## Abstract

Impairment of hippocampus-dependent cognitive processes has been proposed to underlie age-related deficits in navigation. Animal studies suggest a differential role of hippocampal subfields in various aspects of navigation, but that hypothesis has not been tested in humans. In this study, we examined the association between volume of hippocampal subfields and age differences in virtual spatial navigation. In a sample of 65 healthy adults (age 19–75 years), advanced age was associated with a slower rate of improvement operationalized as shortening of the search path over 25 learning trials on a virtual Morris water maze task. The deficits were partially explained by greater complexity of older adults' search paths. Larger subiculum and entorhinal cortex volumes were associated with a faster decrease in search path complexity, which in turn explained faster shortening of search distance. Larger Cornu Ammonis (CA)1–2 volume was associated with faster distance shortening, but not in path complexity reduction. Age differences in regional volumes collectively accounted for 23% of the age-related variance in navigation learning. Independent of subfield volumes, advanced age was associated with poorer performance across all trials, even after reaching the asymptote. Thus, subiculum and CA1–2 volumes were associated with speed of acquisition, but not magnitude of gains in virtual maze navigation.

## Introduction

Spatial navigation is a complex cognitive activity that depends on access to allocentric and egocentric spatial cues, space-specific and general computational mechanisms, and spatial representations in real time and in memory (Wolbers and Hegarty 2010). For more than 3 decades, the Morris water maze (MWM; Morris 1981) has been used to study each of these cognitive components of navigation. In this popular laboratory task, an animal (typically a rat) is positioned in a pool of opaque liquid, in which it can swim until it reaches a hidden goal platform [see D'Hooge and De Deyn (2001) for a review]. To improve the continuity between animal and human studies, a virtual MWM (vMWM) has been introduced (Astur et al. 1998). The vMWM reproduces many aspects of a search for a hidden platform, with some major differences. A human performing the vMWM largely relies upon visual cues for navigation, whereas a rodent swimmer has additional kinesthetic and respiratory feedback. Nonetheless, the vMWM has been shown to be a valid laboratory assessment of navigation behavior, and the lack of kinesthetic cues appears to negligibly affect the subsequent learning and memory for a location (Waller and Greenauer 2007).

To date, the vMWM has been employed in several studies of structural and functional correlates of age-related differences in human navigation. Like older rodents in the traditional MWM (Gallagher et al. 1993), older humans performing a vMWM task traverse longer virtual distance from the start to the goal platform (Moffat and Resnick 2002; Driscoll et al. 2003, 2005), travel more complex paths (Daugherty et al. 2015), commit more heading errors (Moffat and Resnick 2002), and exhibit greater asymmetry in turning behavior than their younger counterparts do (Yuan et al. 2013). There are several viable hypotheses of the source of navigation deficits [see Moffat (2009) for a review], including impaired cognitive mapping abilities (O'Keefe 1990; Daugherty et al. 2015).

The hippocampus is not a uniform structure. It consists of cytoarchitectonically and functionally distinct subfields that include the subiculum, Cornu Ammonis (CA) fields 1–4, and the dentate gyrus (DG), all of which are conserved across mammalian species (Amaral and Lavenex 2006). The heterogeneity of the hippocampus and of the adjacent medial temporal lobe regions, such as the entorhinal cortex [EC; see Jones and McHugh (2011) for a review], is relevant to understanding the neural substrates of spatial navigation. Place cells, pyramidal neurons located in the CA1 sector of the hippocampus (Bures et al. 1997), play a critical role in forming cognitive maps and their example illustrates how navigation functions are differentially related to specific hippocampal subfields [see Lavenex and Lavenex (2013)]. Thus, it is important to establish which part of the human hippocampus is associated with spatial navigation and age-related differences therein.

Although total hippocampal volume declines with age [e.g., Raz et al. 2005; see Raz and Kennedy (2009) for a review], the magnitude of age differences in volume vary across the hippocampal components. The volume of the CA1–2 subfield is negatively related to age (Mueller et al. 2007; Mueller and Weiner 2009; Shing et al. 2011; Bender et al. 2013; Wisse et al. 2014), with some evidence suggesting particular vulnerability to age-related cardiovascular risk factors (Shing et al. 2011; Bender et al. 2013) or genetic risk associated with Alzheimer's disease [Mueller and Weiner 2009; Kerchner et al. 2014; but see Mueller et al. (2008) and Raz et al. (2014)]. The evidence of age differences in CA3–4 and DG volumes is less consistent, with some studies showing negative age differences (Mueller et al. 2007; Mueller and Weiner 2009; Wisse et al. 2014), while others reveal no significant effects of age (Shing et al. 2011; Bender et al. 2013). Subiculum volume appears to be stable across the adult lifespan in most of the published studies [Mueller et al. 2007; Mueller and Weiner 2009; Shing et al. 2011; Bender et al. 2013; but see La Joie et al. (2010)].

The differential contributions of hippocampal subfields to navigation have been established in non-human primates and rodents [Lavenex and Lavenex 2013; see Jones and McHugh (2011) for a review], but at the time of this writing, have not been investigated in humans. In this study, we measured volumes of the hippocampal subfields and the EC in healthy adults, and assessed the role of regional volumes in vMWM navigation. We used 2 indicators of navigation in vMWM—distance traveled in search of the hidden platform and search path complexity. The latter was quantified by its fractal dimensionality, a recently introduced index of complexity (Daugherty et al. 2015). The fractal dimensionality index is complementary to the traditional measure of path length: when compared with travel time, another index of navigation efficiency that is highly correlated with path length, fractal dimensionality exhibits a different pattern of age differences with unique neural correlates (Daugherty et al. 2015). Fractal dimensionality of the search path positively correlates with the volumes of the whole hippocampus and parahippocampal gyrus, which includes the EC, and may be more sensitive to individual differences in cognitive processes underlying mapping than measures of distance alone (Daugherty et al. 2015).

Thus, based on the reviewed literature, we hypothesized that advanced age would be associated with a smaller CA1–2 volume; that larger CA1–2 and EC, but not CA3–DG volumes, would be associated with shorter distance as well as lower path complexity; and that age differences in navigational performance would be, in part, explained by smaller CA1–2 and EC.

## Methods

### Participants

Participants were recruited from the Metro Detroit, Michigan area, as part of an ongoing study of cognitive and neural correlates of aging. A healthy lifespan sample of 65 adults, age 19–75 years, completed cognitive testing and underwent a structural MRI. See Table 1 for a report of the sample demographics. Participants were right-handed dominant (score over 75% on Edinburgh Inventory; Oldfield 1971), spoke English as the first language, and were screened for neurological, psychiatric, cardiovascular, and endocrine diseases; diabetes; cancer; head trauma; learning disorders; and corrected-to-normal vision and hearing. Participants were screened for dementia (Mini-Mental State Exam, MMSE ≥26; Folstein et al. 1975) and depression (Center for Epidemiological Study Depression questionnaire, CES-D ≤16; Radloff 1977). Age was unrelated to years of formal education (r = 0.18, P = 0.95), MMSE (r = −0.07, P = 0.99), or CES-D (r = −0.21, P = 0.54). All participants were normotensive, based on the absence of a medical diagnosis, or observed blood pressure measurements below clinical criteria (140 mmHg systolic and 90 mmHg diastolic). Resting blood pressure was measured by an arm cuff and was the average of 4 measurements in the course of the study. During sample selection, an additional 11 participants were excluded from analyses due to hypertension, 9 participants did not complete the navigation task, and 1 participant was excluded for failure to find the platform on several vMWM trials. Excluded cases did not differ from the retained sample in age, education, MMSE, or CES-D (−0.68 ≤ t ≤ 0.33, all P ≥ 0.50).

Table 1

Descriptive statistics of the sample

Total Female Male t-test
N 65 44 21
% Caucasian 71 66 81
Age (years) 44.99 ± 16.31 45.27 ± 15.90 44.38 ± 17.51 0.20
Education (years) 15.51 ± 1.90 15.48 ± 2.11 15.57 ± 1.40 −0.21
MMSE 28.62 ± 1.07 28.59 ± 1.04 28.67 ± 1.16 −0.26
CES-D 5.00 ± 4.11 5.07 ± 2.11 4.86 ± 3.77 0.20
Total Female Male t-test
N 65 44 21
% Caucasian 71 66 81
Age (years) 44.99 ± 16.31 45.27 ± 15.90 44.38 ± 17.51 0.20
Education (years) 15.51 ± 1.90 15.48 ± 2.11 15.57 ± 1.40 −0.21
MMSE 28.62 ± 1.07 28.59 ± 1.04 28.67 ± 1.16 −0.26
CES-D 5.00 ± 4.11 5.07 ± 2.11 4.86 ± 3.77 0.20

Note: All t-tests for comparisons between sex groups were not significant.

### MRI Acquisition and Volumetry

The high-resolution hippocampus imaging sequence and manual demarcation procedures have been detailed elsewhere (Bender et al. 2013). Briefly, structural imaging was acquired as part of a 1-h protocol on a 3-T Siemens Verio (Siemens Medical AG, Erlangen, Germany) full-body magnet with a 12-channel head coil. For hippocampal subfield and EC measures, we acquired a high-resolution proton density-weighted turbo spin echo sequence in the coronal plane, perpendicular to the long axis of the hippocampus, with the following parameters: voxel size = 0.4 mm × 0.4 mm × 2.0 mm (30 slices); echo time = 17 ms; repetition time = 7150 ms; flip angle = 120°; pixel bandwidth = 96 Hz/pixel; turbo factor 11; field of view = 280 × 512 mm. In addition, a T1-weighted magnetization-prepared rapid gradient-echo (MPRAGE) sequence was acquired with the following parameters: repetition time = 1680 ms; echo time = 3.51 ms; inversion time = 900 ms; flip angle = 9.0°, pixel bandwidth = 180 Hz/pixel, GRAPPA acceleration factor PE = 2; voxel size 0.67 mm × 0.67 mm × 1.34 mm.

Hippocampal subfields and EC volumes were manually demarcated following rules adapted from Shing et al. (2011) [modified from Mueller et al. (2007) and Mueller and Weiner (2009); see Fig. 1 for an example of manual tracings]. Using Analyze v11.0 software (Mayo Clinic, Rochester, MN, USA), 2 expert raters (A.M.D. and A.R.B.) manually demarcated regional boundaries with a stylus on a 21-in. digitizing tablet (Wacom Cintiq). Image intensities were inverted to mimic an inversion-recovery T1-weighted image. Rater reliability was confirmed by an interclass correlation coefficient [ICC(2); Shrout and Fleiss 1979] of at least 0.90 for bilateral and total volume of each region. ICC(2) for total volume of each region were: EC = 0.99; subiculum = 0.93, CA1–2 = 0.91, and CA3–DG = 0.93.

Figure 1.

An example of manual tracing of the EC and hippocampal subfields: EC—red; subiculum—green; CA1–2—yellow; CA3–dentate gyrus—blue.

Figure 1.

An example of manual tracing of the EC and hippocampal subfields: EC—red; subiculum—green; CA1–2—yellow; CA3–dentate gyrus—blue.

Regions included subiculum, CA1–2 as a single region, and CA3–4 and DG as a single region (CA3–DG). Ranges were allowed to differ by starting slice based on anatomical hemispheric differences. To ensure separation between the hippocampus and amygdala, the hippocampal subfield range began with the slice posterior to the uncal sulcus on which the head of the hippocampus was no longer visible. All subfields were traced on 3 contiguous slices of the anterior hippocampus body. EC was traced on 6 contiguous slices, extending 5 slices anterior to the start of the subfield range. This protocol for manual segmentation of the subfields has been implemented by independent laboratories to different populations on various MRI platforms and produced similar estimates of regional age differences (Mueller et al. 2007; Shing et al. 2011; Bender et al. 2013; Raz et al. 2014). Subfield and EC volumes were adjusted for intracranial volume (ICV) via ANCOVA (Jack et al. 1989). ICV was measured from the T1 MPRAGE using the brain extraction tool (Smith 2002) in FSL following previously reported procedures (Bender et al. 2013).

### Testing Procedures

The navigation task was administered as part of a larger battery of cognitive tests. The vMWM task was designed after that described in Moffat and Resnick (2002). The virtual environments were created in Unreal Tournament 2003, using the NavigationUT package. The vMWM task was administered on a computer with a 17-in. LCD screen. The virtual environments were viewed from the first-person perspective at the water level. Participants moved throughout the environment by controlling a joystick with their dominant right hand. Participants could stop movement at will, but travel speed was constant; backward movement was not permitted.

#### Practice

Prior to testing, participants were exposed to a practice pool environment. The pool was placed within a larger room, without external landmark cues. Five platforms were visible above the water in the pool. Each platform was marked by a letter A–E displayed on a cube suspended in the space above the platform. The participants were instructed to use the joystick to travel over each platform in alphabetical order. There was no time limit and successful completion of the trial confirmed adequate control of the joystick. Subsequently, participants were instructed that in following test trials there would be a platform similar to those in the practice pool, but that the platform would be hidden beneath the water.

#### Virtual Morris Water Maze

The test environment was a virtual pool in a larger room with several objects surrounding the pool perimeter, as well as 2 unique wall characteristics on the room boundaries. The features of the room were unchanged throughout the experiment. (See Fig. 2 for an overhead view of the testing vMWM.) The goal platform (∼12% of the size of the pool area) was centered in one quadrant of the pool. The platform was hidden and stationary. Upon reaching the platform, participant motion would be halted, the platform would lift above the water plane, and a sound would play.

Figure 2.

An overhead view of the testing vMWM environment.

Figure 2.

An overhead view of the testing vMWM environment.

The task was repeated for 25 learning trials. The participant started each trial in 1 of 5 locations in the 3 quadrants that did not contain the platform. Each starting location was equidistant from the platform. Presentation of the starting locations was randomized and counterbalanced across participants. The facing direction at each starting location was random. Trials were limited to 2 min of free exploration, with a 5-s delay between trials. The retained sample of N = 65 had complete data for all 25 test trials. Performance was measured by distance (virtual units) traveled from the starting location to the first platform intersection and fractal dimensionality of the search path.

#### Fractal Dimensionality Calculations

Fractal dimension of the search path was calculated following procedures developed in our laboratory (Daugherty et al. 2015). Participant movement in the vMWM during each trial was recorded as Cartesian coordinates sampled at a 100-Hz rate. This record was submitted to fractal dimension calculation using the Fractal software (v 5.20) developed by Nams (Dalhousie University, http://www.dal.ca/faculty/agriculture/environmental-sciences/faculty-staff/our-faculty/vilis-nams/fractal.html; last accessed 2 September 2015). Calculations were performed with the fractal mean function (freeing estimation parameters), which samples the path twice and corrects for truncation at the beginning and end of the path (Nams 2006).

#### Control Variables

Two control measures assessed possible age- and sex-related differences in proficiency of joystick control and prior experience with three-dimensional (3D) virtual environments (i.e., video games). After completing all learning trials, participants repeated the task in the same environment, but the location of the platform was marked by flags suspended above the water. Participants were instructed to move toward the flags as quickly as possible, and distance was treated as a control measure for individual differences in joystick control. Finally, participants completed a 7-point Likert rating (1—Never; 7—Every day) of how often they played video games that displayed a 3D environment.

### Data Conditioning and Statistical Analysis

Distance measures were log-transformed to alleviate skew, and outliers in fractal dimension and regional volumes were winsorized. Partial correlations between path length (distance) and complexity (fractal dimension), controlling for age, were computed for each trial to examine the relation between the 2 navigation indices. Simple effects were examined in a general linear modeling (GLM) framework: repeated measures to test for volume differences by hemisphere (4 regions × 2 hemispheres), and simple age and sex effects in navigation distance and fractal dimension (25-level repeated measures by trial), all models including the control variables.

#### Trial-By-Trial Learning

A two-level hierarchical linear model (HLM) estimated trial-by-trial learning as linear change in distance across 25 learning trials (π1i; slope centered at trial 13) and by change in fractal dimension across trials (π2i; effect centered at the sample mean). This method accounts for the possible limiting effect of trial 1 (π0i; intercept) performance on slope. Age (mean-centered), sex, and the 2 control variables were included as covariates to predict differences in both intercept and slope. In secondary HLM analyses, regional subfield and EC volumes were entered as additional covariates (centered at the sample means) to predict differences in intercept and slope, while controlling for age and sex. Due to correlations among subfields (Table 2), regional volumes were entered into models separately to avoid multicollinearity. False discovery rate (FDR) adjustments were made to correct for the multiple comparisons (q-value). FDR following the two-stage method is a robust approach for multiple comparison correction (Benjamini et al. 2006).

Table 2

Bivariate correlations among age, average distance, and fractal dimension of the virtual water maze search path and regional hippocampal volumes

1. Age
2. Average distance 0.45*
3. Average fractal dimension 0.44* 0.64*
4. EC volume −0.21 0.03 −0.16
5. CA3–DG volume −0.22 0.00 −0.08 0.20
6. CA1–2 volume −0.20 0.06 0.06 0.36 0.54*
7. Subiculum volume 0.12 0.06 0.00 −0.03 −0.27 −0.14

1. Age
2. Average distance 0.45*
3. Average fractal dimension 0.44* 0.64*
4. EC volume −0.21 0.03 −0.16
5. CA3–DG volume −0.22 0.00 −0.08 0.20
6. CA1–2 volume −0.20 0.06 0.06 0.36 0.54*
7. Subiculum volume 0.12 0.06 0.00 −0.03 −0.27 −0.14

Note: Average distance and fractal dimension were calculated across 25 learning trials.

EC, entorhinal cortex; CA, cornu ammonis; DG, dentate gyrus.

*significant correlation, P < 0.05.

#### Example HLM

Level-1 Model

$Distanceti=π0i+π1i(Trialti)+π2i(FractalDimensionti)+ϵti$
Level-2 Model
$π0i=β00+β01(Agei)+β02(Sexi)+β03(ROIVolumei)+β04(3DExpi)+β05(Joysticki)+r0i$

$π1i=β10+β11(Agei)+β12(Sexi)+β13(ROIVolumei)+β04(3DExpi)+β05(Joysticki)$

$π2i=β20+β21(Agei)+β22(Sexi)+β23(ROIVolumei)+β04(3DExpi)+β05(Joysticki)$

#### Shared Variance Between Age and ROI Volumes with Trial Learning

A shared-over-simple (SOS) effects analysis determined the interaction between age and ROI volume in predicting trial learning. A theoretical conceptualization of aging suggests that the cognitive changes that occur over time are at least in part due to the cumulative change in neural correlates. In the present cross-sectional study, this degree of dependency statistically manifests as collinearity between age and regional volumes in predicting differences in navigation, which can be expressed with SOS as a percentage of shared variance. SOS was calculated according to Lindenberger and Pötter (1998) [also see Lindenberger et al. (2011)], and variance components were calculated after Kreft and de Leeuw (1998) and Singer (1998).

#### Asymptote of the Learning Curve

Asymptotes of the learning curves were identified by inspecting plots of average distance and fractal dimension across trials and comparing standard error of the sample mean across trials. The trial corresponding to the nadir of the learning curve was considered to be the beginning of the asymptote. Stable performance was confirmed by comparing distance and fractal dimension across identified asymptote trials in a repeated-measure GLM. A non-significant difference across successive trials was taken as evidence of an asymptote. From this analysis, individual differences in asymptote were tested with respect to age, sex, regional volumes, and control variables.

## Results

### Correlations Between Path Length and Complexity Across Learning Trials

To demonstrate the relation between navigation path length (distance) and path complexity (fractal dimension), we calculated partial correlations, controlling for the mutual relation with age. See Supplementary Table 1 for all partial correlation across the 25 learning trials. When examining the correlations between path length and complexity, an interesting pattern emerges. First, the 2 measures were not significantly correlated on the first trial (rage = 0.22, P = 0.08, Bonferroni α′ = 0.002). After the first trial, path length and complexity were positively correlated with a varying degree, but all correlations were significant (rage = 0.42–0.80, all P≤ 0.001; Bonferroni α′ = 0.002). Second, the magnitude of correlations between path length and complexity during the first phase of learning (trial 2–14: rage = 0.42–0.71; average correlation = 0.55) was smaller when compared with later trial performance that approached asymptote (trail 15–25: rage = 0.56–0.80; average correlation = 0.71; F1,12 = 24.79, P < 0.001). Therefore, the 2 measures of navigation ability are related only when both measures are improving with repeated trial learning, and the correlation increases when performance approaches an asymptote. Taken together, the 2 measures are correlated but potentially capture 2 different qualities of navigation behavior: path length and complexity [also see Daugherty et al. (2015)]. We further test this proposition by examining potential differences in the association between age and each index and in the slope of change in each measure across repeated learning trials, as well as testing for differential correlations between hippocampal subfield volumes and each index.

### Average Age Differences: Simple Effects Analysis

A 4 (region) × 2 (hemisphere) repeated-measure GLM revealed neither hemispheric differences in regional volumes (F1,62 = 2.11, P = 0.15), nor age by hemisphere interaction (F1,62 = 0.04, P = 0.84), and therefore, in the remaining analyses, we used total volumes collapsed over 2 hemispheres for each region. In these analyses, advanced age was associated with smaller volumes of the subfields and EC (F1,62 = 5.15, P = 0.03), and the age effect did not differ by region (F1,62 = 2.25, P = 0.10). Regional volumes (adjusted for ICV) did not differ between men and women (F1,62 = 0.36, P = 0.55).

Subfield and EC volumes were unrelated to average distance (all F1,56 ≤ 0.47, P ≥ 0.43) or average fractal dimension (all F1,56≤ 1.68, P ≥ 0.20). Advanced age was associated with greater average path length (F1,56 = 7.89, P < 0.01) and greater path complexity (F1,56 = 6.94, P = 0.01). There were no sex differences in search path length (F1,56 = 0.91, P = 0.35) or complexity (F1,56 = 0.56, P = 0.46). Although older adults reported less experience playing games with 3D environments than younger participants did (F1,62 = 22.83, P < 0.001), there were no age differences in joystick control (F1,62 = 1.94, P = 0.17). Women had less 3D gaming experience (F1,62 = 10.76, P = 0.002) and also performed worse on the joystick control trial (F1,62 = 6.81, P = 0.01) than their male counterparts. However, neither control measure was related to average distance (F1,56 = 2.11 and 0.61, P ≥ 0.15, 3D games experience and joystick control, respectively) or fractal dimension (F1,56 = 0.92 and 0.01, P ≥ 0.34, experience and control, respectively).

### Trial-By-Trial Learning: Hierarchical Linear Modeling

In a two-level HLM, we modeled change in distance across 25 learning trials and change in fractal dimensionality of the search path across trials, and evaluated individual differences in learning slope components related to age, sex, and regional volumes, including control variables. Search distance (−0.01, t1550 = −3.06, P = 0.002; Fig. 3) and fractal dimensionality of the search path (−0.001, t1559 = −5.78, P < 0.001) significantly decreased across trials. The decrease in fractal dimensionality was associated with the distance shortening (5.24, t1550 = 8.17, P < 0.001) beyond the effect of repeated trials alone.

Figure 3.

(A) Change in average distance traveled in search of the platform (P = 0.002) and (B) change in average fractal dimension of search paths (P < 0.001) across 25 learning trials. Error bars represent standard error of the mean.

Figure 3.

(A) Change in average distance traveled in search of the platform (P = 0.002) and (B) change in average fractal dimension of search paths (P < 0.001) across 25 learning trials. Error bars represent standard error of the mean.

Age deficits in navigation learning were observed in path length and its fractal dimensionality. Older adults who traveled more complex paths (0.004, t60 = 2.60, P = 0.01) on trial 1 did not improve after 25 trials as much as their younger counterparts did. Furthermore, advanced age was associated with lesser reduction in path complexity across trials, which in turn accounted for lesser shortening of the search distance in the course of learning (−0.04, t1550 = −3.19, P = 0.001; Fig. 4). Age alone did not explain differences in search path length (intercept = 0.002, t60 = 1.29, P = 0.20; slope = 0.00005, t1550 = 0.74, P = 0.46). Regardless of age, participants who traveled longer distance (3.60, t60 = 59.62, P < 0.001) or had evidenced more complex paths (1.05, t60 = 125.89, P < 0.001) on trial 1 had steeper learning slopes, likely due to a floor effect. Navigation distance and fractal dimensionality were unrelated to sex (all t ≥ −0.50, P ≥ 0.62) or control variables (−0.44 ≤ t≤ 1.25, all P ≥ 0.21).

Figure 4.

A 3D scatter plot of the associations among age, fractal dimension slope, and distance learning slope (P = 0.001). The regression plane illustrates on a gray scale the three-way interaction: from black—younger age, greater improvement in fractal dimension, and greater improvement in distance to pale gray—older age, lesser improvement in fractal dimension and lesser shortening of the search path. As can be seen by the tilt of the regression plane labeled in darkening shade, older adults who had a large improvement in fractal dimension did not improve in search distance as much as their younger counterparts did.

Figure 4.

A 3D scatter plot of the associations among age, fractal dimension slope, and distance learning slope (P = 0.001). The regression plane illustrates on a gray scale the three-way interaction: from black—younger age, greater improvement in fractal dimension, and greater improvement in distance to pale gray—older age, lesser improvement in fractal dimension and lesser shortening of the search path. As can be seen by the tilt of the regression plane labeled in darkening shade, older adults who had a large improvement in fractal dimension did not improve in search distance as much as their younger counterparts did.

### Association Between Regional Volumes and Trial-By-Trail Learning

Differences in subfield volumes were linked to individual differences in navigation learning. Independent of age, larger subiculum volume was associated with greater reduction in path complexity, which was associated with a greater improvement in distance measures across trials (0.03, t1548 = 2.97, P = 0.003, q = 0.01; Fig. 5). A similar effect was observed in the EC—larger EC was associated with a greater improvement in distance via decreased path complexity, but the effect became a non-significant trend after the FDR correction (0.01, t1548 = 2.04, P = 0.04, q = 0.06). Age differences in subiculum volume accounted for 10% (SOS = 0.10) and EC volume for approximately 12% (SOS = 0.12) of the individual differences in change in distance by fractal dimension. Independent of the interaction with fractal dimension, change in distance did not correlate with subiculum volume (−0.00005, t1548 = −1.22, P = 0.22, q = 0.24), and the negative correlation between EC volume and change in distance alone did not survive correction (−0.00003, t1548 = −1.96, P = 0.04, q = 0.06).

Figure 5.

A 3D scatter plot of the relation between subiculum volume, fractal dimension learning slope, and distance learning slope (P = 0.004; q = 0.01). The regression plane illustrates on a gray scale the three-way interaction: from black—larger subiculum volume, greater improvement in fractal dimension, and greater improvement in distance to pale gray—smaller subiculum volume, lesser improvement in path complexity (fractal dimension), and lesser shortening of search distance.

Figure 5.

A 3D scatter plot of the relation between subiculum volume, fractal dimension learning slope, and distance learning slope (P = 0.004; q = 0.01). The regression plane illustrates on a gray scale the three-way interaction: from black—larger subiculum volume, greater improvement in fractal dimension, and greater improvement in distance to pale gray—smaller subiculum volume, lesser improvement in path complexity (fractal dimension), and lesser shortening of search distance.

Whereas larger subiculum and EC volumes were related to greater reduction in path complexity, larger CA1–2 volume was associated with a greater improvement in distance across trials (−0.0001, t1548 = −2.90, P = 0.004, q = 0.01; Fig. 6) and not with fractal dimensionality of the path (0.01, t1548 = 1.73, P = 0.08, q = 0.11). Age differences in CA1–2 volume accounted for approximately 1% of the age differences in change in distance across trials (SOS = 0.01).

Figure 6.

Differences in learning slope related to CA1–2 volumes. CA1–2 volume was treated as a continuous variable in the analyses, and only for illustration, volumes were divided at the sample median and plotted as 2 groups: small and large volumes. Error bars represent standard error of the mean.

Figure 6.

Differences in learning slope related to CA1–2 volumes. CA1–2 volume was treated as a continuous variable in the analyses, and only for illustration, volumes were divided at the sample median and plotted as 2 groups: small and large volumes. Error bars represent standard error of the mean.

Notably, subiculum (0.0001, t59 = 0.10, P = 0.93), EC (0.0005, t59 = 1.66, P = 0.10), and CA1–2 volumes (0.0004, t59 = 0.78, P = 0.44) were unrelated to the search distance on trial 1. Thus, participants with larger volumes of subiculum, EC, and CA1–2 began the task at the same level of performance as those with smaller volumes, but improved faster across trials. CA3–DG volume was unrelated to search path length (intercept = 0.001, t59 = 1.23, P = 0.23; slope = −0.00003, t1548 = −0.89, P = 0.38) or path fractal dimensionality (−0.0001, t1548 = 0.02, P = 0.99).

### Asymptote of the Learning Curves: Distance and Fractal Dimension

Inspection of Figure 3 indicates that participants reached asymptote by trial 15 in distance and path complexity, as indicated by the overlapping standard error of the mean intervals across all successive trials. Indeed, distance traveled (F10,560 = 0.51, P = 0.88) and fractal dimension of the path (F10,560 = 0.66, P = 0.76) did not differ across the last 11 trials. Subfield volumes were unrelated to asymptotes of distance (all F1,56≤ 0.40, P ≥ 0.53) and fractal dimensionality (all F1,56≤ 1.06, P ≥ 0.31). Thus, larger volumes of EC and hippocampal subfields were associated with faster acquisition (i.e., steeper slope) in the beginning, but not greater gains at the end of the acquisition process. Independent of subfield volume, age was positively associated with average distance (F1,56 = 8.79, P < 0.01) and average fractal dimension (F1,56 = 5.62, P = 0.02) in the asymptote portion of the acquisition curve. Although older adults demonstrated stable performance by the end of the acquisition trials both in path length (F10,560 = 0.72, P = 0.70) and fractal dimension (F10,560 = 0.66, P = 0.76), by either measure the level of performance was still worse than their younger counterparts. Differences in the asymptotes of path length and fractal dimensionality were unrelated to sex (F1,56 = 1.99, P = 0.16 and 1.27, P = 0.26, respectively), 3D game experience (F1,56 = 1.80, P = 0.19 and 0.49, P = 0.49, respectively), and joystick control (F1,56 = 0.24, P = 0.63 and 0.04, P = 0.85, respectively).

## Discussion

The main finding in this study is the dissociation between volumes of hippocampal subfields and 2 related, yet distinct, aspects of human place navigation. As the search paths became less meandering with practice, larger subiculum was associated with faster reduction in path complexity over trials, whereas shortening of the search path length was related to larger CA1–2 volume. Moreover, whereas there was no direct association between path length with subiculum volume, larger volume was related to greater reduction in path complexity, which in turn was associated with more pronounced search path shortening. A larger EC volume was also associated with path shortening, both directly and indirectly via greater reduction in path complexity; however, neither effect survived correction for multiple comparisons. Differences in the volumes of subiculum, EC, and CA1–2 collectively accounted for 23% of the age-related variance in vMWM navigation learning, making these regions plausible candidates for neural substrates of age-related declines in place navigation.

Complexity of the search path as measured by fractal dimensionality has been proposed as an indicator of cognitive mapping processes that are engaged while navigating an environment (Daugherty et al. 2015). A cognitive map, or internal representation of the environment including landmarks, is formed in the course of learning an environment and is at least indirectly informed by an individual's movement through that environment (O'Keefe and Nadel 1978). Moreover, the cognitive map is thought to be referenced when planning prospective movement and assessing past movements (O'Keefe 1990, 1991). The multifaceted internal processing may be reflected in the complexity of the navigation path and unnecessarily complex, meandering paths suggest a deficit in cognitive mapping processes (Moffat and Resnick 2002; Daugherty et al. 2015). The fractal dimension index, therefore, indirectly measures this internal navigation decision process that shapes a navigation path by quantifying the path complexity. These processes that are inherent to navigation are believed to depend on the integrity of hippocampal and other medial temporal lobe circuits (O'Keefe and Nadel 1978). Indeed, smaller volumes of total hippocampus and parahippocampal gyrus were associated with age-related differences in path complexity on a different version of the vMWM (Daugherty et al. 2015). In this study, we noted that the association between fractal dimensionality and volumes of subiculum and EC with age differences in vMWM navigation was substantially stronger than that between CA1–2 volume and path length. Our findings provide further validation of fractal dimensionality as an index of distinct cognitive processes that may have separate brain substrates.

The observed association between subiculum volume and success in spatial navigation learning is a novel finding that adds to the extant literature on human spatial navigation. Although originally cognitive mapping was at first assigned to the grossly defined hippocampal complex (O'Keefe and Nadel 1978), later research indicated that it also relies on activity of the grid-like cells in the EC (Hafting et al. 2005; Derdikman and Moser 2010). Furthermore, integration of new knowledge about the environment and accurate update of an existing cognitive map requires information flow through CA1–EC connections [Lavenex and Lavenex 2013; see Jones and McHugh (2011) for a review]. The primary efferent pathway from CA1 to EC passes via the subiculum, which may thus play an important role in facilitating path integration and cognitive mapping [see O'Mara et al. (2009) for a review]. Evidence from rodent lesion studies lends credence to this notion (Morris et al. 1990; Oswald and Good 2000). We find further support in the dissociation between the roles of subiculum and CA1–2 in reducing complexity and length of the search path observed in our study. Of note is a previous report of rodents with lesioned subicula that persistently swam complex paths in the MWM, despite eventually completing the task (Morris et al. 1990). Our novel observation in humans is in accord with these earlier findings in rodents.

Notably, smaller volumes of EC and hippocampal subfields were associated with slower acquisition, but unrelated to the differences in the asymptotic performance. When healthy adults are allowed sufficient time for practice, smaller volumes of the medial temporal structures are not associated with a persistent deficit. This finding is in line with the evidence from animal studies, in which rodents with hippocampal lesions can often overcome the initial deficit if given an ample number of learning trials (Schenk and Morris 1985; Morris et al. 1990; Oswald and Good 2000). This convergence of findings across mammalian species is consistent with the notion of the cognitive map as a tool for efficient navigation (O'Keefe and Nadel 1978), which is not a necessary prerequisite for eventually reaching the destination [see Morris et al. (1990) and Oswald and Good (2000)].

The distinction between accuracy and efficiency is critical in our conceptualization of navigation ability and the source of age deficits therein. Cognitive mapping is considered to inform both accurate and efficient navigation (O'Keefe and Nadel 1978). Thus, path complexity reflects the internal decision-making in reference to a cognitive map, and path length as an index of efficiency measures the consequence of this process. This is further substantiated in the pattern of correlations between the 2 indices across repeated learning trials, and the strengthened correlations when performance approaches an asymptote [also see Daugherty et al. (2015)]. However, just as path complexity and length are complementary measures, the differential correlations between the indices and hippocampal subfield volumes must also be viewed as integrative components that serve a singular navigation behavior. Subiculum may more specifically represent the formation of a cognitive map that indirectly informs navigation efficiency, whereas CA1–2 more specifically represents the optimization of navigation efficiency. However, neither subfield will function independent of the other or the EC; collectively, the structures compose a network that may represent cognitive mapping functions [see O'Mara et al. (2009); Jones and McHugh (2011); Lavenex and Lavenex (2013)]. Based on this reasoning, it appears that age deficits in efficient vMWM navigation arise from impaired acquisition of novel landmark cues and subsequent development of a cognitive map, which are associated with the structural integrity of the subiculum and CA1–2, and possibly the EC. Critically, despite impairment to acquisition and subsequently less-efficient navigation, older adults in this study were still able to learn the location of the platform, thus highlighting the distinction between accuracy and efficiency.

In contrast to age-related volume deficits that are eventually overcome, advanced age was still associated with persistent deficits in vMWM navigation, even after asymptotic levels of skill were reached. Older adults began the task by traveling greater distance and taking more complex paths, and did not improve as quickly as their younger counterparts did. Impaired acquisition of navigation skill in advanced age has been reported before in studies that raised questions about the ability of older navigators to overcome the deficit (Kirasic 1991; Gallagher et al. 1993; Harris and Wolbers 2012). Here, we observed that older adults reached an asymptote after 14 trials and thus showed clear evidence of relatively intact and stable learning processes. However, the asymptotic level of performance of the older participants remained worse than that of the younger adults. Thus, successful acquisition of a navigation skill was insufficient to mitigate age-related deficit in performance.

The observed persistence of age differences may be in part explained by suboptimal cognitive mapping. Even when shortening of the path length indicated improvement in navigation efficiency, the paths traveled by older adults remained more complex and meandering than those of younger participants. Yet, volumes of medial temporal lobe structures were unrelated to asymptotic performance, suggesting additional mediators of age-related differences. These contributors may include individual and age-related variation in knowledge and use of strategies (Rodgers et al. 2012; Harris and Wolbers 2014), as well as in such functions as working and associative memory (Magnusson et al. 2003).

The CA3–DG subfields may serve as neural substrates of the associative component in navigation (Jones and McHugh 2011), but we found no evidence for CA3–DG contribution to explain individual differences in the present task. Associative memory is vulnerable to normal aging (Bender et al. 2010) and in older adults, reduced associative memory performance correlates with smaller volume (Shing et al. 2011; Bender et al. 2013) and decreased activation (Yassa et al. 2011) of CA3–DG. The associative memory component is essential for successful navigation, especially when discriminating between old and novel cues (Wolbers and Hegarty 2010; Jones and McHugh 2011). In this study, we may have not identified CA3–DG involvement in vMWM navigation due to the task design that stressed immediate learning in a stable environment across many trials and de-emphasized novel discrimination. It is plausible that, in a dynamic environment, differences in CA3–DG volume might have emerged as contributors to deficits in novel discrimination (Jeewajee et al. 2008; Leutgeb et al. 2008; Nakashiba et al. 2008), and future studies should test this hypothesis.

The reported findings must be interpreted in the context of several limitations. First, the volumes of hippocampal subfields were obtained from three 2 mm slices of the anterior hippocampal body. These slices are taken as representative of the hippocampal body [see Mueller et al. (2007); Mueller and Weiner (2009)] and the resulting volume estimates consistently show age-related differences (Shing et al. 2011; Bender et al. 2013; Raz et al. 2014). However, it is possible that posterior hippocampal regions play a differentially important role in spatial navigation [Maguire et al. 2000, 2006; Nadel et al. 2012; but see Broadbent et al. (2004) and Poppenk et al. (2013) for reviews]. On the other hand, evidence of a clear anterior–posterior distinction of hippocampal-dependent navigation function is lacking. For example, functional activation in the anterior hippocampus and surrounding cortex correlates with the ability to recall relative spatial information (Ekstrom et al. 2011) and representation of distance relationships (Morgan et al. 2011)—key aspects of a cognitive map (O'Keefe and Nadel 1978). Indeed, initial evidence from functional neuroimaging in humans suggests that grid-like activation in the EC and anterior subiculum region correlates with spatial navigation ability (Doeller et al. 2010). Thus, attention to that part of the structure has substantial justification. Moreover, the proposed anterior–posterior subdivisions within the hippocampus are not anatomically distinct entities and are defined ad hoc, based on specific research hypotheses [see Poppenk et al. (2013) for a review]. In contrast, decades of work in animal models have shown the hippocampal subfields to be anatomically, cytoarchitectonically, and functionally distinct entities, and thus are more plausible targets of inquiry (Duvernoy 1988; Jones and McHugh 2011; Lavenex and Lavenex 2013).

Nonetheless, expanding the range from which hippocampal subfield volumes were sampled would improve validity of the comparisons and is certainly a worthy goal for future studies. Inclusion of the most anterior region of the hippocampus that has complex morphometry results in reduced reliability of the measures, and therefore reduces their validity. Furthermore, poor visualization of the subfields in the tail of the hippocampus on the high-resolution T2 sequence acquired on the 3-T magnet make reliable measurement in this portion of the hippocampus difficult. In the future, studies with higher magnetic field strength and even higher resolution may be able to address these barriers to complete subfield segmentation. Despite the limitation, the three 2 mm slices that are measured in the present study are representative of the hippocampal body and provide reliable and valid estimates of subfield volumetry [see Shing et al. (2011); Bender et al. (2013); Raz et al. (2014)], if not total hippocampal volume.

Second, because of the statistical power constraints, we did not include multiple age-related covariates in the analysis. For example, some of the hippocampal subfields measured in this study are differentially vulnerable to vascular insults such as hypoxia and ischemia (Pulsinelli et al. 1982; Petito and Pulsinelli 1984; Suyama 1992) that may be present at subclinical levels in older participants who carry vascular risk factors. Indeed, we previously reported that CA1–2 volumes were smaller in participants with diagnosed hypertension (Shing et al. 2011; Bender et al. 2013) and were affected by genetic risk for inflammation (Raz et al. 2014). Here, we intentionally excluded participants with hypertension to avoid this possible confound. In a larger sample that included cardiovascular risk factors, a larger effect for CA1–2 may be identified to explain additional variability related to age.

Third, we have tested for differential correlations between subfields and age-related differences in navigation. Although their functional specificity is evidence-based (Jones and McHugh 2011; Mueller et al. 2011; Lavenex and Lavenex 2013), the subfields do not function independent of the rest of the hippocampal complex. Functional and structural integrity in one region affects similar characteristics of another. Therefore, the study of subfields can provide insights into the neural correlates of age-related differences in vMWM navigation, but we cannot claim completely independent effects of a given subfield. Investigation of connectivity of the subfields with the rest of the brain and among themselves is an important goal for future studies. Furthermore, our interpretation of the effects in the context of a cognitive map is limited by the lack of an egocentric navigation comparison. Future studies that are designed to distinguish ego- and allocentric navigation may identify a clearer differentiation of cognitive mapping functions between the hippocampal subfields and EC.

Finally, a significant limitation of this study is its cross-sectional design, which is inherently incapable of revealing the dynamics of age-related change and, most importantly, individual differences therein (Lindenberger et al. 2011). Because the participants of this study are enrolled in a longitudinal follow-up, we hope to alleviate this limitation in the near future.

In conclusion, in healthy adults of a wide age range, we found differential associations between regional medial temporal lobe anatomy and distinct aspects of spatial navigation. Greater reduction in path complexity was linked to larger volumes of subiculum and the EC, whereas a shortening of the path length was associated with larger CA1–2. Age-related differences in the rate of spatial skill acquisition could be explained in part by individual differences in volumes of medial temporal lobe structures. The results suggest future directions of exploring specific involvement of medial temporal lobe regions in various aspects of navigation, such as generation and updating of cognitive maps and the formation of associations.

## Supplementary Material

Supplementary material can be found at http://www.cercor.oxfordjournals.org/.

## Funding

This work was supported in part by a grant from the National Institute on Aging, R37-AG011230 to N.R.

## Notes

We thank Cheryl Dahle and Yiqin Yang for assistance in data collection. Conflict of Interest: None declared.

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