The phrase 'the heart of this problem' is perfectly correct and usable in written English.
You can use it to refer to the core, central or essential part of an issue or problem. For example: "The heart of this problem is the issue of funding, which needs to be resolved before any other solutions can be implemented."
We must get to the heart of this problem".
The "efforts of others" prong of Howey aims at the heart of this problem.
One of the Bush administration's most damaging postinvasion decisions is at the heart of this problem.
"Honour" is at the heart of this problem, whether it's that of a country or an individual woman.
At the heart of this problem lies the reluctance of true believers, whatever their belief happens to be, to accept that anyone can oppose them in good faith.
At the heart of this problem lies the cowardly stance taken by the 1997 Labour government, which could have used its landslide majority to outlaw selection everywhere.
Carol Rosenberg, of the Miami Herald, calls this concept "Guantánamo North," a name that gets to the heart of the problem: this would not close Guantánamo, just move it.
My worry is that the authors' wobble, unknowingly, gets to the heart of the problem, of this or any radical idea about how we improve our health, through diet, exercise or any other known means.
At the heart of this relationship problem is something Neufeld and Maté call "peer orientation".
At the heart of this wicked problem is money: the market forces that drive the drugs trade, the illusion of easy cash for kids who have none, the economic deprivation in those areas in which knife crime is most prevalent and the years of sustained cuts to the very public services that support the most vulnerable young people.
The conundrum of meeting the challenges of food security while at the same time improving health outcomes lies at the heart of this "wicked problem".
