Please check AirQ+ it has used BC as one of the pollutants to determine health risk assessment. The glossary provides details of the equations and things you need to work. Try it out, let me know if you need any help.

http://www.euro.who.int/__data/assets/pdf_file/0004/162535/e96541.pdf

https://ehp.niehs.nih.gov/1003369/

Article Assessing public health burden associated with exposure to a...

AirQ+ it used BC as one of the environnemental modèle to determine health risk assessment

In general, black carbon is often used as a tracer for combustion sources, which is the primary source of most fine particulates, and the health effects of PM2.5 are well documented in many papers throughout the past few decades. An indirect health consequence of black carbon would be it's radiative forcing in the Earth's atmosphere. It is widely considered the second most important, anthropogenic, warming agent in the atmosphere. See Bond et al. 2006 for a comprehensive review of black carbon, particularly in the climate context.

In addition to the other answers you might check next article: Ostro B, et al. Occup Environ Med 2015;72:123–129. "The risks of acute exposure to black carbon in Southern Europe: results from the MED-PARTICLES project", doi:10.1136/oemed-2014-102184, link:

https://oem.bmj.com/content/72/2/123

The authors report on the association between short term exposure to Black Carbon and mortality in Barcelona and Athens. In the reference list you may find some other studies on this until now little researched subject. Try also a search at BMJ: https://oem.bmj.com/search/black%252Bcarbon%20jcode%3Aoemed