Hi, I’m a medical doctor in Japan.
I have a question on usage of an article ‘the.’

We are going to host a congress of wound healing society in Japan and preparing a poster to introduce the congress.
We’ve decided our theme of the congress ‘’A new borderless approach to the wound healing.’ We want to include our image of ‘cooperate with many co-workers multidisciplinary, do not restrict in ordinal clinical procedure but elucidate the effectiveness of new materials and techniques into a phrase of ‘borderless approach.’
In this case, do we need ‘the’ in front of ‘wound healing?’ Which is better ‘A new borderless approach to the wound healing’ or ‘A new borderless approach to wound healing?’

I will be glad to have your answer.
I would not use the definite article here. You're not talking about a specific wound healing, but about "wound healing" in general - an abstract notion. So drop the definite article.
wound healing society in Japan

But here you are referring to a specific society, so say
The Wound Healing Society of Japan.

Is the term 'wound healing' commonly used and understood in your field?
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To Xerxes,

Thank you for your reply.
I understand your advice. We'll drop off 'the' from our theme.
 Clive's reply was promoted to an answer.
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To Clive,

Thank you for your reply.
Correctly, the name of our society is 'The Japanese Society for Wound Healing.' Besides, the phrase of 'wound healing' is common words in clinical use to indicate healing situation or mechanism of injured tissues.