This paper introduces an innovative methodology developed within the Homo Medicinalis (HoMed) project for adapting automatic speech recognition (ASR) models to handle sensitive audio data domains, specifically focusing on privacy-sensitive patient-provider medical consultations. By utilizing AI and deep learning algorithms, the project successfully addresses GDPR compliance while enhancing ASR technology's performance through domain-specific adaptation. The methodology involves adapting and testing three state-of-the-art ASR models for Dutch using highly sensitive audio-visual recordings, with data preparation emphasizing privacy-compliant methods and secure training environments. Through this approach, the study not only advances ASR technology's capabilities in specialized audio domains but also provides a blueprint for developing publicly shareable, domain-specific ASR engines while safeguarding the confidentiality of sensitive audio information.