Designing low-cost “heart healthy bread”: optimization using linear programing and 15-country comparison
© Wilson et al. 2016
Received: 26 November 2015
Accepted: 9 April 2016
Published: 18 April 2016
Bread is an important component of the diet in many countries and provides needed nutrients but also typically too much of other nutrients e.g., sodium. We therefore aimed to use linear programing to determine the optimal design of low-cost “heart healthy bread” (HHB) and to compare the results with commercial breads in 15 countries.
Optimization using linear programing focused on achieving set loaf prices (at NZ$1.5 and $3) and for a range of minimal sodium levels. Then within those constraints, levels of alpha-linolenic acid (ALA) were maximized, then dietary fiber, and then polyunsaturated fatty acids. Data from New Zealand (NZ) was used for the HHB designs and comparison nutrient and price data came from breads in 15 high-income countries.
The optimized loaf costing NZ$1.50 in ingredients (HHB$1.5) was superior to the commercial white loafs in three out of the eight heart health nutrient categories. The optimized loaf that was high in linseed and cost NZ$3 in ingredients (HHB$3), was nutritionally superior to the commercial loafs with seeds/nuts in six out of the eight heart health categories (i.e., in terms of sodium, potassium, fatty acid ratio and fiber). In terms of value-per-weight, a commercial white loaf from the UK was slightly cheaper than the HHB$1.50 loaf (at US$0.07 vs US$0.10 per 100 g loaf). But compared to the other seed/nut loafs, the HHB$3 loaf was the best value at US$0.17 per 100 g, vs a mean of US$0.85 per 100 g across international comparators.
This proof-of-concept study suggests it is possible to design breads that are nutritionally superior to commercially available breads from a heart health perspective, as well as being lower cost. Such HHB designs could be promoted by health agencies and utilized in conjunction with a government-funded bread voucher system for those at high risk of cardiovascular disease.
KeywordsCardiovascular disease Bread design Linear programing Optimization Sodium Fiber Alpha-linolenic acid Saturated fat
The global burden of non-communicable diseases (NCDs) accounted for two of every three deaths (34.5 million) worldwide in 2010 . Furthermore, a global estimate for 2013 indicated the high burdens of years lived with disability from: diabetes (29.5 million), cardiovascular disease (21.2 million) and cancer (6.7 million) .
Dietary risk factors are particularly important for NCDs such as cardiovascular disease (CVD)  and these include dietary intakes of sodium, fiber and types of fatty acids. One food which has all three of these nutrients is bread. It is also one of the most popular foods in many developed countries e.g., 8.7 % of total energy in the United States, albeit the combined category of “bread, rolls and crackers” . Even more so in Canada, “refined breads” contributed more dietary energy than all the other food groups in those aged 18 to 65 years (range by age/sex groups: 10.5 to 11.8 %), with whole-grain breads contributing another few percent (range: 2.4 to 4.1 %) . For men in the United Kingdom, white bread was the second highest non-beverage food in those aged 19–64 years (by weight with a median of 46 g per day; interquartile range [IQR]: 18–93) after vegetables . But for women it was less at a median of 27 g per day (IQR: 9–61).
Based on commercial varieties of bread available, there appears to be substantial flexibility around the levels of the main ingredients (e.g., flour, yeast, salt) and also additional ingredients such as nuts and seeds. For example, a number of European governments aim to reduce sodium intakes by regulating the maximal level of sodium in bread [7, 8]. This action is supported by various modeling studies that suggest both health and economic advantages of reducing sodium in bread (e.g., for Argentina [9–11], Australia [12, 13], New Zealand  and South Africa ). Furthermore, there have been successful studies and interventions to replace sodium chloride in bread with potassium salts [16–18].
But other aspects of bread design can also be considered from a CVD prevention perspective given the evidence from systematic reviews around: increasing dietary fiber [19, 20] and increasing linseed (flaxseed) intake which is high in alpha-linolenic acid [21, 22]. Yet despite this evidence, our examination of the literature (as of June 2015) identified no optimization studies specifically relating to the design of heart healthy bread, and none concerning the design of low-cost healthier bread.
So to further progress thinking around this issue, we aimed to design optimized versions of low-cost “heart healthy breads” (HHBs). Our specific major aim was to determine, at a “proof-of-concept” level, if it was possible to design breads that had both improved nutrient levels from a CVD prevention perspective and which were relatively low-cost. Our secondary aims were: (i) to determine how these HHBs compared with commercial breads in 15 high-income countries; and (ii) to estimate the cost of mass production of HHB loafs using publicly-available data for the cost-structure data of bread manufacture.
We specifically aimed to use linear programing in our methods as this is an established tool in studying the optimization of food and diets where there are multiple nutritional and other objectives . It has also been used previous around bread in diets e.g., for studying sodium and iodine in the diets of Indigenous Australians , for the inclusion of wholemeal bread in food aid in France , and for changing bread intake as part of improving nutrient intakes for the Italian population .
While more detailed steps follow, in summary this work began with literature searches for identifying potential bread ingredients and their nutritional value from a CVD prevention perspective. This was then followed by a determination of the specific nutrient constraints to be applied and optimization priorities set, for the analysis using linear programing. New Zealand nutrient and price data were used for the HHB designs and data for comparison with commercial breads were obtained for 15 high-income (OECD) countries from freely accessible nutrient databases that could be identified online. Publicly-available data for the cost-structure of bread manufacture from the Canadian baking industry was then used to better estimate the cost of mass production of HHB loafs.
Potential ingredients considered for bread designs
A high potassium salt substitute, as this type of salt has been associated with blood pressure reduction in a meta-analysis . There is also evidence that potassium chloride can achieve flavor compensation that allows for large reductions in sodium levels in bread .
Wholemeal flour, given the evidence for reduced CVD risk as per three systematic reviews [19, 20, 29] and an analysis of two large prospective studies . Although outside of the CVD perspective, we note that dietary fiber from whole grains also appears to protect against colorectal cancer in another systematic review .
Linseed, as this is high in dietary fiber, lignans and n-3 polyunsaturated fatty acids (PUFA) and there is some evidence for CVD-related benefits as per three reviews [32–34] and a recent trial . More specifically, two meta-analyses report blood pressure reduction associated with linseed consumption [21, 22].
Walnut (English walnut), as there is evidence that this food can benefit cardiovascular health as per a systematic review  and another recent review . Indeed, nut consumption more broadly is associated with reduced risk of both CVD and cancer according to a systematic review  and a large cohort study . Given this we also considered the addition of other seeds that are known to be commonly used in commercial breads, i.e., sesame seeds, sunflower seeds and pumpkin seeds.
Potential ingredients not included
Plausible healthy bread ingredients from a CVD perspective identified in the literature included: soy protein , sourdough , and high phenolic olive oil . But in this initial work we did not include these ingredients on the grounds of potentially relatively lower consumer acceptability.
Constraints and optimization approach used for the linear programing
Constraints and optimization targets for the design of the “heart healthy breads”
Ingredients and nutrients
Constraints and optimization targets
Cost and weight
Cost per loaf (ingredient costs only)
Set target values for baseline analyses (with the highest value still substantially less than commercial artisan bread loafs in the current NZ setting in the $NZ8 plus range).
Total weight of dry ingredients
Makes around one kg of HHB loaf (given the addition of water to the recipe: see below).
Active yeast mixture
3 to 4 tsp (12–16 g)
Basic requirement for bread design to ensure the bread rises, with 12 g for the HHB$1.5 loaf but slightly more (16 g) for the HHB$3 loaf given the increased weight of the seed ingredients.
White or wholemeal flour
Set at 50 % each for white and wholemeal flour for the HHB$1.5 loaf; but at 25 % white and 75 % wholemeal for the HHB$3 loaf (to avoid excessive density and chewiness).
450 mls added to HHB$1.5 and 500 mls to HHB$3
Evaporation of the water during baking is a determinant of the final loaf weight.
Total weight of added seeds/nuts
This was an arbitrary upper limit to constrain bread density and chewiness (especially relevant for older people and those with suboptimal dentition). Nevertheless, it is a level still below that found in some commercial breads e.g., one Finnish bread has 17 % seeds by weight (“Fazer Alku Jyväpala”). Ground linseed was used rather than whole linseed, given data on bioavailability and gastrointestinal tolerance .
Key CVD-related nutrients
<350 mg/100 g
Range for all the dry ingredients collectively (with a goal of <300 mg/100 g for the cooked loafs). The salt substitute with potassium chloride (KCl) was the preferred source of sodium (over normal salt) but was limited to a maximum of 1.5 tsp (9 g) per loaf to avoid any bitterness. The range of 250 to 300 mg/100 g in a final loaf would be substantially less than the mean level in 2013 in NZ (410 mg/100 g)  and for most breads in other high-income countries e.g., the USA .
Alpha-linolenic acid (ALA)
Maximized ahead of fiber and PUFA (first priority of the objective function).
Maximized ahead of PUFA (second priority of the objective function).
Polyunsaturated fatty acids (PUFA)
Maximized after maximizing fiber and ALA (third priority of the objective function).
Not specifically optimized
Given the use of a KCl containing salt-replacement, we focused on lowering sodium rather than increasing potassium.
The simplex algorithm was used to solve these linear programing problems (see Briend et al.  for a detailed description of the linear programing). The problem of multiple objectives with priority levels is addressed with lexicographic goal programing, which involves a sequence of linear programing steps . Most of the scenarios were modeled in Microsoft Excel 2010 (Excel Solver, Simplex method), but where there was a high level of complexity with the food combination options the R programing language was used (version 2.15.0, lpSolve package).
Nutrient and price data for the HHBs
The nutrient data for the HHBs was sourced from a New Zealand food composition database . But, in some cases we had to use other sources such as a study on levels of alpha-linolenic acid covering nuts and seeds  and from the nutrient panel on the packaging (i.e., for the salt substitute). For the price data for HHB ingredients, the cheapest retail source for the ingredients were used, with these typically being supermarkets and online stores in New Zealand.
Country comparisons of commercial breads
For country comparisons we considered just OECD countries and we conducted internet searches for those which had online documentation of nutrient profiles on commercial breads. In particular we used the EuroFIR database  which had 15 freely accessible nutrient databases. Ultimately, the only OECD countries with such databases were: Canada, Czech Republic, Denmark, Finland, Greece, Iceland, Italy, the Netherlands, New Zealand, Slovakia, Sweden, Switzerland, United States and the United Kingdom. For these countries the nutrient data on the most standard pre-packaged white bread was obtained. Only six of these countries had nutrient data on any breads containing seeds or nuts (Denmark, Finland, Iceland, Netherlands, New Zealand and Switzerland). Where there were multiple such breads, the one with the highest level of PUFA was selected as a proxy for the highest level of seeds/nuts.
Bread price information was sourced from online supermarkets in each country. At first, an attempt to identifying the largest supermarket chain in each country was made. Failing this, a search of the online supermarkets in the capital city was performed. Out of the breads marketed in these online supermarkets, the lowest priced most standard white pre-packaged loaf was selected for price information. For breads with seeds/nuts, the price data was from the one with the highest seed/nut level (based on the ingredient listing). For all the prices we calculated cost per 100 g and cost per 1000 kJ in US dollars using OECD exchange rates and purchasing power parity adjustments . For specific nutrient and price methods details for each country see Additional file 1.
Estimating mass production costs of HHBs
To estimate the cost of mass production of HHB loafs, publicly-available data for the cost-structure data of bread manufacture from the Canadian baking industry was used. Such data are not readily available in other countries (including New Zealand), presumably due to reasons of commercial sensitivity. This Canadian cost-structure covered: “materials and supplies”, “energy, water and vehicle fuel” and “production worker wages” . We applied this to the cost of the cheapest supermarket white bread from New Zealand (NZ$1.00 or US$0.68 for a 600 g loaf) and assumed at this price it was basically “cost price” i.e., with no profit. Using recipes for a white loaf of bread , we then estimated how much more cheaply the ingredients for this commercial bread might typically cost the baking industry, compared to ingredient prices in the supermarket. This scalar was then applied to all the HHB ingredients and varying levels of profit margin were also considered (for the manufacturer and retailer). We assumed HHBs would be mass produced by existing bread manufacturers with existing plant and machinery and distribution networks. Further details on the methods are shown with the tabulated results.
Optimized HHB ingredient selection
Dry ingredients of the two optimized “heart healthy breads” per 100 g of dry ingredient weight
Quantity of dry ingredients (g)
Percentage of dry ingredients
Quantity of dry ingredients (g)
Percentage of dry ingredients
Nuts and seeds
All dry ingredients
All nuts and seeds
Heart health and other nutrients in the loafs
Comparisons of the nutrient levels of the “heart healthy bread” loafs with commercial breads (nutrients and costs, all values per 100 g unless indicated otherwise)
White breads (n = 15 countries)
Rank of HHB$1.5a
Breads with seeds/nuts (n = 6 countries)
Rank of HHB$3a
Eight heart health relevant characteristics b
Alpha-linolenic acid (ALA)
0.05 – 0.17
0.64 – 1.44
Total polyunsaturated fatty acids (PUFA) (g)
0.51 – 1.33
2.98 – 5.73
Total saturated fatty acids (SFA) (g)
0.29 – 0.70
0.89 – 1.83
1.7 – 2.5
3.0 – 4.7
457 – 528
437 – 472
115 – 157
195 – 277
Ratio of potassium to sodium
0.2 – 0.3
0.4 – 0.6
Dietary fiber (g)
2.6 – 4.3
4.3 – 5.4
54 – 110
37 – 43
Folate (mcg) (including synthetic forms in some fortified white breads)
27 – 41
44 – 57
1.2 – 6.0
3.1 – 16.2
1.1 – 2.5
1.4 – 2.7
2.6 – 14.3
4.1 – 8.0
0.7 – 1.0
1.1 – 1.9
Selected other macronutrients
Dietary energy (kJ)
1026 – 1169
2/14 (if low is best)
1168 – 1291
2/5 (if low is best)
8.3 – 9.1
9.5 – 11.6
Sugars (total) (g)
1.7 – 4.8
1.45 – 3.4
Cost (relevant to food security) c
Cost per 100 g of loaf (US$)
0.21 – 0.34
0.64 – 0.95
Cost per 1000 kJ of food energy (US$)
0.12 – 0.20
0.33 – 0.38
The HHB$3 loaf appeared to be nutritionally superior to the commercial loafs with seeds/nuts from six countries in six out of the eight heart health categories (Table 3, Fig. 2). While it had the best PUFA/SFA ratio, it did not have the highest levels of PUFA and lowest levels of SFA. It also appeared superior to the HHB$1.5 loaf in all eight heart health categories except for low saturated fat. Some of the differences were relatively large, such as the ALA level in the HHB$3 loaf being 26 times the median for the white loafs and 2.2 times the median for the commercial high seed/nut loafs.
In terms of other nutrients, the HHB$1.5 bread appeared to perform better than most commercial white breads (e.g., highest in iodide and zinc) (Table 3). But it was competing with some breads which were fortified with calcium, folate and iron. However, relative to the commercial seed breads, the HHB$3 loaf was in the top two rankings for: calcium, folate, iodide, iron, low sugars, and low energy density.
In terms of value-per-weight, a commercial white loaf from the UK was slightly cheaper than the HHB$1.50 loaf (at US$0.07 vs US$0.10 per 100 g loaf, Table 3). The HHB$1.5 loaf also performed relatively well in terms of price per kJ of food energy (fourth equal). But compared to the other seed/nut loafs, the HHB$3 loaf was by far the best value-per-weight at US$0.17 vs a mean of US$0.85 per 100 g.
Possible mass production costs of HHB loafs
Estimated mass production costs for “heart healthy bread” designsa
Commercial white loaf in NZ
Vehicle fuel costs, energy and water
Total price after profit mark-up of 10 %
– of 25 % mark-up
– of 50 % mark-up
Loaf weight (g) – average
1004 to 1057
1184 to 1195
Price NZ$/100 g at 25 % mark-up (US$)
Where commercial manufacturers/retailers produced and sold HHB loafs (e.g., as per contracts for a government voucher system for provision of HHB) a profit margin would be relevant (Table 4). For example, a 25 % profit margin shared by producers and retailers would push up the price to: US$1.24 for the HHB$1.5 loaf and US$2.19 for the HHB$3 loaf (Table 4). Based on these estimates and a 25 % profit mark-up, the HHB$1.5 loaf at US$0.12 per 100 g would remain well under half that of the median for the commercial white loafs from the 15 high-income countries in Table 3. Likewise the HHB$3 loaf at this mark-up would still be the lowest cost per 100 g out of the seed/nut loafs in Table 3.
Main findings and interpretation
This proof-of-concept work generated two potential HHB designs which were generally superior to commercial breads from 15 high-income (OECD) countries from a nutrient/CVD prevention perspective (i.e., in terms of sodium, potassium, fatty acid ratios and dietary fiber). The higher levels in the HHB$3 bread were often substantial e.g., 26 times the median ALA level of the white loafs. Furthermore, in principle the higher fiber levels in the HHBs could contribute to non-CVD benefits such as colorectal cancer prevention . Similarly, the walnut in the HHB$3 loaf could potentially contribute in a small way to cancer prevention [38, 39], but obviously a diet designed to minimize cancer risk has many other aspects such as being high in fruit and vegetables.
Of relevance to food security, the HHB$1.5 loaf was better value-per-weight than all but one of the commercial white loafs from the 15 countries. The HHB$3 also outperformed all the seed/nut loafs at a fifth the cost per 100 g of the average. Furthermore, the relatively higher level of dietary fiber in the HHB loafs might mean they also provide better value in terms of inducing satiety. Such a satiety benefit has been reported in a study on wholegrain vs refined bread , but not in one of nut-enriched bread vs nut-free bread .
The mass production cost estimates (Table 4) suggest it would be feasible to produce the HHB$3 loaf in a place like a hospital kitchen at around US$1.75 per loaf. The voucher costs for government for this type of loaf might be US$2.19 per loaf when assuming a 25 % mark-up by the contracted manufacturer and retailers (or US$2.63 if a 50 % mark-up is assumed). At two loafs a week per person (e.g., for a patient at high risk of CVD) this would be US$274 per year in voucher costs for a 100 % subsidized loaf supply (albeit not including the voucher delivery and other administration costs). Whether this is justified from a funder perspective would depend on many issues such as the priority given to protecting public health and the health economics (e.g., the cost-effectiveness of such a program should ideally be modeled before any implementation).
Study strengths and limitations
This study was, to our knowledge, the first to study the issue of the optimized design of bread from a heart health and a low-cost perspective using linear programing. We consider that the constraints imposed, and the typical ingredients used, will help ensure that such designs have at least some acceptability in high-income countries where there is often a majority of adults who currently consume at least a light-grained bread (e.g., as per New Zealand ). Indeed, some countries currently have seed/nut breads sold commercially at up to 17 % seeds by weight (for Finland, see Table 1).
Nevertheless, this was still just a proof-of-concept study which only considered two potential designs of HHB. Indeed, the full “design-universe” of such potential breads is large and might include other relatively healthy additional ingredients such as: soy, sourdough, dried fruit, high phenolic olive oil, and extra fiber sources (e.g., wheat bran and rye flour), (see the Methods ). A version particularly suitable for women of child-bearing age could also include added folic acid for preventing neural tube defects.
A further limitation was the relatively simplistic nature of our cost estimates for mass production of the two HHB designs. Nevertheless, it is plausible that the cost-structure of Canadian bread manufacture is not markedly different from other high-income countries. Our costing estimates also didn’t consider administrative costs associated with setting up and running any HHB voucher system (e.g., for people with CVD risk factors). It also did not consider the environmental impact, as per Swedish work on emissions of oxides of carbon, sulfur and nitrogen from bread production . Finally, we did not explore various other complexities with bringing any HHB to market. For example, consumer taste testing would be required (see below), and packaging would need to be designed. For example, packaging would probably need to display potassium levels to help people with renal disease or on particular medication such as diuretics to avoid excessive intake.
Implications for further research and policy
Consumer testing prior to mass production of any HHB could be done by a commercial bread manufacturer as part of their routine product development processes. Similarly, an institution such as a public hospital could “market test” the acceptability of various HHBs on staff in a hospital cafeteria. The latter could be done in conjunction with health orientated non-governmental organizations which exist in many countries and sometimes have “endorsement label programs” for heart healthy foods (e.g., as in New Zealand ). If there were concerns about public acceptability of bread design, then a more incremental approach could involve slowly phasing down the levels of white flour and sodium while phasing up the levels of linseed and salt substitute in the HHBs promoted for mass consumption. Final bread products could also be considered in terms of the health claims that could be justifiably made on HHB packaging or in marketing about these being “functional foods”. Many countries have rules around such claims with one example being the European Food Safety Authority’s process for European Union countries .
Epidemiological and economic modeling should also attempt to quantify the effectiveness (in quality-adjusted life-years gained) and cost-effectiveness of a government-run voucher system for a HHB version for those at increased CVD risk (and even for those at increased risk of cancer given the extra fiber and seeds in the HHB$3 loaf).
This proof-of-concept study suggests it is possible to design breads that are nutritionally far superior from a heart health perspective to commercially available breads as well as being lower cost. Such HHB designs could be utilized in conjunction with a government-funded voucher system for those at high risk of CVD. This could be one (albeit small) part of comprehensive CVD prevention programs which ideally should cover multiple nutritional and physical activity interventions.
This was not relevant for this modeling study which did not involve human subjects.
Consent to publish
Availability of data and materials
All supporting data is in Additional file 1.
heart healthy bread
Organisation for Economic Co-operation and Development
polyunsaturated fatty acid
saturated fatty acid
We thank our work colleagues for their helpful comments on bread design issues, Pascale Otis for the photography, and the journal’s reviewers for constructive critique.
The Burden of Disease Epidemiology, Equity and Cost-Effectiveness Programme is funded by the Health Research Council of New Zealand (10/248).
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