkinson's Disease using Smooth Pursuit Eye Movements

J. Camilo Puerta-Acevedo; Maria F. Alcala-Durand; Julián D. Arias-Londoño; Elisa Luque-Buzo; Francisco Grandas-Pérez; Juan I. Godino-Llorente

eess.SPOct 23, 2026

Automated screening of Parkinson's Disease using Smooth Pursuit Eye Movements

Authors: J. Camilo Puerta-Acevedo, Maria F. Alcala-Durand, Julián D. Arias-Londoño, Elisa Luque-Buzo, Francisco Grandas-Pérez, Juan I. Godino-Llorente

Organizations: ETSI Telecomunicación. Universidad Politécnica de Madrid. Spain · Movement Disorders Unit, Neurology Department, Hospital General Universitario Gregorio Marañón, Madrid. Spain

Abstract

Smooth pursuit eye movements are frequently altered in Parkinson's disease, but previous studies have relied mainly on conventional parameters that describe the relationship between gaze and target. This study investigates whether complexity and nonlinear dynamics measures of the gaze position sequences can support the automatic screening of Parkinson's disease. Gaze position sequences were recorded with a video eye tracker in 41 participants with early Parkinson's disease and 47 healthy controls during 12 smooth pursuit tasks. Four experimental frameworks and four embedding delay strategies were compared. The selected experimental setting combined baseline wander removal with a fixed embedding delay. After feature selection, a support vector machine was trained for each task and axis and their outputs were combined in a mixture of experts. The pipeline was developed in 70 participants and evaluated on an external test set of 18 participants. On the external test set, the pipeline obtained an area under the receiver operating characteristic curve of 0.86. The most informative features described less persistent and more irregular gaze position sequences in Parkinson's disease, mainly along the horizontal axis. These results support complexity and nonlinear dynamics measures of smooth pursuit as candidate markers for Parkinson's disease screening, pending validation in larger independent cohorts.

Figures & tables

Variable	All participants ( $n=88$ )	PD ( $n=41$ )	HC ( $n=47$ )
Age, years	$63.17\pm 8.56$	$62.29\pm 8.91$	$63.96\pm 8.26$
Male sex, $n$ (%)	$44$ ( $50.00\%$ )	$24$ ( $58.54\%$ )	$20$ ( $42.55\%$ )
MoCA score	$26.39\pm 3.04$	$26.03\pm 3.56$	$26.70\pm 2.52$
UPDRS score	$8.01\pm 10.68$	$17.58\pm 9.38$	$0.28\pm 0.83$
Age at diagnosis, years	—	$60.18\pm 8.36$	—
Time since diagnosis, years	—	$1.73\pm 0.78$	—

Table 1: Demographic and clinical characteristics of the participants included in the main analysis. Continuous variables are mean

\pm

standard deviation and male sex is number (percentage). Dashes denote variables specific to participants with PD .

Panel of Figure 1 — Figure 1: Stimulus trajectories used in the 12 SPT : (a) horizontal trajectories used in SPT 1– SPT 4; (b) vertical trajectories used in SPT 5– SPT 8; (c) horizontal lemniscate trajectories used in SPT 9 and SPT 10; and (d) vertical lemniscate trajectories used in SPT 11 and SPT 12. Participants were instructed to fixate on the white central point for 200 ms before a red target moved in the direction indicated by the arrows. Target frequency and amplitude varied across SPT as detailed in Table 2 .

		X frequency (Hz)	X amplitude ( ∘ )	Y frequency (Hz)	Y amplitude ( ∘ )
Horizontal	SPT 1	0.2	6	0	0
	SPT 2	0.2	9	0	0
	SPT 3	0.4	6	0	0
	SPT 4	0.4	9	0	0
Vertical	SPT 5	0	0	0.2	4
	SPT 6	0	0	0.2	7

Table 2: Target frequency and amplitude for the 12 SPT .

Figure 2: Blink imputation for participant HF011 ( HC ) during SPT 12, using the gaze position sequence from the left eye along the X axis. Grey regions denote segments reconstructed with SSA .

Figure 3: Four EF for participant HF009 ( HC ) during SPT 11 along the X axis: gaze position sequences and estimated BW for the left and right eyes before removal (a,b); both gaze position sequences after removal (c); and CERM sequences obtained without (d) and with (e) prior BW removal.

Family	Measures	Sequence property	Delay vectors
Informational entropy	ShEn [ 38 ] , MaxEn [ 39 ] , DiffEn [ 38 ] , PowEn [ 38 , 36 ] , TE [ 40 ] , HEn [ 41 ] , CEn [ 42 ]	Uncertainty and distributional information in sequence amplitudes.	No
Temporal entropy	ApEn [ 43 ] , cApEn [ 44 ] , SampEn [ 45 ] , QSE [ 46 ]	Regularity and recurrence of temporal patterns.	Yes
Ordinal and permutation entropy	PE [ 47 ] , wPE [ 48 ] , cPE [ 49 ] , cwPE [ 48 , 49 ] , cRPE [ 42 , 49 ] ; plain, normalised and conditional forms of FGPE [ 50 ] , mPE [ 51 ] , AAPE [ 52 ] , ePE [ 53 ] and UQPE [ 54 ]	Diversity, transitions, amplitudes and modifications of ordinal patterns.	Yes
Symbolic complexity	LZC [ 55 ]	Novelty rate of symbolic patterns.	Yes
Geometric and fractal	KFD [ 56 ] , PFD [ 57 ]	Geometric waveform complexity.	No
Phase space dynamics	LLE [ 58 ] , CD [ 59 ]	Divergence and dimensionality of reconstructed trajectories.	Yes

Table 3: Complexity and nonlinear dynamics measures, the sequence property described by each family and whether its measures are computed from delay vectors.

Delay Strategy $\rightarrow$ Experimental Framework $\downarrow$	DS 1 Fixed delay 25 samples	DS 2 Target position AMI first minimum	DS 3 Gaze position AMI first minimum	DS 4 Gaze position AMI $1/e$ decay
EF 1 No BW removal No CERM extraction	EF 1– DS 1	EF 1– DS 2	EF 1– DS 3	EF 1– DS 4
EF 2 BW removal No CERM extraction	EF 2– DS 1	EF 2– DS 2	EF 2– DS 3	EF 2– DS 4
EF 3 No BW removal CERM extraction	EF 3– DS 1	EF 3– DS 2	EF 3– DS 3	EF 3– DS 4
EF 4 BW removal CERM extraction	EF 4– DS 1	EF 4– DS 2	EF 4– DS 3	EF 4– DS 4

Table 4: The 16 experimental settings formed by the four EF and four DS .

Figure 4: Overview of the pipeline: from preprocessing and feature extraction to participant-level classification and external evaluation.

Choice	Selected option	Main quantitative evidence
Delay strategy	DS 1	AUC : $0.68\pm 0.07$ with all features and $0.65\pm 0.14$ with features computed from delay vectors; temporal span of the delay vectors: $50$ – $75$ ms
Organisation of the base models	One base model for each SPT and axis, using features from both eyes; $24$ base models in total	AUC : $0.68\pm 0.07$ for the X axis and $0.51\pm 0.06$ for the Y axis; $0.68\pm 0.07$ for the left eye and $0.70\pm 0.08$ for the right eye along the X axis
Experimental framework	EF 2	AUC : $0.76$ for EF 2, $0.71$ for EF 1, $0.66$ for EF 4 and $0.60$ for EF 3

Table 5: Development set evidence used to select the experimental setting and organisation of the base models.

	Development set			External test set
Metric	All features (38)	RFS (20)	HFS + FFS (13)	HFS + FFS (13)
AUC	$0.88\;(0.05)$	$0.90\;(0.08)$	$\mathbf{0.91\;(0.06)}$	$\mathbf{0.86}$
Sensitivity	$0.78\;(0.17)$	$0.78\;(0.18)$	$\mathbf{0.84\;(0.11)}$	$\mathbf{0.75}$
Specificity	$0.78\;(0.18)$	$0.78\;(0.21)$	$\mathbf{0.84\;(0.16)}$	$\mathbf{0.80}$
G-mean	$0.76\;(0.10)$	$0.77\;(0.15)$	$\mathbf{0.83\;(0.06)}$	$\mathbf{0.77}$

Table 6: Participant-level performance of the three feature sets. Numbers in parentheses are measures; each measure provided one feature per eye. Development values are the mean (standard deviation) across the 20 holdouts. The external test set was evaluated with the selected feature set, shown in bold.

Figure 5: Performance of the selected pipeline. (a) ROC curves; the development curve uses the mean validation probability of each participant across the 20 holdouts and the inset magnifies the upper-left corner. (b) MoE probabilities of the YC cohort and of the HC and participants with PD in the development set (CV) and the external test set. The YC cohort is compared with the external test set because neither was used to develop the pipeline. Symbols denote individual participants and curves show density estimates.

Target movement: X			Target movement: Y			Target movement: 2D
SPT	X	Y	SPT	X	Y	SPT	X	Y
SPT 1	12.13	0.00	SPT 5	20.87	9.94	SPT 9	18.27	1.41
SPT 2	0.80	0.00	SPT 6	2.37	0.07	SPT 10	2.67	0.00
SPT 3	6.84	0.00	SPT 7	2.44	0.00	SPT 11	$<0.01$	0.00
SPT 4	18.52	0.00	SPT 8	2.55	0.00	SPT 12	1.12	0.00

Table 7: Contribution (%) of the individual base models to the combined output, grouped by target movement. X and Y indicate the axis of each base model. Values of

0.00

correspond to base models without influence on the combined output.

		Left eye			Right eye
Measure	Total (%)	Contr. (%)	Direction	$d$	Contr. (%)	Direction	$d$
wPE	$13.40$	$7.55$	PD ( $13/15$ )	$0.45$	$5.85$	PD ( $12/15$ )	$0.36$
HE	$10.81$	$7.81$	HC ( $14/15$ )	$-0.47$	$3.00$	PD ( $10/15$ )	$0.03$
LZC	$10.42$	$6.41$	HC ( $14/15$ )	$-0.16$	$4.01$	PD ( $8/15$ )	$0.15$
Conditional UQPE	$9.51$	$4.95$	PD ( $9/15$ )	$0.29$	$4.56$	PD ( $8/15$ )	$0.20$
CD	$8.71$	$3.11$	PD ( $13/15$ )	$0.07$	$5.60$	PD ( $10/15$ )	$0.07$

Table 8: Eight measures with the highest contribution to the combined output, reported separately for each eye. Each value combines the X and Y axes. Contr.: contribution, expressed as a percentage of the total across all features and base models; the total adds both eyes and determines the order of the rows. Direction: diagnostic group with which the model associated higher values and, in parentheses, number of the 15 active base models with that direction.

d

: median Cohen’s

d

across the active base models, computed as the difference between the PD and HC means divided by the pooled standard deviation.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Figure A.1 : Four DS for participants HG060 ( HC ) and HF014 ( PD ) in SPT 11, left eye, X axis, before BW removal. (a) AMI curves of the gaze position sequences for HC (dashed) and PD (solid); coloured lines denote the selected delays. (b) AMI curve of the target position sequence; the coloured line denotes the shared DS 2 delay. (c–f) Three-dimensional phase space reconstructions for DS 1– DS 4 in HG060 ( HC ). (g–j) Corresponding phase space reconstructions for HF014 ( PD ).

Figure A.2 : EDel distributions for DS 3 (first two columns) and DS 4 (last two) by SPT and axis. Colours denote EF 1– EF 4; dotted lines show DS 2. The horizontal axis is logarithmic and expressed in milliseconds.

Figure A.3 : EDim distributions for DS 1– DS 4. Colours denote EF 1– EF 4, and bars show the percentage of sequences for each embedding dimension.

DS	Approximate temporal span	All features	Computed from delay vectors	Computed directly from the sequence
DS 1	50–75 ms	$\mathbf{0.68\pm 0.07}$	$\mathbf{0.65\pm 0.14}$	$0.64\pm 0.10$
DS 2	approximately 2.20 s	$0.66\pm 0.07$	$0.62\pm 0.04$	$0.64\pm 0.10$
DS 3	approximately 3.20 s	$0.67\pm 0.06$	$0.63\pm 0.04$	$0.64\pm 0.10$
DS 4	approximately 1.50 s	$0.61\pm 0.08$	$0.56\pm 0.11$	$0.65\pm 0.10$

Appendix

Table S1 : Development set AUC for PD classification across the DS using the gaze position sequences along the X axis. Values are reported as the mean

\pm

standard deviation across the four EF .

Data included at DS 1	All features	Features computed from delay vectors
Both eyes, X and Y axes pooled	$0.66\pm 0.07$	$0.64\pm 0.12$
Both eyes, X axis	$\mathbf{0.68\pm 0.07}$	$\mathbf{0.65\pm 0.14}$
Both eyes, Y axis	$0.51\pm 0.06$	$0.55\pm 0.05$
Left eye, X axis	$0.68\pm 0.07$	$0.64\pm 0.14$
Right eye, X axis	$0.70\pm 0.08$	$0.66\pm 0.14$

Appendix

Table S2 : Development set AUC for PD classification according to the analysed axis and the eye from which the features were extracted at DS 1. Values are reported as the mean

\pm

standard deviation across the four EF . Separate eyes along the Y axis are not shown; their AUC was close to chance (approximately

0.50

Statistic	BW removal EF 2/ EF 1	CERM extraction EF 3/ EF 1	CERM extraction EF 4/ EF 2
Standard deviation of the sequence	$0.17\;[0.15,\,0.19]$	—	—
Standard deviation of the first differences	$0.97\;[0.97,\,0.98]$	—	—
Relative local variation, complete sequence	—	$0.93\;[0.92,\,0.93]$	$0.95\;[0.94,\,0.95]$
Relative local variation, 50 ms windows	—	$0.81\;[0.81,\,0.81]$	$0.89\;[0.89,\,0.90]$
Windows with $R<1$ (%)	—	$80.88\;[79.76,\,81.15]$	$70.70\;[69.06,\,71.87]$

Appendix

Table S3 : Changes in the gaze position sequences of the development set produced by BW removal and CERM extraction. Relative local variation is the standard deviation of the first differences divided by the standard deviation of the sequence. Values are median paired ratios

R=M_{\mathrm{after}}/M_{\mathrm{before}}

with

95\%

confidence intervals;

R<1

indicates a reduction.

Family / representative measure	EF 1	EF 2	EF 3	EF 4
Memory and scaling: DFA	-0.39	-0.19	-0.26	-0.24
Memory and scaling: HE	-0.16	-0.29	-0.11	-0.22
Symbolic complexity: LZC	+0.32	-0.08	+0.16	-0.06
Geometric and fractal: PFD	+0.23	+0.18	+0.25	+0.16
Phase space dynamics: LLE	+0.40	+0.35	+0.30	+0.33
Phase space dynamics: CD	+0.06	+0.19	-0.30	+0.08

Appendix

Table S4 : Representative effect sizes by family at DS 1 in the development set. Cohen’s

d

was calculated as the difference between the PD and HC means divided by the pooled standard deviation. Positive values therefore indicate higher feature values in participants with PD , whereas negative values indicate higher values in HC . Bold rows identify the measures whose direction reversed after CERM extraction both with and without BW removal.

Target: X	SPT 1	SPT 2	SPT 3	SPT 4
X axis	$\mathbf{0.77\,(0.06)}\,/\,0.48$	$0.70\,(0.11)\,/\,0.80$	$0.66\,(0.15)\,/\,0.80$	$\mathbf{0.82\,(0.08)}\,/\,0.70$
Y axis	$0.47\,(0.08)\,/\,0.50$	$0.51\,(0.03)\,/\,0.50$	$0.47\,(0.07)\,/\,0.50$	$0.53\,(0.10)\,/\,0.50$
Target: Y	SPT 5	SPT 6	SPT 7	SPT 8
X axis	$\mathbf{0.80\,(0.15)}\,/\,0.75$	$0.52\,(0.15)\,/\,0.90$	$0.72\,(0.15)\,/\,0.74$	$0.67\,(0.11)\,/\,0.79$
Y axis	$0.67\,(0.15)\,/\,0.64$	$0.53\,(0.09)\,/\,0.40$	$0.47\,(0.06)\,/\,0.50$	$0.47\,(0.07)\,/\,0.50$
Target: 2D	SPT 9	SPT 10	SPT 11	SPT 12

Appendix

Table S5 : AUC of the base models by SPT , target movement and axis. Cells report the mean (standard deviation) across the 20 holdouts, followed by the AUC on the external test set. Bold values identify the three highest development values.

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Parkinson's disease (PD) manifests early neuromotor impairments that become observable in controlled hand-drawn patterns such as spirals and meanders, where tremor-induced oscillations, stroke irregularity, and curvature instability reflect underlying motor degradation. In this work, we present an explainable framework for PD screening from offline hand-drawn patterns that integrates discriminative visual modeling with clinically grounded reasoning. The predictive model captures distributed structural distortions and fine-grained texture variations. It is evaluated under subject-disjoint protocols to ensure reliable generalization. To move beyond black-box classification, we introduce a multi-stage explainability pipeline that combines visual attribution with structured symptom abstraction. Salient regions are identified using attention- and gradient-based localization, followed by extraction of clinically meaningful motor descriptors quantifying contour roughness, curvature irregularity, stroke variability, and tremor-frequency energy. These descriptors are subsequently translated into coherent clinical rationales through a language-based reasoning module, linking model evidence to established PD symptomatology. By bridging visual attribution and clinical interpretation, the proposed framework advances interpretable document intelligence for neurological screening using hand-drawn patterns. Experimental results on publicly available Parkinson's disease handwriting datasets demonstrate competitive predictive performance and clinically consistent explanations.

Abstract

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