Good morning,

I think the relationship with the sympathetic branch of the autonomic nervous system is well established, but I am less certain about parasympathetic.  The only thing I can link is the presence of bradycardia during vaso-vagal response to stress, and it is ordinarily associated with something like venipuncture.  I did find this:

https://www.researchgate.net/profile/Mats_Fredrikson/publication/51896662_A_meta-analysis_of_heart_rate_variability_and_neuroimagine_studies_Implications_for_heart_rate_variability_as_a_maker_of_stress_and_health/links/0f31752f24304d59e0000000/A-meta-analysis-of-heart-rate-variability-and-neuroimagine-studies-Implications-for-heart-rate-variability-as-a-maker-of-stress-and-health.pdf 

as well as this meta-analysis

http://journal.frontiersin.org/article/10.3389/fpsyt.2014.00080/full

and this study regarding PTSD and HRV

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4197067/

Hope this helps, good luck!

Rich

Article A meta-analysis of heart rate variability and neuroimagine s...

The two limbs of autonomic system respond differently to different stimuli and are not always opposite to each other. Studies have shown that parasympathetic system activates rapidly after exercise regardless of the high level of sympathetic activity(Billman, G. E. 2009). Animal studies also found that stimuli of certain regions of the hypothalamus evoked the activation of both sympathetic and parasympathetic systems(Koizumi, K., & Kollai, M. 1981). According to Shattock et al., submersion into cold water triggered both the ‘diving response’ and the ‘cold shock response’(Shattock, M. J., & Tipton, M. J. 2012). The ‘cold shock response’ induces sympathetic activation, whereas the ‘diving response’ elicits bradycardia driven by cardiac vagal activation. Therefore, I think certain stress can induce the coactivation of both sympathetic and parasympathetic systems.

The HF power of HRV is widely considered as an index of parasympathetic neural activity. However, the validity of the LF power as a reflection of sympathetic neural activity remains controversial. Thus, I suppose HRV may reflex parasympathetic activity but not sympathetic activity.

The effects of sympathetic and parasympathetic nerves are generally antagonistic; in a few cases, however, they can be complementary or cooperative. So, 1) the effects of sympathetic and parasympathetic stimulation on salivary gland secretion are complementary due stress\pain. The secretion of watery saliva is stimulated by parasympathetic nerves, which also stimulate the secretion of other exocrine glands in the digestive tract. Sympathetic nerves stimulate the constriction of blood vessels throughout the digestive tract. The resultant decrease in blood flow to the salivary glands causes the production of a thicker, more viscous saliva. 2)The effects of sympathetic and parasympathetic stimulation on the reproductive and urinary systems are cooperative. There is also cooperation between the two divisions in the micturition (urination) reflex. Although the contraction of the urinary bladder is largely independent of nerve stimulation, it is promoted in part by the action of parasympathetic nerves. This reflex is also enhanced by sympathetic nerve activity, which increases the tone of the bladder muscles. Emotional states that are accompanied by high sympathetic nerve activity (such as extreme fear) may thus result in reflex urination at bladder volumes that are normally too low to trigger this reflex. I do not think that HRV can help in assessing  the coactivation of both sympathetic and parasympathetic systems.