With the global population expected to increase to 9 billion by 2050 coupled with concerns about food security in relation to climate change and increasing prosperity in many parts of the world causing desire for a less monotonous diet, efficient use of resources such as food becomes ever more important. While the prevalence of obesity is a cause for concern in many parts of the world, many people still go to bed hungry, and in many communities, obesity co-exists with poor diet quality. The result is a series of complex and challenging nutrition problems, such as the access to nutritionally adequate and affordable diets and the development of dietary recommendations. Diet modelling is a useful tool to help identify solutions to such complex questions and this paper summarises a session on this topic at the International Congress of Nutrition that took place in September 2013.
This paper summarises a series of presentations in a session focusing upon diet modelling, sponsored by Danone Nutricia Research,1 from the International Congress of Nutrition that took place in Granada (Spain) in September 2013. The session was introduced by Dr Anne Lluch from Danone Nutricia Research and chaired by Dr André Briend who also gave an introduction to the history of mathematical modelling of diets. Other speakers in the session were Professor Judith Buttriss, who set the scene by summarising the global public health challenges in the field of nutrition; Dr Nicole Darmon, who described the added value of the use of linear programming to examine public health nutrition questions, drawing upon examples from high-income countries; Dr Elaine Ferguson, who discussed the application of linear programming in low-income countries; and Dr Matthieu Maillot, who discussed the application of linear programming techniques to the diets of individuals in high-income countries.
Public health nutrition challenges
It is now widely recognised that a number of global food, nutrition and health challenges exist, and that these are very complex and often inter-related. Even in the 21st century, 1 billion people go to bed hungry and another billion have micronutrient deficiencies (Foresight 2011). Insufficient energy and poor diet quality result in poor growth and development in childhood, infection and inter-generational effects. Yet alongside this, more than 1 billion adults are overweight or obese and, in many cases, excessive energy intake is accompanied by poor diet quality and inadequate intakes of essential nutrients. By 2050, a global population of over 9 billion is predicted as a result of increased life expectancy, improved child mortality rates and continued increase in birth rates in some parts of the world. In Western countries such as the UK, life expectancy has been increasing by two years per decade for some time, and birth rate is still rising slightly (Office for National Statistics 2012), but healthy life expectancy is not keeping pace with increases in overall life expectancy (Salomon et al. 2012), emphasising the importance, now more than ever, of promoting a healthy diet and lifestyle.
A high profile focus upon the importance of achieving food security, not just now but for future generations, has been triggered by these trends coupled with increased prosperity in previously low-income countries (and consequent desire for a less monotonous or more ‘Western’ diet), concerns about the impact on the environment of climate change, and growing concerns about future needs for land to grow food, for water and also for energy. Food security has been defined by the UK's Global Food Security Programme as occurring when everyone has access to safe, affordable and nutritious food, all of the time and in ways the planet can sustain into the future (Global Food Security 2012). The reality is that food availability is unevenly distributed around the globe, and wastage along the food chain, from production through to consumption, remains high. If less food were to be wasted [it is estimated that about 30% is wasted (Foresight 2011)] and people ceased to eat in excess of their energy needs, we could be more food secure from a worldwide perspective (Global Food Security 2013). A recent report from WRAP, responsible for the Love Food Hate Waste campaign in the UK that highlighted the level of household food wastage, has revealed that the amount of food and drink thrown away in the UK that could have been eaten fell by 21% between 2007 and 2012 (Quested et al. 2013), so progress can be made.
In contrast, obesity levels continue to rise in many parts of the world, affecting over 30% of the population in the USA and 20–25% in many European countries (Central Intelligence Agency 2013). But it is not a phenomenon restricted to high-income countries, and in many developing low-income and middle-income countries, obesity can be found alongside undernutrition and poor micronutrient intakes.
Even in Europe, there are inadequate intakes of some essential vitamins and minerals in some population groups, particularly teenage girls (Mensink et al. 2013), and excess intakes of saturated fatty acids, sugars and salt are widespread. Clearly, there is a need for clear and evidence-based dietary advice that can help steer people towards healthier diets and, increasingly, emphasis is being placed on the need for diets now and in the future to be more sustainable too.
The challenges faced in harnessing sustainability alongside good nutrition are considerable and, in considering and shaping recommendations, it is essential that unintended consequences are avoided, or at least their potential recognised and mitigated (Buttriss 2013). This can be illustrated by the information presented in Table 1. A number of vitamins and minerals have been identified as in short supply in the diets of some people in the UK (SACN 2008; Bates et al. 2012) and elsewhere in Europe (Mensink et al. 2013), using the lower reference nutrient intake (the amount sufficient for only 2.5% of a population) as a point of reference. Using data from the UK (Henderson et al. 2003), Table 1 shows the current UK dietary sources of these micronutrients and it is evident that several of the foods that are currently in the spotlight from a sustainability perspective (meat, milk and fish) are important sources of a number of these micronutrients.
Table 1. Contribution of specific foods to nutrient intakes (i.e. selected vitamins and minerals) in the UK diet
Contribution (%) of food types to average daily intake of specific nutrients
Diet modelling is a useful tool to help solve complex questions, not least because we need nutrients but eat foods, nutrients are not evenly distributed in the foods available to us, a wide variety of foods exists and there is a broad spectrum of food consumption patterns and contexts. As well as being a tool to explore more traditional diet and nutrition questions in both low-income and high-income countries, it is already being used to define sustainable dietary guidelines from a global food security perspective and could also be used to help identify sustainable food systems. But, first, what is the history of mathematical modelling of diets?
Introduction to mathematical modelling of diets
Mathematical modelling of diets can be defined as the use of mathematical techniques to formulate and optimise diets. Its origin can be traced back to the 1940s, when George Stigler, a US economist, tried the technique to determine the minimum cost of a diet providing the amounts of energy, proteins, minerals and vitamins considered as adequate (Stigler 1945). This diet could include any of 77 foods available on the US market at that time with a known nutrient composition and cost. Although he was a bright mathematician (he was awarded the ‘Nobel Prize’ in Economic sciences in 1982), Stigler could not find the exact solution to this problem, which turned out to be incredibly complex. The Stigler ‘diet problem’ is a typical question of resource optimisation or, in mathematical terms, of minimisation of a linear function subject to multiple linear constraints, also called linear programming. During World War II, this question became of prime importance to mathematicians involved in the war efforts. The question was also pursued in the USSR, for the purpose of economy planning and distribution of food supplies (Dorfman 1984). Among the mathematicians who contributed to the solution of this problem, George Dantzig had the idea of testing an algorithm he had developed as a means to solving Stigler's ‘diet problem’ and he was the first to provide the exact mathematical solution in 1947 (Dantzig 1990).
The basic mathematical notions behind linear programming are simple and boil down to combining several inequalities, which implies solving several linear equations simultaneously, a problem within the reach of secondary school mathematics. The difficulty, however, is that the number of equations increases exponentially with the number of variables that require optimisation and rapidly become very time-consuming to solve. Although Dantzig's simplex algorithm considerably reduced the number of equations to solve, finding the solution required several weeks, with clerks working with mechanical calculators. In practice, diet modelling became possible only with the advent of computers. Optimisation modules based upon linear programming are now part of standard spreadsheets.
Despite the role of the ‘diet problem’ in the history of linear programming, this approach received little attention in human nutrition until recently. The need to have computers and easy-to-use software is only part of the explanation, as animal nutritionists have been using these optimisation techniques for years. Key to the challenge is the need to introduce among the model constraints some functions that take into account the acceptability of different foods and food groups, making sure the proposed diet is realistic. In other words, Stigler's diet problem is a very simplified version of real life, and food acceptability constraints, ideally based upon the findings of food consumption surveys in a relevant population, should be added to the constraints he initially introduced. With these caveats, linear programming can be used to identify ways to minimise the cost of nutritionally and culturally acceptable diets, to see whether it is affordable to low-income social groups or to predict the effect of cost constraints on diet quality (Darmon et al. 2002).
Food-based recommendations are formulated in terms of the different food groups that constitute a healthy, balanced diet and are needed every day, such as a minimum daily number of servings of fruit and vegetables or dairy products, or twice a week in the case of fish. Nutrient recommendations are formulated in terms of intakes of energy, protein, essential fatty acids, vitamins and minerals. These two sets of recommendations (food and nutrient recommendations) are often developed independently and their consistency is difficult to assess. This is a major public health challenge because when dietary intakes are inconsistent with food-based recommendations, it is difficult to determine whether this is because of poor compliance or because following the recommendations requires dietary changes that are difficult to implement. Linear programming can be used as a rigorous approach to formulate food-based recommendations that are consistent with nutrient recommendations and current food habits. The approach used to achieve this is to minimise a mathematical function that measures the deviation of the recommended diet from the diet currently consumed, while taking into account nutritional constraints, such as the need to achieve an appropriate energy intake or to achieve recommendations for salt or saturated fatty acid intake (Santika et al. 2009).
Setting limits of acceptability for different foods and food groups improves the formulation of food-based recommendations, but this alone is not enough to reproduce the complexity of human food behaviour. To improve food-based recommendations, more advanced techniques may be considered, particularly simulation techniques reproducing the variability of intake of different foods in the population within observed limits (Katamay et al. 2007). However, the difficulties associated with this should not be underestimated. The challenge is to obtain intake distributions for each food that are realistic and also capable of resulting in an overall energy intake that is consistent with the observed energy intake distribution in the population. This is difficult to achieve because individuals adjust their total energy intake over time, meaning that intakes of individual foods are not independent of one another. Randomly assigning an intake to each food within observed limits, without taking this complex regulation of food consumption into account, will result in unrealistically high variability in energy intake.
The remaining sections of this article discuss how linear programming can add value in a public health context and provide examples of how linear programming can be used in a variety of public health settings to establish practical and nutritionally robust food-based dietary guidelines (FBDGs).
Linear programming: what is the added value for public health nutrition?
Public and private stakeholders involved in public health nutrition often develop tools and guidelines to promote healthy eating. Within such efforts, the very challenging ambition is to make the healthy choice the easy choice for everybody, everywhere, and to take into account food security and sustainability principles. Linear programming can help tackle such a complex task because of its ability to integrate a large number of different kinds of variables and constraints.
Testing the compatibility of sets of recommendations or public health goals
A particular strength of linear programming concerns its ability to test the compatibility of sets of recommendations or public health goals, provided they can be expressed as ‘mathematical constraints’. This is carried out by evaluating the feasibility and/or the realism of diets designed with linear programming models, including such constraints. In some countries, linear programming has been used to assess the relevance of nutritional recommendations. In France (Martin 2001) and Australia/New Zealand (Australian Government et al. 2006), the committees in charge of defining the national nutrient-based reference intakes used linear programming to verify their feasibility and to identify the most limiting nutrients [i.e. the nutrient(s) for which needs will be the most difficult to achieve given the foods currently available and the actual food habits of the population].
Moreover, linear programming is the relevant tool to explore which food changes are needed to fulfil an entire set of nutrient recommendations. Taking France as an example, the changes in food intake indicated by the optimisation process as necessary to achieve nutrient recommendations were shown to be in line with usual dietary advice (Darmon et al. 2006).
Linear programming can also be used to verify the implications of FBDGs in terms of nutrient intakes. For example, in the USA, Gao et al. used linear programming to simulate the fulfilment of the food-serving recommendations of the 2005 Food Guide Pyramid. The results showed that adhering to the Food Guide Pyramid food-based recommendations would ensure adequate intakes of most nutrients, except for potassium and vitamin E (Gao et al. 2006).
Linear programming was also used to estimate the deviation of existing American diets from the WCRF/AICR (World Cancer Research Fund/American Institute of Cancer Research) recommendations, which include both general guidelines on maximal energy density, daily intake of sodium, fibre and some key food groups, and a final recommendation to meet all nutritional needs through diet alone. The results showed that achieving the general goals required little modification of existing diets and had minimal impact on diet quality, but that the final recommendation required a large increase in food volume and dramatic shifts from the observed food intake patterns (Masset et al. 2009).
The capacity of linear programming to translate nutrient recommendations into concrete and quantified advice may have very tangible public health implications. For instance, in an analysis of the French diet, current nutrient recommendations were compatible with consumption of some foods with an unfavourable nutrient profile (together comprising one-fifth of the basket weight), provided that almost two-thirds of the diet comprised foods with the most favourable profile (Maillot et al. 2011a). In the USA, energy allowances for solid fats and added sugars in nutritionally adequate American diets were estimated at 17–33% by a linear programming model (Maillot & Drewnowski 2011).
Combining nutritional constraints and other dimensions of foods and diets
As well as affording the possibility of testing the compatibility between nutritional constraints, linear programming also provides an opportunity to look at the compatibility between nutritional constraints and constraints on other dimensions of food and diets. For instance, linear programming was used to help identify sustainable food patterns, which means food choices that are socially acceptable, affordable, healthy and also environmentally friendly. Data on food consumption, food composition, food price and the carbon impact of food were introduced in linear programming models to derive nutritious diets with a low carbon impact, first for the UK (Macdiarmid et al. 2012), then for France, Sweden and Spain (Thompson et al. 2013) and lastly for New Zealand (Wilson et al. 2013).
A particular example of the strength of linear programming for analysing the relationships between different dimensions is its role in the study of diet affordability, a paramount question both in public health nutrition and in the diet sustainability field. In the USA, the USDA (United States Department of Agriculture) has been applying diet modelling since 1975 to generate balanced, cheap menus: the ‘Thrifty Food Plan’ (TFP) (Carlson et al. 2007). A French study has combined diet modelling and nutrient profiling approaches to identify foods with a very good nutritional quality/price ratio (i.e. the foods that should be preferentially selected to provide a healthy diet on a low food budget) (Maillot et al. 2008).
Besides the classical application of diet modelling for designing low-cost nutritious diets, linear programming has also been used to explore the causal link between the nutritional quality of diets and their cost. Using a model where all the nutritional constraints (except energy) were replaced by social acceptability constraints, Darmon et al. showed unambiguously that economic constraints have a negative impact on food choices (Darmon et al. 2002, 2003). When the cost constraint increases, it induces a reduction in the quantity of fruit, vegetables, meat and fish in the baskets modelled, and an increase in refined cereal products and fatty and sweet products, which, in turn, induces a steep decline in the nutritional quality, with a reduction in the level of almost all protective nutrients (Darmon et al. 2002), an increase in the percentage of fat, and a very steep increase in the energy density (in kcal/100 g) (Darmon et al. 2003) (see Fig. 1).
This work suggests that economic factors play a role in the less healthy food choices associated with poverty. In particular, the increase in energy density supported the hypothesis that economic constraints play a role in the high prevalence of obesity among low-income people.
Nutrition intervention programme planning and policy in low-income countries
Undernutrition in low-income countries contributes to high rates of maternal and child morbidity, mortality and poor development outcomes. To help address undernutrition, tools based upon mathematical modelling have been developed recently to strengthen and inform nutrition programmes and government policy decisions and support advocacy efforts. Focusing upon low-income countries, illustrations of user-friendly tools based upon mathematical modelling that are currently available for these purposes are described, namely Save the Children UK's Cost of Diet tool, World Health Organization (WHO)'s Optifood and WHO's IMAPP (www.side.stat.iastate.edu). Owing to time constraints, a fourth tool based upon linear programming analysis – Nutri-survey – was not described in detail. However, interested readers are referred to its website (www.nutrisurvey.de).
The first of these tools, the Cost of Diet tool, has been used by field practitioners from both Save the Children and the UN World Food Programme to examine the role of the economic constraints as a driver of malnutrition and to inform feasibility studies for fortification programmes and for advocacy purposes. It can be used to identify the lowest cost of a nutritionally adequate diet, the limiting nutrients and to compare economic implications of fortifying different foods (Frega et al. 2012). Inputs into the model are a list of foods and their average serving sizes, an acceptable food pattern range and the average household composition. The model identifies the minimum cost of a nutritious diet for a household, using constraints to ensure energy and nutrient requirements are met, in a ‘realistic’ diet (defined by its food patterns) without exceeding upper tolerable nutrient levels. It also identifies the percentage achievement of the reference nutrient intakes (RNIs) and the cost of each food in the lowest cost diet.
Such information can be used to inform social protection programmes, for advocacy purposes, or to compare the cost implications of fortifying alternative food vehicles. For example, in Mozambique, Frega et al. (2012) showed that the minimum cost of a nutritious diet exceeded the average weekly food expenditures of households from all socio-economic groups, except the highest quintile group. Furthermore, they predicted that the minimum cost of a nutritious diet would be lower when maize flour instead of wheat flour was fortified with iron, zinc, folic acid and vitamin B12 (i.e. 544 vs. 584 metical per week); and in both cases, it was lower than a diet without fortified foods (i.e. 664 metical per week). However, even if fortified foods were made available, the lowest cost of a nutritious diet would exceed the average weekly food expenditure of the three lowest socio-economic quintile groups (Frega et al. 2012).
This example from Mozambique illustrates how mathematical modelling can be used to show when diet affordability must be addressed (e.g. via food subsidies or social protection programmes) to ensure dietary adequacy for a population because even the lowest cost nutritionally adequate diet exceeds the average food expenditure of most socio-economic groups in this population. It also shows how the Cost of Diet tool can be used to inform fortification programme decisions from a cost perspective. However, many other criteria would also be taken into account in the final decisions.
The second of these tools, Optifood, was developed by the London School of Hygiene and Tropical Medicine in collaboration with WHO and the Food and Nutrition Technical Assistant III project (FANTA III) (Daelmans et al. 2013). It has been used to inform food value chain interventions, design food-based interventions for women and young children, and develop a regional micronutrient strategy in Southeast Asia (Santika et al. 2009; Berger et al. 2013).
The inputs required in the Optifood model are similar to Cost of Diet except it is applied at an individual instead of a household level. It requires information on the foods commonly consumed by the target population and, for each food, an estimated average serving size (per meal or per day) and the minimum and maximum number of times per week this serving size could be consumed by any individual. Also required is information on food patterns in a realistic range (lower, median and upper) for the number of servings per week that individuals in the target population might consume foods from different food groups and subgroups.
Unlike the Cost of Diet tool, which runs one linear programming model, Optifood runs hundreds of different linear programming models to answer different questions; and all of these modelled diets must be realistic to draw correct conclusions. In Optifood, there are four modules of analysis: one to check that model parameters ensure realistic diets; one to select the nutritionally best diet for the target population; one to test alternative sets of food-based recommendations (FBRs); and one to run a cost analysis. This last module is similar to the Cost of Diet model, except it models at the individual instead of household level and so will not be described in detail here. In all models, there are constraints to ensure modelled diets are realistic for the target population, and in the third and fourth modules, there are additional constraints to define the FBRs being tested (third module) or to ensure the lowest cost diet achieves or exceeds a desired level for each nutrient (fourth module). This desired level is the RNI, unless the RNI is unachievable, in which case, it is the highest nutrient content achieved in the best diet for that nutrient.
Optifood has been specifically created to formulate and test FBRs to help inform decisions when planning a food-based intervention. By modelling the nutritionally best diet (module 2), it shows whether or not locally available foods together can provide all the nutrients needed by a target population; and when it is not feasible, it identifies the nutrient gaps. As such, it informs behaviour change strategies by identifying the food patterns (e.g. the number of servings per week of vegetables) or individual foods (e.g. liver) that will best ensure a nutritious diet. It identifies micronutrients whose requirements are unlikely to be met in the available diet, indicating when programmes need to address issues related to the availability, accessibility and/or affordability of nutritious foods.
As mentioned, Optifood can also be used to test and compare alternative FBRs, in terms of their ability to ensure dietary adequacy. It simulates the lower tail of each nutrient intake distribution (i.e. ‘worst-case scenario’) for up to 12 nutrients; and for each set of FBRs tested, it compares their ‘worst-case scenario’ levels expressed as a percentage of their RNIs. If these tails exceed 65% or 70% of the RNI, then there would be a low percentage of the population at risk of inadequate intakes. This process is illustrated in Figure 2, which shows the comparative nutritional advantages of promoting seven FBRs versus four FBRs versus ‘no recommendations’ and their cost implications. In this example, successful adoption of the set of seven FBRs would be likely to ensure dietary adequacy (defined as worst-case scenario >65% RNI and illustrated using the horizontal line in the histogram; Fig. 2) for 8 of the 10 nutrients modelled, compared with five and zero nutrients for the set of 4 FBRs or no FBRs, respectively. Programme planners can use such information to help select a set of FBRs to promote.
The third tool, IMAPP (Intake, Monitoring, Assessment and Planning Programme), was developed by the University of Hawaii, Iowa State University, USDA Agriculture Research Service, UC Davis and WHO. It does not use linear programming analyses but is based upon mathematical simulations. It informs fortification programmes, particularly choice of food vehicle and level of fortification, and provides information on the predicted shifts in the percentage of the population at risk of inadequate intakes for the nutrient(s) of interest associated with different fortification strategies. Required inputs are daily nutrient intakes (ideally for two independent days for each person or at least a subgroup), daily intake of each food vehicle (including ingredients disaggregated from composite foods) and possible fortification levels. The outputs of the programme are the prevalence at risk of inadequate intakes at baseline and at different fortification levels, and the prevalence at risk of excessive intakes above the UL at baseline and at different fortification levels. Programme planners can use this information to select fortification levels and combinations of food vehicles that are likely to maximally reduce the percentage of the population at risk of inadequate nutrient intakes without unduly increasing the percentage of the population at risk of excessive nutrient intakes.
In summary, tools are now freely available that are able to inform nutrition planning and policy decisions. In fortification programmes, they can be used to identify appropriate food vehicles and fortificant levels. They can help determine whether a nutritious diet is affordable, to justify a social protection or food subsidy programme, and help identify the lowest cost of a nutritionally adequate diet. In food value chains and agriculture programmes, these tools can identify locally available foods that together provide all the nutrients needed by a target population and/or identify what types of food need to be produced or introduced to help achieve nutritional adequacy by addressing nutrient gaps in local diets. Finally, in behaviour change programmes, linear modelling can identify which food-based recommendations could be promoted to improve the nutritional quality of diets consumed by a target population.
Using linear programming to translate nutrient recommendations into realistic and individual-specific food choices
Linear programming is usually used to design one optimal diet for one given population (Fletcher et al. 1994; Gao et al. 2006; Rambeloson et al. 2008) or a subgroup of a population (Wilde & Llobrera 2009; Maillot & Drewnowski 2011) (e.g. by gender or age classes). Population-based optimisation is based upon the average consumption estimated in a dietary survey. This approach (which does not need complex dietary data) is a practical way to allow researchers to investigate many public health questions. To bring added value to diet modelling in public health nutrition, by integrating diversity of eating behaviours, an individual diet model (ID model) has been developed for which linear programming is applied to data from each individual of a given population in order to translate a whole set of nutrient recommendations into individual specific food choices. This methodology requires precise dietary consumption data at the individual level. The individual diet model (Maillot et al. 2010) has been developed based upon the French INCA1 dietary survey in which 1171 adults (>20 years old) reported their dietary intake with a 7-day food record. Individual diet models were developed to design, for each INCA participant, a new weekly diet that met current nutritional recommendations and that was as close as possible to his or her individual food intake pattern (Maillot et al. 2010, 2011b).
Parameters of the linear programming model
For each individual, the objective function was aimed at: (1) preferentially choosing foods from his or her food repertoire; (2) minimising only the decrease in the quantity of each repertoire food; and, if necessary, (3) introducing non-repertoire foods, preferentially selecting the most frequently consumed foods by the French population. The set of nutritional constraints were imposed to keep total energy equal to the observed energy intake (isocaloric), and allowed an increase in total weight of foods up to 115% of the observed total weight. The WHO recommendations were used for total carbohydrates, free sugars and saturated fatty acids; the Nordic Nutrient Recommendations were used for the sodium upper limit; and the French recommendations were used as targets for all other nutrients (protein, total fat, polyunsaturated fatty acids, dietary fibre, vitamins, minerals and cholesterol). Social acceptability constraints placed an upper limit [i.e. 95th percentile of observed intake (OI)] on the quantity of each food variable and each food group, subgroup and category. However, when, for a given individual, the OIs of foods, food groups, subgroups or categories exceeded the 95th percentiles (i.e. the upper boundary), the OIs defined the upper constraint limits in the corresponding model (Maillot et al. 2010).
Public health concerns investigated using the ID model
The French INCA dietary survey (n = 1171) was used to illustrate the potential of this new individual diet modelling approach to: (1) estimate the feasibility of achieving a whole set of nutrient recommendations by restricting the list of foods to the individual food repertoire; (2) identify the foods needed to reach nutrient goals; and (3) show how foods with different nutrient profiles can fit into nutritionally adequate diets. Firstly, individual diet models were run for all subjects by restricting the list of foods to the individual food repertoire. Among the 1171 modelled diets, only 22% (27% for men and 19% for women) were mathematically feasible, showing that 78% of French adults would need to expand their weekly food repertoire in order to fulfil their nutrient needs (Maillot et al. 2009). Compared with unfeasible diets, feasible diets were characterised by a higher observed energy intake, a higher food diversity in the repertoire, a higher observed energy cost and a lower energy density. Regarding the foods consumed, fruits and vegetables made the most important contribution to overall feasibility (i.e. they were positively associated with feasibility). These results were consistent with evidence that low energy density and high fruit and vegetable consumption (Ledikwe et al. 2006; Schroder et al. 2008), high energy cost (Maillot et al. 2007) and high food variety (Foote et al. 2004; Murphy et al. 2006) are important indicators of nutritional quality.
Secondly, individual diet models were run for all subjects by expanding the food repertoire. Nutritionally adequate diets (n = 1171) were obtained and the food changes between observed and optimised diets were analysed. Among individual repertoires, the amount of unsalted nuts, unrefined grains, legumes, fruit, fish and vegetables increased significantly, whereas the amount of red meats, mixed dishes, cheeses, deli meats and animal fats significantly decreased; other categories remained stable (Maillot et al. 2010, 2011b). Unsalted nuts, unrefined grains, legumes, fruits and fish were frequently added in the modelled diets when they were not present in the observed diet. This meant that plant-based foods as well as seafood products were key foods to reach nutrient goals.
Lastly, individual diet modelling was matched to the French SAIN,LIM nutrient profiling system (Darmon et al. 2009). The SAIN,LIM system is based upon two independent scores and enables the classification of individual foods into four classes according to their nutritional quality. Class 1 represents foods with favourable nutrient profiles [e.g. (most) fruits and vegetables and low-energy-dense dairy products], whereas class 4 represents foods with unfavourable nutrient profiles (e.g. animal fats, biscuits, cream). Class 2 (e.g. refined grains) and class 3 (e.g. fatty fish, cheeses, red meats) are intermediate. The percentage contribution of all classes to total weight of food was computed among observed and optimised diets. On average, subjects consumed 51% of foods with a favourable nutrient profile (class 1), and they consumed 32% of foods with an unfavourable nutrient profile (class 4) (Fig. 3). Foods from classes 2 and 3 represented 8% and 9% of the total weight of food consumed, respectively. In optimised diets, the contribution of class 1 increased up to 61%, whereas the contribution of class 4 decreased down to 22% of total weight (Maillot et al. 2011b). Class 3 slightly decreased (from 9% to 7%) and class 2 slightly increased (from 8% to 10%). These results showed that all foods can fit in a nutritionally adequate diet, but the maximal contribution of foods with an unfavourable nutrient profile was estimated to be 22% of total weight on average. Nutrient profiling systems may be an easy way to characterise nutritional quality of individual foods in order to help people to make healthier food choices.
In summing up the presentations and associated discussion, the chairman of the session, Dr André Briend, made some observations about the limitations of linear programming. The first limitation of linear programming and indeed other modelling approaches is that they are very sensitive to the quality of the data entered in the model. Such approaches are also influenced by the quality of the data on the nutrient composition of foods, as given in food composition tables, and by the nutrient requirements entered in the model. Given the uncertainties related to both food composition and nutritional requirements, the interpretation of diet modelling should be cautious.
A second limitation of the models is that they are unable to handle some very important factors, which have an impact on food constraints, particularly variations in behaviour and the influence of social pressures. Although these tools are very effective in handling the mathematical complexity of making sure that food-based recommendations are consistent with existing food patterns and nutritional composition, users should be aware of their limitations if they are used to examine the broader picture. Many of these limitations can be overcome, by performing sensitivity analysis and utilising expert consultation to design the models and interpret the results.
In conclusion, diet modelling is a flexible and robust approach to translate nutrient recommendations into realistic food choices. It can be adapted to different forms of dietary data and it can include a very large spectrum of constraints, not only nutritional ones but also, for example, constraints on cost, habits and environment. Dr André Briend concluded that diet modelling can inform the development of dietary recommendations and public health policy in many different contexts.
Since the International Congress of Nutrition in Granada, Danone Research has become Danone Nutricia Research.