Yu-Chia Cheng^{1}, Yi-Jui Liu^{2}, Yi-Hsiung Lee^{3,4}, Hing-Chiu Chang^{5}, Hui-Chu Chiu^{6}, Ta-Wei Chiu^{7}, Kang Hsu^{8}, Hsian-He Hsu^{4,9}, and Chun-Jung Juan^{4,9}

The parotid gland function is evaluated by gustatory stimulation using scintigraphy in clinic. Due to the saliva secretion of parotid, it is supposed to measure the water component of parotid gland using PD MRI instead of scintigraphy. Normally the drop magnitude and recover rate of signal-time curve after gustatory stimulation was used to evaluate the function of parotid gland. For more physiology and quantitative parameters of characteristics of signal-time curve, we developed a mathematical model for drainage and refill of a toilet tank to quantify the parotid gland function in this study.

**Results**

1. Gune S, Yilmaz S, Karalezli A, Aktas A (2010) Quantitative and visual evaluation of salivary and thyroid glands in patients with primary Sjogren's syndrome using salivary gland scintigraphy: relationship with clinicopathological features of salivary, lacrimal and thyroid glands. Nucl Med Commun 31:666-672 2. Kogawa EM, Grisi DC, Falcao DP et al (2016) Salivary function impairment in type 2 Diabetes patients associated with concentration and genetic polymorphisms of chromogranin A. Clin Oral Investig 20:2083-2095

3. Giess R, Werner E, Beck M, Reiners C, Toyka KV, Naumann M (2002) Impaired salivary gland function reveals autonomic dysfunction in amyotrophic lateral sclerosis. J Neurol 249:1246-1249

4. Jen YM, Lin YC, Wang YB, Wu DM (2006) Dramatic and prolonged decrease of whole salivary secretion in nasopharyngeal carcinoma patients treated with radiotherapy. Oral Surg Oral Med Oral Pathol Oral Radiol Endod 101:322-327

5. Fallahi B, Beiki D, Abedi SM et al (2013) Does vitamin E protect salivary glands from I-131 radiation damage in patients with thyroid cancer? Nucl Med Commun 34:777-786

6. Ingrand J, Danchot J, Menkes CJ, Delbarre F, Roucayrol JC (1975) [Quantitative functional exploration of the salivary glands. Measurement of salivary elimination of technetium 99]. Nouv Presse Med 4:395-400

7. Murata Y, Yamada I, Umehara I, Okada N, Shibuya H (1998) Diagnostic accuracy of technetium-99m-pertechnetate scintigraphy with lemon juice stimulation to evaluate Warthin's tumor. J Nucl Med 39:43-46 Loutfi I, Nair MK, Ebrahim AK (2003) Salivary gland scintigraphy: the use of semiquantitative analysis for uptake and clearance. J Nucl Med Technol 31:81-85

Fig. 1. Cartoon illustration
of parotid responses to gustatory stimulation. (1A) At resting stage, the
parotid gland is full of water. (1B) During gustatory stimulation, the salivary
output of water overwhelms the arterial input of water, causing immediate
reduction of water in the parotid gland. (1C) After swallowing, the salivary
output of water has stopped, while the arterial input of water persists,
causing gradual refill of water in the parotid gland. The parallel change of
water in a toilet tank is also shown for conceptual comparison.

Fig. 2. Graphic
demonstration of semi-quantitative parotid functional parameters. The time
point of initial drop is indicated by a black arrow. The time point of maximal
drop is indicated by a white arrow. PD: proton density; MDR: maximal drop
ratio; TTP: time to peak; DS: drop slope; RS: recovery slope; RR: recovery
ratio

Fig. 3. Signal ratio time curves of PD expressed
by a bi-exponential curve (solid line) combining an exponential decay curve
(dashed line) and an exponential growth curve (dotted line).

Fig. 4. Simulation of PD ratio time curves as a
function of (A) draining
rate constants ko and (B) refilling rate constant ki.

Fig. 5. The semi-quantitative parametric values
as a function of (A) draining rate constants ko and (B) refilling rate
constant ki.