Background
Adequate nutrient intake is important for the maintenance of health and prevention of chronic diseases [
1]. Many countries have therefore set nutrient-based recommendations, generally referred to as Dietary Reference Intakes (DRIs), for the assessment and planning of dietary intake [
2-
4]. When considering the application of DRIs, it is necessary to design a food intake pattern that meets as many nutrient recommendations as possible while maintaining the intake of local and culture-specific foods. Food intake patterns meeting these requirements are useful in the development of practical and achievable dietary guidelines that promote healthy food choices.
Previous studies have suggested that the diet optimization method is useful in achieving these goals [
5,
6]. Diet optimization by linear programming is a mathematical approach that optimizes (minimizes or maximizes) a linear function of decision variables while respecting multiple constraints. This methodology has been used to formulate nutritionally-optimal dietary patterns [
7-
12], to examine the relationship between diet cost and diet quality in Western countries [
13-
15], and to develop food-based dietary guidelines in developing countries [
16]. A study in the Pacific Northwest of the USA generated sex-specific food plans that met both the key 2007 dietary recommendations for cancer prevention issued by the World Cancer Research Fund/American Institute of Cancer Research and the DRIs set by the Institute of Medicine [
7]. Results showed that achieving cancer prevention goals required little modification of existing diets, but that fulfilling all nutrient recommendations required a large increase in food volume and a dramatic shift from existing diets. Such studies are necessary to identify the dietary modifications required to achieve all nutrient-based recommendations at the population level. To our knowledge, however, no comparable study has been reported in Asian countries, including Japan. The typical Japanese food intake pattern has characteristics seldom observed in Western and other populations, including high intake of refined grains, fish, seaweeds, soybean products, green tea, and salt and low intake of fat. Thus the nutritionally-optimal food intake patterns and the dietary modifications required may differ from those in Western and other populations [
7,
12,
17]. Here, we applied a diet optimization model using linear programming to generate nutritionally-optimal food intake patterns that met the recommended DRIs [
3] based on typical Japanese food selections.
Results
The characteristics of the subjects who provided our dietary data have been previously reported [
18,
19]. Mean age, energy intake, and the ratio of reported energy intake to EER (EI/EER) of input dietary data (i.e. observed dietary intake data) for linear programming models were as follows: 39.3 years, 1856 kcal/day, and 0.93, respectively, for women aged 30–49 years (
n = 45); 59.4 y, 1898 kcal/day, and 0.97 for women aged 50–69 years (
n = 47); 40.9 y, 2391 kcal/day, and 0.90 for men aged 30–49 years (
n = 40); and 59.6 y, 2457 kcal/day, and 1.00 for men aged 50–69 years (
n = 42).
Mathematically optimized food intake patterns satisfying all nutritional constraints were obtained for each sex and age group using the linear programming model. Table
3 shows a comparison of nutrient contents between the observed and optimized food intake patterns. The number of nutrients for which nutritional goals were not achieved in the observed food intake pattern was 13 for women aged 30–49 years, four for women aged 50–69 years, 13 for men aged 30–69 years, and six for men aged 50–69 years. In contrast, all optimized food intake patterns achieved the nutritional goals of the DRIs for all nutrients. It should be noted, however, that all optimized diets generated in the present analysis contained exactly 100 % of the salt upper limit proposed by the DRIs, suggesting that salt-equivalent is a limiting nutrient for all sex and age groups. The other limiting nutrients in the present models were SFA and iron for women aged 30–49 years; SFA, total dietary fibre, and vitamin B
1 for women aged 50–69 years; n-6 PUFA, total dietary fibre, retinol activity equivalent, vitamin B
1, and magnesium for men aged 30–69 years; and total dietary fibre and retinol activity equivalent for men aged 50–69 years.
Table 3
Comparison of nutrient contents between the observed and optimized daily food intake patterns
Energy | kcal | 1856 | 2000 | 1898 | 1900 | 2391 | 2650 | 2457 | 2450 |
Protein | g | 66.8 | 82.6 | 74.9 | 73.1 | 81.3 | 104.9 | 89.5 | 89.3 |
Total fat | %E | 29.1 | 23.0 | 26.0 | 25.5 | 26.2 | 23.5 | 24.0 | 23.5 |
SFA | %E | 8.5a | 7.0 | 7.2a | 7.0 | 7.3a | 6.1 | 6.3 | 6.1 |
n-3 PUFA | g | 2.3 | 1.9 | 2.7 | 2.7 | 2.8 | 3.2 | 3.3 | 3.2 |
n-6 PUFA | g | 10.7 | 8.1 | 10.2 | 10.1 | 12.7 | 10.0 | 11.9 | 12.0 |
Carbohydrate | %E | 53.8 | 59.1 | 56.7 | 57.8 | 53.1 | 55.7 | 54.4 | 54.9 |
Total dietary fibre | g | 13.1a | 21.2 | 17.3 | 18.0 | 13.6a | 20.0 | 17.5a | 20.0 |
Vitamin A | μgRAE | 584a | 804 | 682a | 700 | 628a | 900 | 786a | 850 |
Vitamin D | μg | 6.2 | 8.1 | 10.2 | 10.2 | 7.4 | 13.1 | 12.0 | 11.9 |
Vitamin Ed | mg | 7.1 | 7.4 | 8.1 | 8.3 | 8.0 | 9.3 | 9.0 | 9.9 |
Vitamin K | μg | 211 | 308 | 279 | 292 | 212 | 292 | 283 | 311 |
Vitamin B1 | mg | 0.87a | 1.3 | 0.96a | 1.00 | 1.1a | 1.4 | 1.1a | 1.3 |
Vitamin B2 | mg | 1.2 | 1.7 | 1.5 | 1.4 | 1.4a | 1.7 | 1.6 | 1.7 |
Niacine | mgNE | 15.9 | 36.4 | 18.0 | 30.0 | 20.9 | 45.8 | 23.1 | 40.3 |
Vitamin B6 | mg | 1.1a | 1.7 | 1.4 | 1.4 | 1.4a | 1.9 | 1.7 | 1.9 |
Vitamin B12 | μg | 6.5 | 8.3 | 9.1 | 8.8 | 8.0 | 13.1 | 11.5 | 11.4 |
Folate | μg | 309 | 469 | 423 | 431 | 339 | 475 | 455 | 473 |
Pantothenic acid | mg | 5.8 | 7.9 | 6.5 | 6.6 | 6.8 | 8.6 | 7.5 | 8.2 |
Vitamin C | mg | 90a | 150 | 141 | 148 | 92a | 158 | 138 | 147 |
Salt equivalentf | g | 12.2a | 7.0 | 12.4a | 7.0 | 16.2a | 8.0 | 14.5a | 8.0 |
Potassium | mg | 2393a | 3403 | 3049 | 3004 | 2672a | 3595 | 3209 | 3346 |
Calcium | mg | 526a | 674 | 656 | 650 | 544a | 677 | 641a | 700 |
Magnesium | mg | 249a | 385 | 310 | 310 | 286a | 370 | 348a | 401 |
Phosphorus | mg | 1015 | 1337 | 1173 | 1166 | 1197 | 1520 | 1350 | 1492 |
Iron | mg | 7.4a | 10.5 | 9.5 | 9.1 | 8.3 | 10.1 | 10.3 | 10.7 |
Zinc | mg | 7.9a | 10.1 | 8.6 | 8.7 | 9.6a | 12.1 | 10.4 | 10.9 |
Copper | mg | 1.1 | 1.5 | 1.3 | 1.3 | 1.3 | 1.7 | 1.5 | 1.6 |
Manganese | mg | 3.1a | 5.0 | 4.3 | 4.6 | 3.8a | 4.9 | 4.8 | 5.7 |
Alcohol | %E | 1.5 | 1.4 | 0.9 | 0.9 | 5.4 | 5.0 | 5.8 | 6.2 |
Table
4 shows a comparison of food quantity between the observed and optimized food intake patterns. For convenience in data interpretation, we assumed that dietary modification (either increase or decrease) was required when the difference between the observed and optimized food intake patterns was more than 10 or −10 %. In the younger age groups (30–49 years), large modifications were required to increase the intake of food items in the following food groups: vegetables, which needed to be increased by 65 % for women and 55 % for men, particularly green and yellow vegetables, other vegetables, pulses, and seaweeds for both sexes and mushrooms for women; meat and alternatives, which needed to be increased by 38 % for women and 47 % for men, particularly eggs for women and fish for men; and fruit, which needed to be increased by 96 % for women and 172 % for men. Furthermore, the intake required to satisfy all nutritional constraints reached the upper limit (95th percentile of observed intake) in several food groups, reflecting the fact that their consumption by this sample was low; these were vegetables, including green and yellow vegetables and other vegetables, for both sexes; pulses, seaweeds, and meat and alternatives including eggs for women; and fish for men. In contrast, little modification of the existing diet was required in the older age groups (50–69 years), particularly in women, although increased intake of green and yellow vegetables for men (25 %) and increased intake of other vegetables for women (14 %) were still required. Across all sex and age groups, optimized food intake patterns called for greatly increased intake of whole grains and reduced-fat dairy products in place of intake of refined grains and full-fat dairy products. The optimized food intake pattern also called for a marked reduction (by 65–80 %) in salt-containing seasoning for all sex and age groups in order to keep salt consumption within the limits.
Table 4
Comparison of food amounts (g/day) between the observed and the optimized food intake patterns
Grains | 401 | 393 | 396 | 426 | 564 | 642 | 567 | 580 |
Whole grains | 4 | 125b | 12 | 57 | 2 | 35 | 14 | 164b |
Refined grains | 397 | 267 | 384 | 369 | 562 | 607 | 554 | 416 |
Vegetables | 349 | 577b | 486 | 522 | 372 | 579b | 489 | 526 |
Green and yellow vegetables | 77 | 127b | 125 | 134 | 79 | 140b | 118 | 148 |
Other vegetables | 147 | 278b | 188 | 214 | 155 | 286b | 199 | 206 |
Pulses | 44 | 68b | 76 | 76 | 44 | 54 | 71 | 71 |
Potatoes | 61 | 66 | 64 | 64 | 73 | 73 | 70 | 70 |
Mushroom | 9 | 16 | 14 | 14 | 10 | 10 | 14 | 14 |
Seaweeds | 11 | 22b | 18 | 18 | 11 | 16 | 16 | 16 |
Meat and alternatives | 170 | 235b | 182 | 182 | 225 | 329 | 241 | 241 |
Eggs | 38 | 63b | 37 | 37 | 45 | 45 | 46 | 46 |
Meat | 69 | 88 | 48 | 48 | 97 | 118 | 71 | 71 |
Fish | 63 | 83 | 97 | 97 | 83 | 166b | 124 | 124 |
Milk products | 138 | 134 | 165 | 164 | 110 | 110 | 124 | 174 |
Full-fat dairy products | 121 | 0 | 130 | 120 | 100 | 73 | 101 | 71 |
Reduced-fat dairy products | 17 | 134 | 35 | 44 | 10 | 36 | 24 | 103 |
Fruit | 89 | 175b | 144 | 144 | 75 | 204b | 115 | 115 |
Others | | | | | | | | |
Fats and oils | 19 | 0 | 15 | 15 | 24 | 9 | 19 | 19 |
Salt-containing seasoning | 55 | 18 | 63 | 22 | 66 | 13 | 71 | 23 |
Sugars and confectionary | 59 | 93 | 65 | 65 | 48 | 48 | 50 | 50 |
Alcoholic beverages | 83 | 83 | 48 | 48 | 322 | 322 | 311 | 311 |
Non-alcoholic beverages | 750 | 1184 | 808 | 808 | 773 | 885 | 796 | 796 |
Discussion
Using the linear programming model, we mathematically obtained sex- and age-specific optimized food intake patterns that achieved a set of 28 nutrient recommendations given in the DRIs for Japanese adults. The present study demonstrates how nutrient-based recommendations can be translated into nutritionally adequate food intake patterns with minimal modification of current dietary habits among Japanese adults. To our knowledge, the application of mathematical diet optimization models by linear programming to develop recommended food intake patterns in an Asian population has not been described before.
With the exception of fruit and vegetable intake among the younger age groups, our optimized food intake patterns did not strongly differ from the observed intake patterns at the food group level (Table
4). At the food subgroup level, in contrast, achieving nutritional goals required substantial dietary modifications, namely, an increase in whole grains of more than 10-fold, an increase in reduced-fat dairy products of 26–705 %, a decrease in full-fat dairy products of 7.8–100 %, and a decrease in salt-containing seasoning of 65–80 %. These results were generally consistent with food choices recommended by the dietary guidelines developed in Western countries [
9,
26-
28]. However, the current Japanese dietary guidelines make no mention of such dietary modifications (i.e. increased whole grains and reduced-fat dairy products and decreased full-fat dairy products and salt-containing seasoning), probably due to insufficient evidence [
21]. The present findings might therefore facilitate the revision of these guidelines.
Although the nutritional constraints set by the DRIs did not differ substantially between younger and older age groups (except in the case of iron among women), the dietary modifications necessary to achieve the established nutritional goals differed according to age group: more marked increases in food volume were required in younger age groups. In older age groups, on the other hand, observed intake of most food groups and subgroups was already very close to optimized intake, except for dairy products in men. Furthermore, the number of nutrients for which nutritional goals were already satisfied by the observed food intake patterns was higher in older age groups (24 for women and 22 for men) than in younger age groups (15 for both sexes). These results are partially consistent with those of a previous study in a large US population showing that sodium levels were closer to the proposed guideline in the observed diets of adults aged >50 years, particularly men, than in those of younger adults aged 20–30 or 30–50 years [
12]. The reasons for these differences in the degree of dietary modification required for each age group are unclear, but they might be at least partially explained by age-specific dietary habits and differences in dietary awareness. Indeed, according to the National Health and Nutrition Survey in Japan, older people tended to pay more attention to their diets than younger people did [
29], and the percentages of subjects who evaluated their current diets as “excellent/good” were 57.4, 60.4, 63.5, and 79.6 % among women aged 30–39 years, 40–49 years, 50–59 years, and 60–69 years, respectively, and 67.1, 68.3, 76.2, and 83.9 % among men aged 30–39 years, 40–49 years, 50–59 years, and 60–69 years, respectively [
30]. Few studies have examined the differences in necessary diet modifications according to age, a fact which hinders comparison of our results with those of other studies. Further study is therefore required to confirm whether this tendency is consistently observed in other populations.
Here, we demonstrated that, for younger age groups, meeting nutritional goals requires a drastic increase in consumption of specific food groups and food subgroups such as green and yellow vegetables, other vegetables, and fruit for both sexes; pulses, seaweeds, and eggs for women; and fish for men. Consequently, in our optimized diets, these food groups and subgroups reached the upper boundary limits for this study population, while fats and oils reached the lower limits among young women. However, whether such substantial increases in food consumption are even feasible at the population level remains questionable, as the achievement of goals for specific nutrients, such as iron and sodium, within the stringent consumption constraints required may be difficult. The present findings in younger age groups should therefore be interpreted carefully, and the issue of feasibility must be addressed.
Previous studies using diet optimization models have found that achieving nutritional goals with regard to population- or culture-specific nutrients is difficult [
7,
9,
11,
17,
24,
26]. For the American population, for example, intake of vitamin E at all energy levels, potassium at lower energy levels, and sodium at higher energy levels did not meet nutritional goals [
7,
12,
17,
26]. For the French population, the key problem nutrients were vitamin D, magnesium, sodium, and SFA for both sexes, cholesterol for men, and iron, calcium, and vitamin E for women [
9,
24]. In the present study, as in similar studies from other countries, salt equivalent (sodium) was the most difficult constraint to fulfil for all sex and age groups. In addition, iron for young women only, SFA for all women, and total dietary fibre and vitamin A for men were also identified as limiting nutrients. The fact that different limiting nutrients have been identified in different countries might be explained by differences not only in dietary habits but also in dietary standards. For example, the recommended intake of α-tocopherol in Japan is 6.0–6.5 mg/day [
3], compared to 15 mg/day in the USA and Canada [
2] and 12 mg/day in France [
9]. Recommendations for dietary fibre, potassium, calcium, and magnesium are also substantially lower in Japan than in the USA and France [
2,
9]. As part of the present study, we attempted to formulate optimal food intake patterns for Japanese adults, using typical Japanese food selections, that would achieve the DRIs used in the USA/Canada as an experiment on the application of linear programming models. However, we were unable to generate food intake patterns that met these criteria. This outcome shows that the optimal solution for a given population might be dependent on the reference values selected as nutritional constraints. Therefore, suitable and achievable country-specific dietary goals should be selected with consideration for the realistic consumption levels of each population when linear dietary optimized models are used to generate nutritionally-optimal food intake patterns.
Several limitations to the present study warrant mention. First, the study subjects may not have been representative because they were not randomly sampled from the general Japanese population; rather, they were volunteers. Moreover, the participants might be highly health-conscious because almost all of them completed the study despite the strict study design. Second, the sample size was relatively small for both women (
n = 92) and men (
n = 82). Therefore, our estimates of food and nutrient intake, particularly the distribution of food consumption levels, might not be stable. Third, the present analysis was based on the secondary dietary data which was collected during 2002–2003. The stability of food intake pattern and change in dietary habits during the time gap between data collection and analysis might have slightly influenced the conclusion. Additional studies using latest dietary data are therefore needed to confirm our findings. Fourth, reporting errors such as under- or over-reporting could not be avoided because, as in many other studies [
31], dietary intake information was self-reported. This may induce bias when reported dietary intake levels are compared with corresponding optimized dietary intake (because the latter does not consider this problem). Nevertheless, EI/EER values in the present study were close to 1.00 (0.90–1.00), suggesting sufficient accuracy at least at the group level. Additionally, the results were not materially changed when food and nutrient intakes were adjusted for EI and then standardized to EER in consideration of possible under- or over-reporting of intake. Fifth, the validity of results obtained using diet optimization models is dependent on the accuracy of the model’s simulation and the quality of the input data. In addition, the linear programming optimization model generated only a single food intake pattern for each sex and age group, and variation due to individual food choices was not taken into account. Finally, and most importantly, the reliability of the DRI for each nutrient, which is used as a nutrient constraint in linear programming models, is dependent on the accuracy of the available studies on that nutrient [
3].
In conclusion, diet optimization using linear programming models can effectively translate nutrient-based recommendations into realistic food intake patterns for a Japanese population. Substantial dietary modification was required to increase the intake of whole grains and reduced-fat dairy products as well as fruit and vegetables, and to decrease that of full-fat dairy products and salt-containing seasoning to meet nutrient recommendations. Further studies are required to confirm our observations in a more representative sample of the Japanese population and to examine the application of linear programming optimization models in other Asian populations.
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Competing interests
The authors declare that they have no competing interests.
Authors’ contributions
HO created the nutrient profile for optimization, conducted the statistical analysis, interpreted the data and wrote the manuscript. SS was responsible for the study design and assisted with data interpretation and manuscript preparation. KM assisted with manuscript preparation. TY assisted with statistical analysis. NH, AN, MF and CD were responsible for the data collection. All authors provided suggestions during the preparation of the manuscript and approved the final version submitted for publication.