Final answer:
Sinus arrhythmia involves the autonomic nervous system's regulation of heart rate, primarily via the vagus nerve (CN X), not cranial nerve IX (CN IX), making the statement false.
Step-by-step explanation:
The phenomenon of sinus arrhythmia is indeed related to the autonomic nervous system's influence on the heart, but it is not associated specifically with cranial nerve IX. Instead, it involves the vagus nerve, which is cranial nerve X. The autonomic nervous system regulates the heart's sinus rhythm through a balance of sympathetic and parasympathetic input, originating from the cardiovascular centers in the medulla.
The sympathetic nervous system increases heart rate, while the parasympathetic nervous system, primarily through the vagus nerve, decreases it. Sinus arrhythmia, which often occurs when inhaling and exhaling, reflects normal fluctuations in heart rate due to parasympathetic (vagal) activity and is not typically a cause for concern.
Therefore, the statement that the phenomenon of sinus arrhythmia is due to autonomic nervous fluctuations to the heart associated with CN IX is false.