PEBL TECHNICAL REPORT 2011-05 http://sites.google.com/site/pebltechnicalreports/home/2011/pebl-technical-report-2011-05

The relationship between dietary antioxidant vitamin status and working memory capacity in young and older adults1

Robert D. McEwan Aston University Psychology, School of Life and Health Sciences, Aston University, Birmingham B4 7ET, UK [email protected]

1

This paper was submitted in partial completion of an undergraduate degree in Human Psychology at Aston University. An archive of the data reported in this report is available as a download that accompanies the technical report.

April 24, 2011

Dietary antioxidant vitamin status and working memory capacity

McEwan, R. D.

The relationship between dietary antioxidant vitamin status and working memory capacity in young and older adults Robert D. McEwan Aston University Psychology, School of Life and Health Sciences, Aston University, Birmingham B4 7ET, UK [email protected]

ABSTRACT Previous research has suggested that antioxidants serve to maintain cognitive function during normal aging. The present study investigated the relationship between dietary antioxidant vitamin levels and subcomponents of working memory in a young and older adult population. Both young (N = 16) and old (N = 19) groups completed three tasks (Tower of London task, mental rotation task and item-order task), each loaded on to a specific sub-component of working memory. Participants also completed a food diary which captured dietary intake over three days. This was analysed for mean daily intake measurements of antioxidant vitamins E and C. Results revealed a significant association between vitamin E levels and Tower of London task performance in older adults. No other meaningful associations between task performance and antioxidant vitamin levels were observed for both young and old groups. These findings suggest that vitamin E may play a role in maintaining the capacity of the Central Executive during normal aging.

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Introduction As the number of elderly people increases, so does the number of people exhibiting age-related cognitive deficits, and it is becoming more and more important to identify ways to preserve cognitive function in old age (Tinker, 2002). Cognition encompasses a number of key functions including memory and perception. As we age, these processes decline, yet the severity of these deficits depend on the specific function in question. For example, research has shown that age-related deficits in primary memory are minimal (Grady & Craik, 2000), whereas there are more significant deficits when stored information has to be actively manipulated (Craik & Jennings, 1992). A decline in cognitive function can often lead to difficulties living independently and a reduction in overall activity (Meydani, 2001). Theories of aging have been put forward to better understand such processes, how they relate to one another, and how we can achieve a good quality of life throughout the aging process. While there are a number of theories of aging, rooted in a variety of disciplines, there is one theory which has received considerable attention because of its potential for nutrition-based intervention. Proposed by Harman, the free radical theory of aging hypothesises that the aging process is the result of increased cellular damage caused by free radicals (Harman, 1956). Free radicals are atoms or molecules with unpaired electrons on their outer shell. While seeking to capture these missing electrons, and the subsequent chain reaction this causes, they can damage and destabilise cells. Free radicals are formed naturally during metabolism and play a role in the body’s immune system, but can also occur as a result of external factors in the environment such as radiation and pollution (Gerschman et al., 1954). The prevalence of free radicals increases with age and oxidative stress (the imbalance between free radical production and the ability to provide adequate defence) has been implicated in a number of diseases including Alzheimer’s disease (Markesbery, 1997) and Parkinson’s disease (Fahn & Cohen, 1992). By acting as reducing agents and donating an electron to these free radicals, antioxidants can provide a line of defence against oxidative stress. In an elderly population it is common for antioxidant status to fall short of the recommended levels, due to both the biological aging process itself and the socio-economic factors associated with aging (Robertson & Montagnini, 2004). For this reason, and because antioxidant intake can be adjusted so readily (through the use of supplements or changes in diet), the area has become a centre of much investigation. Research has indicated a relationship between age-related memory deficits and oxidative stress which suggests that antioxidants have a possible protective effect against memory decline (Joseph et al., 1999). In addition to this, antioxidants have been implicated in cardiovascular disease, with research showing the benefits of antioxidants in promoting cardiovascular health (Kris-Etherton & Keen, 2002). The link between cardiovascular health and cognitive health implies that antioxidants may play a role in cognitive function through this mechanism (Perkins et al., 1999). However, research into the possible benefits of antioxidants in non-elderly populations has revealed no association between antioxidants and cognition in young (Benton et al., 1995) or middle-aged (Peacock et al., 2000) adults, thus supporting the notion that the protective role of antioxidants is specific to age-related decline. The majority of research identifies vitamin E and C specifically as those antioxidants which are of value in the prevention of cognitive decline (Howes, 2008). The combination of vitamin E and C is effective because it defends against free radical damage in both parts of the cell: the cell membrane (vitamin E, fat soluble) and within the cell itself (vitamin C, water soluble) (Kaczmarski et al., 1999). A study by Maxwell et al. (2005) examined participants aged 65 and over on their antioxidant vitamin PEBL Technical Report 2011-05

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supplement usage and assessed their performance on the Modified Mini-Mental State examination (3MS). They found that the combined usage of vitamin E and C supplements not only deterred the effects of cognitive decline, but was also associated with fewer cases of vascular cognitive impairment (Maxwell et al., 2005). Furthermore, Wengreen et al. (2007) analysed the relationship between dietary intake of vitamin E and C (measured using food frequency questionnaires (FFQs)) and cognitive function (assessed by an adapted version of the 3MS). Measures of both dietary intake and cognition were taken at numerous points over a seven year period. Increasing levels of vitamin E and C were related to higher scores on the 3MS at baseline. Additionally, greater 3MS decline was associated with lower levels of these vitamins (Wengreen et al., 2007). The combined benefit of vitamin E and C has not always been observed, with a number of studies finding benefits for vitamin E only. Vitamin E has been described as “the most potent antioxidant” for its role in defending against oxidative stress, which may account for such findings in the research (Gilgun-Sherki et al., 2001, p.965). For example, Grodstein et al. (2003) investigated the use of vitamin E and C supplementation on cognitive function (as assessed by the Telephone Interview of Cognitive Status) and found a modest benefit for vitamin E but not vitamin C supplements. Likewise, results from a longitudinal study conducted over seven years found an association between vitamin E, but not vitamin C, and performance on a number of cognitive measures (Morris et al., 2002). Despite this, studies which have focused specifically on vitamin C have often found an association between the vitamin and fewer cases of severe cognitive impairment (Goodwin et al., 1983; Paleologos et al., 1998). This association has also been found where vitamin E was the sole focus of the research (Ortega et al., 2002). Studies have not always found a relationship between antioxidant vitamins and cognitive decline. Kang et al. (2006) examined the use of vitamin E supplements on healthy older women over three years. Participants were assessed on their general cognition, verbal memory and category fluency, and it was found that vitamin E supplementation had no effect on performance over the three years (Kang et al., 2006). Likewise, Yaffe et al. (2004) found that antioxidant supplementation did not improve performance on a cognitive battery after a median of seven years receiving the antioxidant treatment. Furthermore, using semi-quantitative FFQs to measure dietary intake, both Jama et al. (1996) and Devore, Kang et al. (2010) found no association between antioxidant vitamins and cognitive function. Although no relationship was observed with cognitive function, a follow-up study based on the data obtained in the Rotterdam Study (Jama et al., 1996) found an association between increased dietary vitamin E levels and a reduced risk of dementia and Alzheimer’s disease (Devore, Grodstein et al., 2010). In addition to measures of cognitive function, there has been some research looking at the role of antioxidants in memory. Studies into oxidative stress in Alzheimer’s disease would suggest that antioxidants play a role in the preservation of certain memory functions. Indeed, Perkins et al. (1999) found an association between antioxidant vitamin levels and memory. They analysed blood serum antioxidant levels of elderly participants and found a relationship between serum levels of vitamin E and performance on delayed word and story recall, such that higher vitamin E levels were associated with better memory performance (Perkins et al., 1999). Furthermore, Perrig et al. (1997) examined the relationship between plasma antioxidant vitamin levels and performance on tests measuring: working memory, explicit memory, implicit memory and semantic memory. They found that all measures except for implicit and working memory were associated with plasma antioxidant vitamin levels, such that higher vitamin levels were related to increased performance (Perrig et al., 1997). PEBL Technical Report 2011-05

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More recently, Chan et al. (2010) designed a nutritional formulation (NF), consisting of a number of vitamins (including vitamin E), which was then administered to healthy community dwelling individuals. Cognitive performance was assessed via the California Verbal Learning Test II (CVLT II), the Trail-Making test and the Digit-Memory Test. Each test was completed before, and then two weeks or three months after receiving NF. It was found that participant performance on the CVLT II and TrailMaking Test improved significantly after taking NF, and improvements were also observed for the Digit-Memory Test. More importantly, the removal of NF resulted in baseline performance, and its reinstatement led to significant improvements (Chan et al., 2010). Similarly, Summers et al. (2010) employed an antioxidant blend (containing 34 antioxidants) which was administered to individuals living independently in the community. Participant memory was tested via paired association and immediate recall tests at baseline, and then four months after taking the antioxidant blend. Performance on both tests improved significantly after four months of the blend - of which components included both vitamin E and C (Summers et al., 2010). The idea that antioxidants are beneficial to maintaining cognitive health during aging is rooted in a plausible theory. Research has shown the benefits that antioxidants have to cardiovascular disease as well as a number of neurodegenerative diseases. For these reasons, antioxidant vitamins may also offer a form of defence against more general age-related cognitive decline. While a number of studies have supported this idea, finding an association between increased antioxidant vitamin levels and improved cognition, there have also been a number of studies demonstrating an absence of such an association. The varied results obtained from these studies may be due, in part, to the various methodological approaches adopted. Specifically, the measurement of antioxidant vitamin intake is a factor which can greatly influence the outcome of research in this area. The most common methods measuring/manipulating antioxidant intake include: FFQs, analysis of blood serum levels and the use of supplements. Recent approaches which involve administering a cocktail of antioxidants have certainly proven to be successful. However, due to the practical and ethical limitations of this research, it is not possible to administer supplements, or to obtain blood plasma antioxidant vitamin levels. Therefore, antioxidant vitamin status will be measured by means of a food diary which will capture the dietary-intake of participants over a number of days. The use of a food diary rather than a food frequency questionnaire has the advantage of being able to provide precise information regarding quantities of food consumed (Gibson, 2005). Food diaries are also able to capture data regarding the use of supplements and medications, which may greatly alter antioxidant vitamin status. As with the majority of studies in this area, this research will focus specifically on the antioxidant vitamins E and C. With regards to previous research, few studies make reference to specific aspects of memory, tending to couple scores of memory with results on other tests of cognitive performance. More specifically, few studies have looked at working memory. Research has demonstrated the contribution of oxidative stress to the cognitive deficits associated with aging (Shukitt-Hale, 1999) and working memory is one aspect of cognition which is specifically sensitive to age-related decline (Hertzog et al., 2003). For this reason it may also be increasingly sensitive to antioxidant status, which operates to defend against oxidative stress. While Perrig et al. (1997) observed no association between antioxidant status and working memory (assessed using a single dual-task procedure); the single measurement they obtained does not reflect the multi-component aspect of working memory. It has been proposed that selecting a set of psychological tests that are loaded on to a specific aspect of memory would be a better approach to PEBL Technical Report 2011-05

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measuring antioxidant-induced changes in memory function (Benton et al., 2005). Therefore, this study will investigate the relationship between antioxidant vitamins (vitamins E and C) and working memory, with measures taken for each individual sub-component (Central Executive, Visuo-Spatial Sketchpad and Phonological Loop) as conceptualised by Baddeley and Hitch (1974). In addition to the target population of older adults, this study will employ a group of young adults. The data obtained from this group will be used to draw comparisons between the two populations. It is hypothesised that dietary antioxidant vitamin E and C levels will correlate with working memory performance in older adults, such that increased levels of these vitamins will account for gains in working memory performance. It is hypothesised that there will be no such correlation in a young adult population. These predictions are based on the free radical theory of aging, which suggests that agerelated memory deficits are related to increased oxidative stress, and therefore increased levels of antioxidant vitamins will help defend against this process.

Method Design A correlational design was adopted for this study in order to examine the relationship between dietary antioxidant vitamin levels and working memory task performance. There were two independent variables: the age of participants and levels of dietary antioxidant vitamins E and C. Measurements of total fat and energy (kcal) were also taken to provide a more complete nutritional analysis. The dependent variable was performance on three separate tasks of working memory. The specific measurement depended on the test of working memory in question. For both the mental rotation task and the item-order task, the measurements taken were response times and error rates. For the Tower of London task, the measurements were planning time (time between presentation of the problem and the first move) and number of steps taken for each trial. The choice of tasks mirrored those used by Green et al. (2003).

Participants Thirty-five participants were obtained in total and assigned to one of two groups based on age. Participants were assigned to the young adult group if they were aged between 18 and 30 years and to the older adult group if they were between 60 and 85 years of age. Participants who did not fall within one of these age brackets were not permitted to take part in the study. A total of 16 participants (3 males, 13 females) were assigned to the young adult group (mean age = 20.75, SD = 2.41), and a total of 19 participants (7 males, 12 females) were assigned to the older adult group (mean age = 70.42, SD = 7.31). The young adult population were sampled from undergraduate psychology students at Aston University who had expressed an interest to participate through the web-based Psychology Research Participation System. These students were given research credits in return for participating in the study. The older adult population were recruited on a voluntary basis from independent living facilities and community homes for the elderly. Permission was obtained from these facilities to place posters around the building along with sign-up sheets so that residents could leave their details if they were interested in participating. Posters and sign-up sheets were displayed in a total of five different establishments in the West Midlands.

Materials PEBL Technical Report 2011-05

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Working memory tasks A computer running the Psychology Experimental Building Language (PEBL) version 0.11 was used to present the three working memory tasks (all selected from the PEBL test battery 0.6). The tasks were displayed on a 20 inch monitor and the ‘Fullscreen’ option box was checked on the PEBL Launcher. The three tasks chosen from the battery were: mental rotation (Rotation.pbl); Tower of London (TOL.pbl); and the item-order task (itemorder.pbl). In the default list of configurations for the Tower of London task, the first configuration was used (‘[1] Unconstrained pile heights, {3,4,5} disks, progressive difficulty, 24 trials’). The item-order task was edited so that the lengths of the consonant strings were reduced from seven to six letters. These strings were created from either a set of seven phonologically confusable or seven phonologically non-confusable letters. Additionally, in-task feedback was removed and presentation times of the letter strings were altered (for more specific information about these changes see Procedure). Food diary A three-day food diary was created to capture participants’ dietary intake. The diary comprised a set of instructions, an exemplary set of intake records and sufficient space for participants to record their dietary intake. The diary was structured with headings relating to: time of consumption, actual food eaten, preparation of the food, brand name and amount eaten. A ‘comments’ section was included at the end of each day for participants to write any relevant additional information.

Procedure The study was conducted in the Aston University research laboratories, with each participant completing the three working memory tasks. Before participants completed the tasks they were briefed as to the nature of the study and their full written consent was attained. Participants were informed of their right to withdraw from the study at any time. Following the completion of each task participants were asked if they wanted a short break and were also given the opportunity to ask questions. After completion of the working memory tasks participants were handed a food diary and fully debriefed. They were reminded that their data would remain confidential and were informed that they could retract their data should they wish. The testing session lasted approximately 30 minutes and the procedure was identical for each participant, with the three tasks being completed in the following order. Tower of London task The Tower of London task (Shallice, 1982) is commonly used to assess the Central Executive component of working memory (Baddeley, 1986). Participants were presented with on-screen instructions prior to the task commencing. The aim of the task was to move a number of coloured disks one-at-a-time in order to match the target configuration indicated at the top of the screen. There were three poles with no constraints on pole height and three different coloured disks distributed randomly onto the poles; increasing to four and then five different-coloured disks as the task progressed. The block configuration of both the target arrangement and initial test arrangement was randomised. Participants were required to click a pole in order to lift the top block from that pole, and then click a different pole to drop the block down on to it. There were 24 trials in total. Mental rotation task PEBL Technical Report 2011-05

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This task was designed to measure the Visuo-Spatial Sketchpad component of working memory and is a simple implementation of Shepard and Metzler’s classic mental rotation task (Shepard & Metzler, 1971). Instructions were presented on-screen prior to the task commencing. Participants were presented with pairs of polygons. Each pair was presented simultaneously and participants were required to indicate whether the pair was identical (subject to rotation) or whether they were different shapes (a mirror image of each other). If participants believed that the pairs of polygons were identical, they were to respond by pressing the ‘s’ key on the keyboard for ‘same’. If they thought the pair was different, they were to respond by pressing the ‘d’ key for ‘different’. Each polygon was rotated from its original position by a 0, 45, 90, 135, 180, 225, 270 or 315° angle. The task was counterbalanced for angle of rotation, same/different pairs of polygons, and polygon shape (8x2x2 conditions respectively, with each condition displayed twice). There were 64 trials in total. Item-Order task This task involved the assessment of two consecutive letter strings and determination of whether they were the same or different. This task is loaded on to the Phonological Loop component of working memory and is an implementation of the Item-Order test from the Unified Tri-Services Cognitive Performance Assessment Battery (UTCPAB; see Perez et al., 1987). Letter strings were six characters in length and comprised from a selection of seven phonologically confusable (BCDGPTV) and seven phonologically non-confusable (FHJMQRZ) consonants. Different trials were created by either changing the identity of a letter or by changing the order of two adjacent letters. Participants were presented with a set of instructions prior to commencement of the test. A six-consonant string was presented in the centre of the screen for 2.8 seconds. It then disappeared for 2.2 seconds followed by the appearance of a new string. Participants then had to respond by pressing the left shift key if they thought the consonant strings were the same and the right shift key if they thought the strings were different. After a response was made a fixation point was presented in the shape of a ‘+’ for 1.2 seconds prior to the subsequent trial. There were 40 trials in total which comprised: 20 trials where the second consonant string was identical to the first; 10 trials where the second string had a letter substituted; and 10 trials where a pair of adjacent letters were swapped. Food diary Participants were handed a paper-based food diary to complete in their own time. The diary had to be completed for three days (two weekdays and one day on the weekend – a representative sample of their weekly dietary intake). It was not essential for participants to complete the diary on consecutive days, but it had to be completed within 21 days of completing the working memory tasks. The food diary required participants to write down everything they consumed from the time they woke up until the time they went to sleep.

Analysis Nutritional The nutritional analysis software WISP (Tinuviel Software, version 3.0) was used to analyse the data obtained from participant food diaries and the UK food composition databank was selected as the reference source for nutrient composition. Following the input of participant data recorded over the three days, a mean daily intake analysis was conducted which provided daily averages of participant nutritional intake. Values for vitamin E, vitamin C, total fat and energy (kcal) intake were acquired. PEBL Technical Report 2011-05

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Statistical Data was analysed using the Statistical Package for the Social Sciences (SPSS) version 17.0.0 for Windows. Task performance and nutrition values were subject to a two-way independent ANOVA with factors of age group and gender. Pearson’s product-moment correlation coefficient was used to analyse the relationships between task performance and antioxidant vitamin levels (vitamin E and C). Participant age, fat intake and energy (kcal) were also included in the analysis, but were not reported unless significant.

Results Task performance Descriptive statistics for participant performance on each task of working memory by age group and gender are shown in Table 1. The statistics reveal that, in terms of response and planning times, males and females in the young adult group were faster than males and females in the older adult group. However, error rates and average steps showed less variance between young and old groups (see Table 1). Inferential statistics are reported below. Table 1: Working memory task performance by age group and gendera Young adult group N Tower of London planning b times Tower of London average steps Mental rotation response timesb Mental rotation error ratesc Item-order response timesb Item-order error ratesc

Older adult group

Male

Female

Male

Female

3 5.6 ± 1.3 6.2 ± 0.7 3.9 ± 1.3 46 ± 4.6 1.6 ± 0.6 6 ± 7.9

13 4.4 ± 1.2 7.7 ± 1.3 2.6 ± 1.4 51 ± 8.3 2 ± 0.7 23 ± 11

7 12.4 ± 4.2 8 ± 1.6 7.2 ± 3.7 51 ± 7.1 3.3 ± 0.7 29 ± 12

12 9.8 ± 3.9 7.6 ± 1.1 6.1 ± 2.4 50 ± 6.5 2.7 ± 0.7 29 ± 11

a

Values are means ± SD.

b

Time in seconds.

c

Percentage measurement; calculated as total errors/total trials*100.

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Tower of London task Results revealed that planning times did not satisfy the normality assumption necessary for ANOVA. A logarithmic transformation was therefore applied to the data in order to satisfy this assumption and a two-way ANOVA was conducted on the transformed data. Results of the ANOVA revealed a significant main effect of age group [F(1,31) = 34.32, p<0.001] but not gender [F(1,31) = 3.92, p>0.05], and no significant interaction between the two factors [F(1,31) = 0.001, p>0.05]. This indicates that participants in the older adult group had longer planning times than participants in the young adult group, but that planning times showed little variance between males and females. A two-way ANOVA was also conducted with average steps as the dependent variable. It was found that average steps showed little variance as a function of age group [F(1,31) = 3.1, p>0.05] or gender [F(1,31) = 1.09, p>0.05], and with no significant interaction between these two factors [F(1,31) = 3.31, p>0.05]. See Table 1 for descriptive statistics. Further analysis was conducted to examine the effect of trial difficulty (i.e. trials involving three, four or five disks) on planning times and average steps. Raw means for both planning times and average steps as a function of trial difficulty are shown in Table 2. A two-way ANOVA with factors of age group and trial difficulty was conducted with planning times and average steps as dependent variables.

Table 2: Tower of London planning times and average steps to target by trial difficultya Young adult group

Older adult group

N Planning timesb 3 disks 4 disks 5 disks

16

19

4.6 ± 1.3 4.4 ± 1.6 4.8 ± 1.6

12.1 ± 6.1 10.1 ± 3.5 10.1 ± 4.2

Average steps 3 disks 4 disks 5 disks

4.8 ± 1.3 7.4 ± 1.8 9.9 ± 1.6

5.7 ± 1.4 7.7 ± 1.6 10.9 ± 1.6

a

Values are means ± SD.

b

Time in seconds.

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The results revealed that planning times did not increase as a function of trial difficulty [GreenhouseGeisser corrected degrees of freedom (ε = 0.57); F(1.13,37.34) = 2.58, p>0.05], but did increase as a function of age group [F(1,33) = 33.26, p<0.001]. There was no significant interaction between trial difficulty and age group [F(1.13,37.34) = 2.28, p>0.05]. These findings indicate that planning times were consistent across trials of increasing difficulty, and that younger participants showed significantly shorter planning times under each difficulty condition. Results also revealed that average steps taken increased as a function of trial difficulty [F(2,66) = 194.22, p<0.001] but not age group [F(1,33) = 2.5, p>0.05]. There was no interaction between these two factors [F(2,66) = 1.04, p>0.05]. These findings reflect that as trial difficulty increased, so did the average steps taken in both young and old groups, and that there was little difference in performance between young and old groups. See Table 2 for descriptive statistics. Mental rotation task It was found that response times violated the assumption of homogeneity of variance. Again, a logarithmic transformation of the data was applied to satisfy the assumption of normality and a twoway ANOVA was conducted. The analysis revealed a significant main effect of age group [F(1,31) = 17.97, p<0.001] but not gender [F(1,31) = 3.09, p>0.05], and no significant interaction [F(1,31) = 0.87, p>0.05]. This reflects that participants in the older adult group responded slower than those in the young adult group, with little difference in response times between males and females. The same analysis was conducted with error rate as the dependent variable. There were no main effects of age group [F(1,31) = 0.56, p>0.05] or gender [F(1,31) = 0.51, p>0.05], and no interaction between these factors [F(1,31) = 0.86, p>0.05]. This indicates that error rates showed little difference across age groups and gender. See Table 1 for descriptive statistics. Further analysis was conducted to examine the effect of angle of rotation on response times and error rates. Raw means for both response times and error rates as a function of rotation are shown in Table 3. A two-way ANOVA with factors of age group and rotation angle was conducted with response times and error rates as dependent variables.

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Table 3: Mental rotation response times and error rates by angle of rotationa Young adult group

Older adult group

16

19

2.2 ± 0.8 2.5 ± 1.3 2.9 ± 0.9 3.6 ± 2.9 3.4 ± 2 2.8 ± 1.2 3.2 ± 2.7 2.5 ± 1.3

5.3 ± 3.4 6.3 ± 2.9 6.8 ± 4.1 7.3 ± 3.8 8.1 ± 4.3 5.7 ± 2.9 7.1 ± 3 5.1 ± 2.2

49.2 ± 15.5 46.9 ± 17.4 48.4 ± 18.2 50 ± 17.1 50 ± 12.1 49.2 ± 16.1 55.5 ± 14.4 49.2 ± 19.6

57.2 ± 12 47.4 ± 18.4 47.4 ± 16.4 41.4 ± 15.6 55.3 ± 15.2 51.3 ± 16.1 55.9 ± 21.8 47.4 ± 12.9

N Response timesb 0° rotation 45° rotation 90° rotation 135° rotation 180° rotation 225° rotation 270° rotation 315° rotation Error ratesc 0° rotation 45° rotation 90° rotation 135° rotation 180° rotation 225° rotation 270° rotation 315° rotation a

Values are means ± SD.

b

Time in seconds.

c

Percentage measurement; calculated as total errors/total trials*100.

The results revealed that response times differed significantly as a function of angle of rotation [Greenhouse-Geisser corrected degrees of freedom (ε = 0.32); F(2.23,73.51) = 7.11, p≤0.001]. However, inspection of the means did not reveal any notable trends in the data. There was a significant effect of age group [F(1,33) = 20.38, p<0.001], but no interaction between age group and angle of rotation [F(2.23,73.51) = 1.53, p>0.05]. These findings reflect that participants in the young adult group responded significantly faster than those in the older adult group under all angles of rotation. Results also revealed that error rates showed little variance as a function of angle of rotation [Greenhouse-Geisser corrected degrees of freedom (ε = 0.63); F(4.38,144.43) = 1.68, p>0.05] or age group [F(1,33) = 0.06, p>0.05], and with no interaction between these two factors [F(4.38,144.43) = 0.86, p>0.05]. These results indicate that error rates remained consistent across all angles of rotation and by age group. See Table 3 for descriptive statistics. PEBL Technical Report 2011-05

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Item-Order task Response times were analysed and results revealed a significant main effect of age group [F(1,31) = 16.79, p<0.001] but not gender [F(1,31) = 0.20, p>0.05], and no significant interaction [F(1,31) = 3.39, p>0.05]. A further two-way ANOVA was conducted with error rate as the dependent variable. Results revealed a significant main effect of age group [F(1,31) = 10.6, p<0.05] but not gender [F(1,31) = 3.75, p>0.05], and no significant interaction between the factors [F(1,31) = 3.75, p>0.05]. These analyses indicate that younger participants responded faster and made fewer errors than older participants, and that response times and error rates showed little variance between males and females. See Table 1 for descriptive statistics.

Nutritional analysis Vitamin E levels were analysed using a two-way ANOVA with independent factors of age group and gender. Results of the analysis revealed no significant main effects of age group [F(1,31) = 0.01, p>0.05] or gender [F(1,31) = 0.52, p>0.05], and no significant interaction between the two factors [F(1,31) = 4.09, p>0.05]. The same analysis was conducted with vitamin C levels as the dependent variable. The data violated the assumption of homogeneity of variance and therefore a logarithmic transformation was applied in order to satisfy this assumption. Results of the two-way ANOVA on the transformed data revealed no significant main effects of age group [F(1,31) = 1.16, p>0.05] or gender [F(1,31) = 2.08, p>0.05], and no significant interaction [F(1,31) = 2.38, p>0.05]. See Table 4 for descriptive statistics. Table 4: Nutritional analysis and Dietary Reference Values (DRV) by age group and gendera Young adult group N Vitamin E (mg) Vitamin C (mg) Total fat (g) Energy (kcal)

Older adult group

Male

Female

Male

Female

3

13

7

12

8.2(>4) ± 0.6

4.8(>3) ± 2.6

5.8(>4) ± 3.4

7.5(>3) ± 3.7

102.3(40) ± 33.7

57.6(40) ± 40.8

99.3(40) ± 48

79.5 ± 25.9

66.6 ± 25

119.7(40) ± 109.3 61.7 ± 15.4

1942(2550) ± 348

1577(1940) ± 436

1709(2330) ± 188

1647(1900) ± 243

56.6 ± 17.3

a

Values are Mean Daily Intake (MDI) ± SD; DRV shown in parentheses. DRV for vitamin C levels and caloric intake (kcal) is based on data from the Department of Health. Reference value for total fat intake (not displayed) is set at 33% of the daily total energy intake. There is currently no DRV for vitamin E but safe intake values are shown (Department of Health, 1991).

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Dietary antioxidant vitamin status and working memory capacity

McEwan, R. D.

Total fat intake showed little variation as a function of age group [F(1,31) = 2.77, p>0.05] or gender [F(1,31) = 1.17, p>0.05], and with no significant interaction [F(1,31) = 0.22, p>0.05]. Energy intake (kcal) also showed little variation as a function of age group [F(1,31) = 0.38, p>0.05] or gender [F(1,31) = 2.63, p>0.05], and with no significant interaction [F(1,31) = 1.32, p>0.05]. These results indicate that the intake of vitamin E, vitamin C, total fat and energy (kcal) was fairly consistent across age groups and gender. Due to the fact that caloric intake did not differ significantly across age group or gender, no correctional methods needed to be applied to compensate for increased dietary antioxidant vitamin levels as a consequence of a general increase in caloric intake. See Table 4 for descriptive statistics. Dietary Reference Values Vitamin E levels were above safe intake values and vitamin C levels exceeded the DRV proposed by the Department of Health. Total fat intake also showed little deviation from recommended values. However, energy (kcal) levels fell short of DRV for males and females in both young and older adult populations.

Relationships between task performance, nutrition and participant age Older adult group Tower of London task Analysis of the data revealed a significant negative correlation between planning times and vitamin E status [r(17) = -0.52, p<0.05] but not vitamin C status [r(17) = -0.02, p>0.05]. There was no significant association between average steps and vitamin E status [r(17) = 0.12, p>0.05] or vitamin C status [r(17) = -0.05, p>0.05]. Participant age was found to be significantly related to planning times [r(17) = 0.64, p<0.05]. See Figure 1 and Figure 2 for scatter plots illustrating the relationship between planning times and vitamin E status, and planning times and participant age respectively. Multiple regression analysis was conducted to determine the effect of vitamin E status and participant age on planning times. Together, vitamin E status and participant age accounted for 36.1% of the variance in planning times (adjusted R²); F(2,16) = 6.08, p<0.05. Standardised coefficients and zero-order and part correlations are provided for each predictor variable in Table 5. Standardised regression coefficients revealed that participant age was a stronger predictor of planning times than vitamin E status. Indeed, participant age was a significant predictor of planning times [t(16) = 2.16, p<0.05] whereas vitamin E status was not [t(16) = -0.89, p>0.05]. Table 5: Variance in Tower of London planning times predicted by participant age and vitamin E status Predictor Participant age Vitamin E status

β .51* -.21

Zero-order correlation .64 -.52

Part correlation .41 -.17

* p<0.05

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Dietary antioxidant vitamin status and working memory capacity

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The part correlation for vitamin E status (-0.17) was considerably smaller than the zero-order correlation (-0.52), indicating that much of the predictive power of vitamin E status is due to the variance it shares with participant age (see Table 5). Mental rotation task No significant correlation was observed between response times and vitamin E status [r(17) = -0.39, p>0.05] or vitamin C status [r(17) = -0.37, p>0.05]. However, there was a significant correlation between response times and participant age [r(17) = 0.72, p≤0.001]. There were no significant correlations between error rate and vitamin E status [r(17) = -0.25, p>0.05] or vitamin C status [r(17) = -0.17, p>0.05]. Item-order task There was no significant correlation between response times and vitamin E status [r(17) = -0.18, p>0.05] or vitamin C status [r(17) = 0.06, p>0.05]. Equally, there were no significant correlations between error rates and vitamin E status [r(17) = -0.06, p>0.05] or vitamin C status [r(17) = 0.09, p>0.05].

Figure 1: Relationship between vitamin E status and Tower of London planning times in older adults PEBL Technical Report 2011-05

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Figure 2: Relationship between participant age and Tower of London planning times in older adults

Young adult group Tower of London task No significant correlation was observed between planning times and vitamin E status [r(14) = 0.46, p>0.05] or vitamin C status [r(14) = 0.36, p>0.05]. There was no significant correlation between average steps and vitamin E status [r(16) = -0.23, p>0.05] or vitamin C status [r(16) = -0.19, p>0.05]. Mental rotation task Analysis revealed a significant positive correlation between response times and vitamin E status [r(14) = 0.73, p≤0.001; see Figure 3] but not vitamin C status [r(14) = 0.07, p>0.05]. There were no significant correlations between error rate and vitamin E status [r(14) = 0.35, p>0.05] or vitamin C status [r(14) = -0.09, p>0.05]. Letter string task Response times did not significantly correlate with vitamin E status [r(14) = 0.13, p>0.05] or vitamin C status [r(14) = -0.26, p>0.05]. No significant correlations were observed between error rates and vitamin E status [r(14) = -0.2, p>0.05] or vitamin C status [r(14) = -0.31, p>0.05]. PEBL Technical Report 2011-05

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Figure 3: Relationship between vitamin E status and mental rotation response times in young adults

Summary Younger participants performed significantly better on all measures of working memory except for Tower of London average steps and mental rotation error rates, where performance showed less variance across age group. There was little variance in performance between males and females. On further inspection of both Tower of London and mental rotation tasks, it was found that older adults did not demonstrate greater deficits in performance (relative to younger adults) as a result of increasing task difficulty. Nutritional levels were fairly consistent across both age group and gender. In the older adult group, a significant correlation was found between vitamin E status and Tower of London planning times. Further significant correlations included participant age and Tower of London planning times, and also participant age and mental rotation response times. In the young adult group there was a significant correlation between vitamin E status and mental rotation response times. There were no other significant associations between task performance and nutritional measures.

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Discussion The aim of the present study was to investigate the relationship between dietary antioxidant vitamin levels and working memory. More specifically, the relationships between vitamins E and C and subcomponents of working memory as conceptualised by Baddeley and Hitch (1974). It was hypothesised that dietary antioxidant vitamin levels would correlate with working memory performance in older adults, such that increased levels of these vitamins would account for gains in working memory performance. It was also hypothesised that there would be no such correlation in a young adult population. Overall, performance in the older adult group was poorer than the young adult group, indicating that the tasks were sensitive to age-related cognitive decline in working memory capacity. As expected, participants in the older adult group demonstrated slower response and planning times than the younger adult group in all three tasks of working memory. Older participants also made more errors on the itemorder task than did younger participants. It was found that increasing task difficulty did not increase the disparity in performance between young and older adult groups. It was expected that tasks of increasing cognitive demand would result in more prominent age-related deficits. However, this was not the case. The findings also indicated that nutritional levels were fairly consistent across the two groups and that the dietary intake of vitamin E, vitamin C and total fat met dietary reference values (DRV) proposed by the Department of Health (1991). Importantly, the dietary intake of older adults was not suggestive of malnutrition, which is a common occurrence in elderly populations (Robertson & Montagnini, 2004). The findings of this study suggest that there is no real relationship between working memory and antioxidant vitamin levels. There was no association between vitamin E and performance on both the mental rotation and item-order tasks in the older adult group. Moreover, the current study found that vitamin C status had little bearing on performance in any of the working memory tasks. While disproving the hypothesis, these findings are supported by a wealth of research (Devore, Kang et al., 2010; Jama et al., 1996; Kang et al., 2006; Yaffe et al., 2004). These findings suggest that antioxidant vitamins E and C have no real relationship with performance on cognitive tasks loaded onto the VisuoSpatial Sketchpad and Phonological Loop sub-components of working memory. Furthermore, it was found that participant age and mental rotation response times were strongly related, such that increasing age was associated with slower response times - indicative of age-related cognitive decline. In many cases the effect of participant age was more strongly related to performance than was dietary vitamin E and C status. In the young adult group there were no associations between vitamin E or C status and Tower of London performance, item-order task performance or mental rotation error rates. These findings support the hypothesis and are in line with both the findings of Benton et al. (1995) and, more generally, the free radical theory of aging (Harman, 1956). However, a strong relationship between vitamin E status and mental rotation response times was observed, such that increased levels of vitamin E were associated with longer response times. This finding was somewhat unexpected and while the literature suggests that antioxidant status is not related to cognitive function in young populations, it certainly does not propose that increased antioxidant vitamin levels are related to cognitive shortfalls. It is proposed that this finding is due to some confounding variable that was not controlled for, rather than the result of vitamin E levels per se. The key finding of this study, and one which supports the hypothesis, is the observed correlation PEBL Technical Report 2011-05

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between vitamin E status and Tower of London planning times in older adults, such that higher vitamin E levels were associated with shorter planning times. This finding suggests that vitamin E may play a role in maintaining the capacity of the Central Executive during normal aging. However, the other performance measure taken from the Tower of London task (average number of steps taken to complete each trial) was not associated with vitamin E levels. This suggests that the beneficial role of vitamin E is specific to planning times, which has been recognised as a fundamental measurement of Central Executive capacity. The association between vitamin E status and planning times is in line with a plethora of research indicating the benefits of vitamin E in maintaining cognitive function during aging (Chan et al., 2010; Maxwell et al., 2005; Ortega et al., 2002; Perkins et al., 1999; Perrig et al., 1997; Summers et al., 2010; Wengreen et al., 2007). However, the current study also observed an association between participant age and Tower of London planning times. Indeed, participant age was found to be a stronger predictor of performance relative to vitamin E levels, and therefore somewhat mitigates the role of vitamin E status on planning times. Despite this, the observed benefit for vitamin E, but not vitamin C, replicates the findings of both Grodstein et al. (2003) and Morris et al. (2002). Importantly, this key finding departs somewhat from the previous findings of Perrig et al. (1997) and serves to recognise that working memory is not a single entity and thus should not be measured as one. Taking measurements of each sub-component of working memory, as conceptualised by Baddeley & Hitch (1974), allows for consideration of the multicomponent nature of working memory, and, indeed, this finding somewhat suggests that the subcomponents of working memory are unique. More specifically, the Central Executive (relative to the Visuo-Spatial Sketchpad and Phonological Loop) may be increasingly susceptible to the damage caused by oxidative stress and is therefore more susceptible to dietary antioxidant intervention. However, this explanation is proposed somewhat tentatively, and there are a number of methodological issues with the current study that need to be addressed. The first issue concerns the means by which dietary antioxidant levels were determined. Food intake diaries are subject to bias in both the information they capture, and the sample selection itself (Madden et al., 1976). A key prerequisite for successfully completing a food diary is motivation, and motivated participants may be of this state because they pay particular attention to their dietary habits, which is suggestive of health eating. By the same token, people who are aware that their dietary habits are unhealthy, and are uncomfortable with sharing these, will not put themselves forward to participate in the study. This is especially true of younger adults who are, by disposition, more conscientious about their dietary intake (Hayes & Ross, 1987). This factor somewhat limits the generalisability of the data obtained from the food diaries, particularly from the young adult group. Furthermore, the act of recording dietary intake can have a significant bearing on both what is eaten, and how much is eaten (Rebro et al., 1998). Ironically, while the intention of a food diary is to capture a participant’s everyday dietary intake, the act of completing one may result in atypical dietary habits (Vuckovic et al., 2000). While these issues cast doubt over the generalisability and validity of the nutritional measures obtained, they are of particular relevance to a younger population. With regards to an older population, however, is the fact that specific cognitive processes are required to complete a food diary, especially where recall of dietary intake is delayed. The longer dietary information is stored in memory before it is recorded, the less accurate the data obtained (van Staveren et al., 1994). Furthermore, elderly participants who have special dietary requirements may not report their actual intake, but instead report what they should be eating. In light of these issues, it is quite possible that there is some discrepancy PEBL Technical Report 2011-05

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between actual food eaten and the food recorded in both young and old groups. In addition to these confounding factors, it was observed that some participants did not complete all aspects of the food diary, and consequently some records had to be interpreted with regards to amount eaten. It was not viable to contact participants about specific records, so where quantity-specific information was omitted, it was interpreted as an ‘average’ portion. Furthermore, the finding that energy (kcal) intake was considerably short of recommended values further questions the accuracy of self-report food intake diaries. Research has observed that both men and women underreport total energy intake (kcal), with much of this accounted for by underestimating individual portion sizes (Jonnalagadda et al., 2000). It has been proposed that underreporting can affect up to 15% of food intake records (Krebs-Smith et al., 2000). Consequently, a general underreporting of food intake will result in data that does not reflect a person’s true antioxidant status. The second key issue is that the current study did not measure for levels of antioxidants other than vitamins E and C. This issue is of significance because the effectiveness of individual antioxidants is somewhat determined by levels of a number of other micronutrients (Cutler, 1991). Measuring for these would provide a more complete picture of antioxidant status. Furthermore, the study looked exclusively at dietary antioxidant intake, which does not necessarily reflect blood plasma antioxidant levels. While research has found that, in some cases, dietary antioxidant intake can translate to plasma antioxidant levels (Anlasik et al., 2005), a better approach would be to use some form of biological marker alongside a food intake diary or food frequency questionnaire. Thus, in order to be confident about the association between antioxidant status and memory, it is important to take measures of a number of different micronutrients, coupled with plasma antioxidant levels of these micronutrients. A third issue regards the suitability of the working memory tasks themselves. While the mental rotation and item-order tasks required a simple response via the pressing of a single key, the Tower of London task required participants to use a computer mouse. This was not a problem for a young adult population, but it did pose some difficulty for participants in the older adult group who were not familiar with this device. Difficulties in navigating the cursor to specific components of the task may account for the large variability in planning times between old and young groups. The increased planning times may not, in fact, reflect deficits in the Central Executive of older adults, but may reflect deficits in motor control and coordination. This factor casts further doubt over the relationship found between vitamin E status and planning times. It could be argued that a better predictor of planning times would be a participant’s efficiency and experience using a computer mouse. A manual version of the Tower of London task (as adopted by Green et al., 2003), or an altogether different task which requires simple responses on a keyboard, would be a better approach to measuring the Central Executive component of working memory in older adults. With these particular issues in mind, it is difficult to draw firm conclusions from the present study. The current findings indicate that there is no real relationship between working memory and dietary antioxidant vitamin levels. Nevertheless, working memory is but one specific cognitive system and future research should adopt the same method used in this study of selecting a set of tasks that are loaded onto a specific component of memory. This approach would help identify those cognitive functions which may be more susceptible to antioxidant-induced changes. However, a number of issues with the present study should be remedied to improve both the validity and generalisability of the findings in subsequent works. Namely, the sole use of a food diary to capture dietary antioxidant intake has both general limitations and elderly-specific limitations. It is proposed that using a food intake PEBL Technical Report 2011-05

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diary, or similar methodology, coupled with a biological marker would be a better approach and provide a more accurate measurement of antioxidant status. In addition to this, and as previously discussed, it is important to measure for a number of different micronutrients (as utilised in recent research, see Chan et al., 2010; Summers et al., 2010), rather than vitamin E and C alone, in order to provide a more thorough understanding of antioxidant function. Of particular importance to future research are the criteria for which older adults are recruited. Specifically, selecting a narrower age range would help to omit the effects of participant age on task performance. In the current study, for example, the observed association between planning times and vitamin E status was somewhat overshadowed by a stronger association between planning times and participant age. Designing multiple studies, each of which focuses on a specific age range, would help omit the influence of age, and better identify the precise role of antioxidants during the aging process. While this would make the process of recruitment significantly more time consuming, and may reduce sample sizes, it would help construct a set of age ranges by which cognitive function may be more susceptible to levels of antioxidants. Moreover, while the current study controlled for variables such as age and total energy intake, it did not control for a number of other confounding variables which may have had a significant bearing on performance. Namely the number of years spent in education, time spent engaged in physical exercise, history of illness or disease, history of smoking and information on medications. These variables are of particular relevance to this area and their possible influence on both task performance and antioxidant status was not accounted for. Further research into the area should, where possible, control for as many of these variables as possible. In summary, the findings of this study lean towards disconfirming the hypothesis of an association between dietary antioxidant vitamin E and C levels and working memory capacity in older adults. The results revealed that, on the whole, levels of these vitamins did not account for performance on three separate tasks of working memory. That being said, dietary vitamin E levels were associated with Tower of London planning times, such that increased vitamin E levels accounted for shorter planning times in older adults. This suggests a possible beneficial role for vitamin E in maintaining the capacity of the Central Executive. No meaningful correlations were observed between antioxidant status and working memory performance in the young adult group, thus upholding the hypothesis that vitamin E and C levels would not correlate with working memory in a young population. Nevertheless, these findings should be interpreted somewhat cautiously due to a number of methodological issues.

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Cognitive function in elderly people is influenced by vitamin E status. The Journal of Nutrition, 132(7), 2065-2068. Paleologos, M., Cumming, R. G. & Lazarus, R. (1998). Cohort study of vitamin C intake and cognitive impairment. American Journal of Epidemiology, 148(1), 45-50. Peacock, J. M., Folsom, A. R., Knopman, D. S., Mosley, T. H., Goff, D. C. & Szklo, M. (2000). Dietary antioxidant intake and cognitive performance in middle-aged adults. Public Health Nutrition, 3(3), 337-343. Perez, W. A., Masline, P. J., Ramsey, F. R. & Urban, K. E. (1987). Unified Tri-Services Cognitive Performance Assessment Battery: Review and methodology (Technical Report AAMRL-TR-87). Wright-Patterson AFB, OH: Armstrong Aerospace Medical Research Laboratory. Perkins, A. J., Hendrie, H. C., Callahan, C. M., Gao, S., Unverzagt, F. W., Xu, Y. et al. (1999). Association of antioxidants with memory in a multiethnic elderly sample using the Third National Health and Nutrition Examination Survey. American Journal of Epidemiology, 150(1), 37-44. Perrig, W. J., Perrig, P. & Stähelin, H. B. (1997). The relation between antioxidants and memory performance in the old and very old. Journal of the American Geriatrics Society, 45(6), 718-724. Rebro, S. M., Patterson, R. E., Kristal, A. R. & Cheney, C. L. (1998). The effect of keeping food records on eating patterns. Journal of the American Dietetic Association, 98(10), 1163-1165. Robertson, R. G. & Montagnini, M. (2004). Geriatric failure to thrive. American Family Physician, 70(2), 343-350. Shallice, T. (1982). Specific impairments of planning. Philosophical Transactions of the Royal Society, London, Series B, Biological Sciences, 298(1089), 199-209. Shepard, R. N. & Metzler, J. (1971). Mental rotation of three-dimensional objects. Science, 171(3972), 701-703. Shukitt-Hale, B. (1999). The effects of aging and oxidative stress on psychomotor and cognitive behavior. Age, 22(1), 9-17. Summers, W. K., Martin, R. L., Cunningham, M., DeBoynton, V. L. & Marsh, G. M. (2010). Complex antioxidant blend improves memory in community-dwelling seniors. Journal of Alzheimer’s Disease, 19(2), 429-439. Tinker, A. (2002). The social implications of an ageing population. The Biology of Ageing, 123(7), 729735. van Staveren, W. A., de Groot, L. C., Blauw, Y. H. & van der Wielen, R. P. (1994). Assessing diets of elderly people: problems and approaches. American Journal of Clinical Nutrition, 59(1), 22152235. Vuckovic, N., Ritenbaugh, C., Taren, D. L. & Tobar, M. (2000). A qualitative study of participants’ experiences with dietary assessment. Journal of the American Dietetic Association, 100(9), 10231028. Wengreen, H. J., Munger, R. G., Corcoran, C. D., Zandi, P., Hayden, K. M., Fotuhi, M. et al. (2007). Antioxidant intake and cognitive function of elderly men and women: the Cache County study. Journal of Nutrition, Health & Aging, 11(3), 230-237. Yaffe, K., Clemons, T. E., McBee, W. L., Lindblad, A. S. (2004). Impact of antioxidants, zinc, and cop per on cognition in the elderly: a randomized, controlled trial. Neurology, 63(9), 1705-1707.

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The choice of tasks mirrored those used by Green et al. .... Windows. Task performance and nutrition values were subject to a two-way independent ANOVA with factors of age ...... Volume 41 of Reports on Health and Social Subjects. London: ...

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Participants completed a shortened version of Big Five Inventory (BFI) and a Healthy Eating Behavior and. Attitude scale. We found a significant and ... Their data showed that when the other four traits were controlled, the ..... The Big Five Invento

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Similarly, we show the diagram used by our heuristic in Figure 1. While futurists rarely assume the exact opposite, ... Intel 386s from the NSA's Internet-2 cluster to better understand our mobile telephones. We only characterized ... space of our se

The relationship within and between the extrinsic and intrinsic systems ...
Apr 1, 2007 - aDepartment of Biomedical Engineering, School of Computer and Information .... system. These resting state functional network patterns have been .... peaks in a previous study (Tian et al., in press), and the one for the.

Establishing the Nexus The Definitive Relationship Between Child ...
http://www.missingkids.com/en_US/publications/NC70.pdf [hereinafter ... However, in United States v. Leon,. 6. the Supreme Court. 3. U.S. CONST. amend. IV. 4.

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and for giving me the opportunity to pursue my Masters degree under his ...... activity was discovered du ring fungicide screening programs in the 1 970s (Davis .... with paclobutrazol is increased interveinal distance (Sopher et al., 1999). In.

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that a sense of self-agency can be experienced even if some degree of temporal bias is perceived. Furthermore, they determined that highly schizotypal people ...

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Feb 20, 2014 - Abstract. Many electrical engineers would agree that, had it not been for online algorithms, the evaluation of red-black trees might never have ...

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... to the Bodhisattva from the. 1. Sanyo Gakuen University, Okayama, JAPAN. ..... Bloomington: Indiana University Press, 2012. Heidegger, Martin. The Event ...

The relationship within and between the extrinsic and intrinsic systems ...
Apr 1, 2007 - 360, 1001–1013. Binder, J.R., Frost, J.A., Hammeke, T.A., ... other: a social cognitive neuroscience view. Trends Cogn. Sci. 7,. 527–533.

Input-Output Relationship between 47 Project Management ...
WPD WPD WPD WPD Dlvrbls; WPD WPD WPD WPD WPD. PR Doc Upd. PMP ... Input-Output Relationship between 47 Project Management Processes.pdf.

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recovery (95% after 4% tensile strain) at a training temperature of 873 K. Its residual strain is related to the generation of perfect .... process (the most common data is around 50% shape ... parable to the best results published, especially in re-

Relationship between communities and processes
y = )y, to better demonstrate the relationship between the data and the model. 1202 P. W. ..... analysis (R = 0.592, P = 0.02, and R = 0.725, P < 0.001, for 14–18 ...

Relationship Between Natural Resources and ...
We have ng as the grabbers' number and nf as the producers' number, with N = ng + nf and α being the fraction .... Our model does not take into account the direct relationship between α1 ...... English, French, German, Portuguese, or Spanish.

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39.2. 20.7. 32.76. 25.71. 22.50. 26.97. 153. 212. 338. 230. 0.0054. 2.00. 0.410. 21.6. 28.10. 267. 0.0036. 2.29. 0.303. 19.1. 29.45. 420. 0.0014. 0.96. 0.615. 47.9.

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Apr 28, 2015 - Computer and Evolutionary Programming. Bob, Carol and Alice ... tiplayer online role-playing games and the location-identity split. We con-.

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X. JVM. Trap. Figure 1: An algorithm for atomic methodolo- gies. hurt. This may or may not actually hold in reality. See our prior technical report [19] for details. Similarly, we show the diagram used by our heuristic in Figure ... ware; and finally