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What would be possible causes for high homocysteine but low CRP?

If homocysteine is elevated due to a deficiency of B6, B12, or folate, without inflammation, you can see elevated homocysteine without an elevation in CRP.

Homocysteine can be a marker of inflammation and vascular aging in which both CRP and homocysteine can be elevated. Both markers are also independently associated with sarcopenia (generalized loss of muscle and strength). 1

Research on levels of CRP and homocysteine ~6 years after an ischemic stroke noted that survival was better when CRP was maintained at or below 1 mg/L and homocysteine at or below 9 ug/L. 2

Elevations of hs-CRP 1.9 mg/L or greater, combined with homocysteine of 14.65 umol/L or greater, were associated with 1.9 times greater risk of depression three months after ischemic stroke. 3

RESEARCH

  1. Lee, Wei-Ju et al. “Sex-different associations between serum homocysteine, high-sensitivity C-reactive protein and sarcopenia: Results from I-Lan Longitudinal Aging Study.” Experimental gerontology vol. 132 (2020): 110832. 
  2. Naess, Halvor et al. “C-reactive protein and homocysteine predict long-term mortality in young ischemic stroke patients.” Journal of stroke and cerebrovascular diseases : the official journal of National Stroke Association vol. 22,8 (2013): e435-40. 
  3. Yin, Jieyun et al. “Elevated circulating homocysteine and high-sensitivity C-reactive protein jointly predicts post-stroke depression among Chinese patients with acute ischemic stroke.” Clinica chimica acta; international journal of clinical chemistry vol. 479 (2018): 132-137.