How would you approach unresectable synovial sarcoma of the heart ?

The specific situation described is rare and I'm not aware of any data addressing it directly, but there are general principles for cardiac sarcomas that can be helpful.

For cardiac sarcomas, subsite matters for prognosis and treatment. Left-sided more prone to non-lung visceral mets. (In resectable patients, preop RT seems riskier due to higher filling pressures and risk of postop dehiscence.) Right-sided more prone to lung mets. (In resectable patients, risks of preop RT may be less.)

Among cardiac sarcomas, angiosarcomas are more common. For unresectable cardiac ANGIOsarcoma, I have previously followed an approach described in a case report from WashU of SBRT 30 Gy/5 fx/5 days with concurrent taxol, with anecdotally excellent results.

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I would add the importance of the brain MRI for staging AND surveillance, particularly for left sided tumors. The incidence of brain metastases for cardiac sarcomas is quite high and often occurs within 1 year of diagnosis. This is probably a physiologic consequence and not a unique tropism of cardiac sarcomas. For extremity sarcomas metastasizing hematogenously through venous return, lung metastases predominant for the majority of histologies. For sarcomas within the left heart, the arterial outflow provides relatively direct access to the capillary network of the brain (Siontis et al., PMID 30962762). Brain metastases in these patients can be particularly challenging to manage and the prognosis is generally poor.