Living in an area with little access to fresh and nutritious foods has been linked to high heart disease risk, but a new study suggests that it’s the inability to afford a healthy diet, rather than access, that’s to blame.

Researchers studied Atlanta residents and found that people living in “food deserts,” where there are few places to buy fresh produce and other healthy foods, had more heart risk factors like hardened arteries and inflammation than people with easy access to healthy foods.

But within food-desert neighborhoods, people with high personal income had fewer heart risk factors than those with low incomes, suggesting it’s money, not access, that prevents some people from having a healthy diet that would lower their heart risk, the study team concluded in a report online September 13 in Circulation: Cardiovascular Quality and Outcomes.

“Food deserts are defined as areas that have below average income together with poor access to healthy foods, ie. lack of grocery stores (within 1 mile in urban and 10 miles in rural communities),” lead author Arshed Quyyumi told Reuters Health in an e-mail.

“We found that area income, and even more importantly, personal income was associated with higher cardiovascular risk, and that access to food was not that important a risk,” said Quyyumi, a cardiologist at Emory University School of Medicine in Atlanta.

Researchers have known that neighborhood factors are important social determinants of disease outcomes, he added.

About 13% of participants lived in areas considered food deserts. These people also had higher rates of smoking, were more likely to have high blood pressure and hardened arteries and to be overweight or obese, compared to those not living in food deserts.

When the study team took average neighborhood income and individual incomes into consideration, they found that people living in food deserts in low-income areas had about the same risk of heart disease as their peers living in low-income areas with good food access.

Meanwhile, high-income individuals in low-income neighborhoods had fewer cardiovascular risk factors compared to their lower-income neighbors, and that was true even when they lived in food deserts.