Executive Functions in Aging: An Experimental and Computational Study of the Wisconsin Card Sorting and Brixton Spatial Anticipation Tests

Figures & data

Table 1. Means (and standard deviations) for key dependent measures on the WCST for the two groups of participants

	$\mathrm{C}\mathrm{A}$	$\mathrm{P}\mathrm{E}$	$\mathrm{S}{\mathrm{L}}_3$	$\mathrm{T}\mathrm{E}$
Younger	6.2 (SD = 1.9)	11.3 (SD = 4.29)	0.64 (SD = 1.00)	17.0 (SD = 5.59)
Older	4.5 (SD = 2.8)	13.3 (SD = 6.40)	1.48 (SD = 1.56)	20.9 (SD = 8.97)

Figure 1. Response time violin plot as a function of age group in the WCST, on trials following “correct” versus “incorrect” feedback. Older participants were in general slower than younger participants, and both groups were slower following negative than positive feedback.

Table 2. Means (and standard deviations) for key dependent measures on the BRXT for each group of participants

	${\mathrm{P}}_{\mathrm{R}\mathrm{E}\mathrm{S}\mathrm{P}}$	${\mathrm{P}}_{\mathrm{S}\mathrm{T}\mathrm{I}\mathrm{M}}$	${\mathrm{P}}_{\mathrm{R}\mathrm{U}\mathrm{L}\mathrm{E}}$	$\mathrm{T}\mathrm{E}$
Younger	1.36 (SD = 1.04)	0.44 (SD = 0.91)	4.16 (SD = 1.48)	10.44 (SD = 4.74)
Older	1.63 (SD = 1.74)	0.17 (SD = 0.64)	3.79 (SD = 0.78)	13.83 (SD = 7.03)

Figure 2. Response time violin plot as a function of age group in the BRXT, on trials following “correct” versus “incorrect” feedback. Older participants were in general slower than younger participants, and both groups were slower following negative than positive feedback.

Table 3. Pearson correlations between types of WCST error (rows) and BRXT error (columns). All probabilities are two-tailed

	PRESP	PSTIM	PRULE	TE
PE	r = .367	r = .322	r = −.088	r = .384
	p = .009*	p = .024*	p = .547	p = .006*
SL3	r = .104	r = −.006	r = −.110	r = .535
	p = .477	p = .968	p = .454	p = .001*

Note. Values of p < .05 are marked with *

Figure 3. Schematic of the basal ganglia. STR D1: Striatum D1 receptors, STN: Subthalamic Nucleus, STR D2: Striatum D2 receptors, GPi: Globus pallidus internal segment, GPe: Globus Pallidus external segment, THAL: Thalamus, CTX: Cortex, SNpc: Substantia Nigra pars compacta. Standard arrow heads indicate excitatory connections. Circular arrow heads indicate inhibitory connections.

Table 4. Z statistics for the model fit for the two age groups in the WCST. A value closer to 0 indicates that experimental and simulated values have closer means, and therefore a better model fit. The subscripts near the z value are the Bayes Factor (BF₀₁). A value higher than 1 indicates greater support for the null hypothesis, which suggests a good model fit

	$\mathrm{T}\mathrm{E}$	$\mathrm{P}\mathrm{E}$	$\mathrm{S}{\mathrm{L}}_3$
Younger	${0.019}_{2.99}$	${0.095}_{1.57}$	${0.015}_{3.22}$
Older	${0.042}_{2.35}$	${0.021}_{2.91}$	${0.011}_{3.27}$

Table 5. Values of the parameters $w_{neg}$, $m_r$, ε_str, and ε_sma for the simulations of the two age groups in the WCST

	$w_{neg}$	$m_r$	εstr	εsma
Younger	$.457$	$.000$	$.139$	$.833$
Older	$.106$	$.000$	$.097$	$.000$

Figure 4. Model fit for younger participants, comparing the experimental (Exp) values and the simulated (Sim) values for the WCST.

Figure 5. Model fit for older participants, comparing the experimental (Exp) values and the simulated (Sim) values for the WCST.

Table 6. Z and Bayes Factor BF₀₁ as a subscript for model fits obtained by swapping young and old simulated data. The overall increase in Z values and the presence of three BF_s below zeros suggest that the two models are not interchangeable and they capture the differences between the two groups

	$\mathrm{T}\mathrm{E}$	$\mathrm{P}\mathrm{E}$	SL3
$Y_{exp}$, $O_{sim}$	${.128}_{1.12}$	${.391}_{0.15}$	${467}_{0.34}$
$O_{exp}$, $Y_{sim}$	.2630.30	${.005}_{3.38}$	${.380}_{0.18}$

Table 7. Mean (standard deviation) simulated response time (i.e., number of cycles to generate a response) for each simulated group for trials following positive feedback and trials following negative feedback. Data are based on 25 simulated runs with parameters set as in Table 5

	Positive	Negative
Younger	132.3 (1.4)	132.2 (2.9)
Older	146.9 (5.5)	144.5 (8.8)

Figure 6. Schematic of the BRXT model without the basal ganglia arbitration device. For instance, given that specific filled-in circle as an input, the $+1$ schema (clockwise) excites the following circle, whereas the $-1$ schema (counter-clockwise) excites the preceding one.

Table 8. Z statistics for the model fit for the two age groups in the BRXT. A value closer to 0 indicates that experimental and simulated value have closer means, and therefore a better fit. The subscripts near the z value represent the Bayes Factor BF₀₁. A value higher than 1 indicates greater support for the null hypothesis, which suggests a good model fit

	$\mathrm{T}\mathrm{E}$	${\mathrm{P}}_{\mathrm{S}\mathrm{T}\mathrm{I}\mathrm{M}}$	${\mathrm{P}}_{\mathrm{R}\mathrm{E}\mathrm{S}\mathrm{P}}$	${\mathrm{P}}_{\mathrm{R}\mathrm{U}\mathrm{L}\mathrm{E}}$
Younger	${0.073}_{1.75}$	${0.069}_{2.06}$	${0.024}_{3.08}$	${0.102}_{1.48}$
Older	${0.016}_{3.06}$	${0.001}_{3.54}$	${0.084}_{1.87}$	${0.047}_{2.76}$

Table 9. Value of the parameters $w_{neg}$, $m_r$, ε_str, and ε_sma for the two age groups in the BRXT. Note that for the simulation of the Younger data, m_r was fixed at zero and not a free parameter

	$w_{neg}$	$m_r$	εstr	εsma
Younger	0.162	0.000	0.621	0.512
Older	0.048	0.165	0.377	0.089

Table 10. Z and Bayes Factor BF₀₁ as a subscript for model fits obtained by swapping young and old simulated data. The presence of one BF_s below zeros suggest that the two models are not intercheangable and they capture the differences between the two groups

	$\mathrm{T}\mathrm{E}$	${\mathrm{P}}_{\mathrm{S}\mathrm{T}\mathrm{I}\mathrm{M}}$	${\mathrm{P}}_{\mathrm{R}\mathrm{E}\mathrm{S}\mathrm{P}}$	${\mathrm{P}}_{\mathrm{R}\mathrm{U}\mathrm{L}\mathrm{E}}$
$Y_{exp},O_{sim}$	${0.814}_{0.008}$	${0.093}_{1.85}$	${0.054}_{2.67}$	${0.021}_{3.00}$
$Y_{sim},O_{exp}$	${0.090}_{1.45}$	${0.003}_{3.48}$	${0.060}_{2.20}$	${0.009}_{3.36}$

Figure 7. Model fit for younger participants, comparing the experimental (Exp) values in blue/black and the simulated (Sim) values in orange/white, for the BRXT.

Figure 8. Model fit for older participants, comparing the experimental (Exp) values in blue/black and the simulated (Sim) values in orange/white, for the BRXT.

Table 11. Mean (standard deviation) simulated response time (i.e., number of cycles to generate a response) for each simulated group for trials following positive feedback and trials following negative feedback. Data are based on 25 simulated runs with parameters set as in Table 9

	Positive	Negative
Younger	110.1 (1.3)	112.8 (2.7)
Older	111.2 (1.4)	128.8 (21.4)

Figure 9. Model fit for younger (left) and older (right) participants, across the 3-dimensional parameter space defined by w_neg, ϵ_str and ϵ_sma with m_r = 0.0 for the WCST, based on 25 simulated participants at each of 11³ points in parameter space. The greyscale shows the z-score fit as described in simulation 1, with red/white representing fits with a z-score of less than 0.5 and bluer/darker values representingprogressively poorer fits (i.e., z ≥ 0.5).

Figure 10. Model fit for younger (left) and older (right) participants, across the 3-dimensional parameter space defined by wneg, ϵ_str and ϵ_sma for the BRXT, based on 25 simulated participants at each of 11³ points in parameter space and with m_r = 0.0 for the younger / left panel and m_r = 0.1 for the older / right panel. The greyscale shows the z-score fit as described in simulation 2, with white representing fits with a z-score of less than 0.5 and darker values representing progressively poorer fits (i.e., z ≥ 0.5).