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A 100-year-old chemical formula co-developed by one of the University of Toronto's first female medical graduates has helped ����ֱ�� researchers determine that the global rise in life expectancy is not benefitting everybody equally.

People are living longer on average than they were in 1970, and those extra years of life are being achieved at lower cost, says a paper published in the open access science journal eLife this month by Professor Prabhat Jha of the Dalla Lana School of Public Health, Professor Anita McGahan of the Rotman School of Management, Professor Yu-Ling Cheng, director of the Centre for Global Engineering, and Ryan Hum, a PhD student in chemical engineering and a member of of the Centre for Global Engineering. 

However, the costs for an extra year of life among adult males in lower-income countries are rising, Hum and his colleagues say, while the costs for an extra year of life among children worldwide and for adults in high-income countries continues to drop.

The researchers made the discovery when they took the Michaelis-Menten (MM) equation – a well-known mathematical model first used to analyze enzyme kinetics in 1913 – and applied it to adult and child mortality at different incomes. They reasoned that just as chemical catalysts affect enzyme velocity; the public health catalysts react with income to affect life expectancy.

The MM equation was co-developed by Maud Menten, who received her medical doctorate from ����ֱ�� in 1911.

“We noticed the similarity in the curvature and became fascinated with the beauty of the analogy,” said Hum. "The MM equation is standard curriculum for biochemistry, biology and most chemical engineering undergraduate students and we knew there could be added knowledge that we could decipher purely from the math.”

The study explains that "over the past few decades, research and development of new technologies (drugs, vaccines, policies) have focused mostly on childhood and infectious disease, with fewer worldwide investments for adult chronic diseases. Increasing coverage of inexpensive health interventions such as immunization, insecticide-treated nets, and case management of childhood infections could be contributing to decline in critical income for child survival.”

Hum and his colleagues conclude by recommending that society invest in research and treatment of adult chronic disease, most notably the control of smoking and other risk factors for chronic diseases, and low-cost, widely useful treatments for these diseases.

In the paper, the authors expand on the analogy between enzymes and incomes: “Income directly enables certain technologies, immunization programs, epidemiological knowledge, education, and sanitation systems and other areas, which may themselves be interpreted as 'catalysts' – agents that accelerate the rate of a reaction without being fully consumed in the process," they write.

They came up with a new parameter, critical income, which they define as the level of income needed to achieve half of the maximal overall life expectancy found in high-income countries.

For example, in 1970 the critical income for overall life expectancy (in inflation adjusted 2005 dollars) was $1.48 per day. By the year 2007, critical income had fallen to $1.21 per day. In other words, a lower national income is needed to achieve a higher life expectancy now, compared to 40 years ago.

However, that good news is due mostly to improvements in children’s health and to increased life expectancy in high-income countries, the researchers say. For adults in lower-income countries, critical income has actually risen since 1970. In other words, adults in low- and middle-income countries need to have higher incomes on average in order to add an extra year of life. 

Adult males in these countries are especially affected, though adult females also suffer.

“Under the current conditions, an approximate national income per capita of $2.20 per day would be required in 2007 to attain the same achievable adult male survival rate with $1.25 per day in 1970. Moreover, should the critical income costs for adults continue to rise (in line with current trends),” they warn.

Hum and his colleagues noted that increases in smoking, especially among adult males, and HIV prevalence are responsible for part of the life expectancy gap. By contrast, worldwide attention to childhood health including much research on new technologies, vaccines and political attention mean a rosier future for children – it’s becoming less expensive to give children the chance for longer lives.

See the published paper .