Accurate measurement of gastric emptying is rarely performed in cats, unlike in humans and dogs. This might be partially due to the fact that no routine tool or test is available to accurately assess gastric emptying in a clinical setting or that serial sample collection of blood, intestinal content, or breath is more difficult in cats than in humans and other companion animal species. Hence, data on physiologic feline gastric emptying times are scarce, and techniques used in the past either provide crude estimates of gastric emptying (radiographic assessment of the passage of liquid barium1), are correlated with interdigestive motility rather than physiologic gastric emptying (evaluation of the transit of barium-impregnated polyethylene spheres2–4), or are difficult to use in a routine clinical environment (radioscintigraphy5–7). Test meals used have been of variable composition, making comparison of feline gastric emptying times among studies difficult. Thus, the clinical importance of gastric emptying disorders in cats remains unclear and might be largely underestimated. To our knowledge, there are few case reports regarding delayed gastric emptying in cats that have rare conditions such as pylorospasm,8 hyperplastic gastropathy,9 and dysautonomia.10 Delayed or dysfunctional gastric emptying might be suspected in conjunction with more common conditions like diabetes mellitus, pancreatitis, and inflammatory intestinal, hepatic, or biliary diseases; however, investigations of gastric motility in cats with these disorders have not been performed to date.
For some years, radiolabeled carbon breath tests have been used successfully in people11 and companion animals.12,13 Such breath tests have recently been introduced for use in cats14 as an alternative method for measurement of gastric emptying times because they are noninvasive and do not involve the handling of radioactive isotopes. Breath tests involve the ingestion of a substance labeled with radioactive carbon (the stable isotope 13C), which is absorbed in the small intestine and then rapidly metabolized to 13CO2 and exhaled. Thus, the increase in the 13C:12C ratio in breath samples correlates indirectly to gastric emptying. To our knowledge, breath tests have not been directly compared with gastric radioscintigraphy in cats; therefore, the diagnostic usefulness of such breath tests in this species has not been fully investigated. In humans, breath test results do not correlate well with radioscintigraphic findings,15–17 but in horses18 and dogs,12 data obtained by these 2 methods have good correlation.
The purpose of the study reported here was to directly compare solid-phase gastric emptying times assessed by means of a [13C]-SABT and 99mTc-ACR in healthy cats. The intent was to establish a new method for determination of gastric emptying times in cats, thereby providing a test that might be of clinical value.
Materials and Methods
Cats—Twelve domestic shorthair cats from the research and blood donor colony of the Small Animal Hospital, Justus-Liebig University, Giessen, were used. All cats were castrated males with a median age of 3 years (age range, 2 to 4 years) and a median weight of 5.3 kg (weight range, 4.5 to 5.9 kg). They were deemed healthy on the basis of the absence of clinical signs, absence of abnormal findings detected via physical examination, and unremarkable results of routine hematologic and biochemical analyses. Seven days prior to the start of the study, all cats were treated with fenbendazole (50 mg/kg) for 3 days.
Experimental procedures—Governmental ethical approval was obtained for the study. For each cat, [13C]-SABT and 99mTc-ACR and were performed simultaneously on 2 consecutive days. The test meal provided to each cat at the start of each experiment consisted of commercially available canned cat food,a which was chosen because of its high palatability; 250 MBq of 99mTc and 50 mg of [13C] sodium acetateb were added to each meal. The 99mTc was bound to a commercially available albumin colloidc to avoid absorption. The double-labeled meal was then mixed thoroughly with a household blender to ensure equal distribution of the additives.
After food was withheld for 12 hours, a baseline breath sample was collected from each cat before the test meal was provided. Breath sample collection involved use of an anesthetic face mask that was connected via a 2-way valve to a glass vial.d To obtain a breath sample, each cat was individually placed on an examination table in sternal or sitting position with minimal manual restraint. Thereafter, the test meal was offered to the cat. Immediately after consumption of the entire meal, a baseline scintigraphic image was obtained (0 minutes). For image acquisition, the conscious cat was placed on the collimator of a gamma camerae in sternal position (again with minimal manual restraint) for an acquisition time of 60 seconds. Subsequently, both breath samples and scintigraphic images were obtained 30, 60, 90, 120, 150, 180, 210, 240, 300, 360, 480, and 600 minutes after acquisition of the initial image. At all time points, a breath sample was obtained immediately after the scintigraphic image acquisition was completed, while the cat was still placed on the collimator of the gamma camera. In the periods between data collections, each cat was kept in a kennel holding area that was part of the radiation facilities. Each cat had access to water ad libitum during these periods; however, consumption of water was not assessed or measured.
The 13C:12C ratio in breath samples collected at each time point was determined within 14 days after collection; results of a pilot study had indicated that samples are stable for at least 14 days after collection (data not shown). Breath samples were analyzed in duplicate via gas chromatography with isotope ratio mass spectrometry. Ion currents consistent with the mass of 12C (m/z 44) and 13C (m/z 45) were measured against certified International Atomic Energy Agency reference material. To allow a Craig19 correction for radiolabeled oxygen O 17 (17O), radiolabeled oxygen O 18 (18O; m/z, 46) was also determined. The 13CO2:12CO2 ratio (or deltaover-baseline 13C) was calculated with the integrated software.f The ratio of 13C to 12C was expressed in permille, which reflects the 13C:12C isotope ratio in relation to a primary reference isotope ratio (Pee Dee Belemnite [PDB] standard19). The total area under the curve was calculated over the 600-minute experimental period. Subsequently, quartiles of gastric emptying (25%, 50%, and 75%) were determined.
For analysis of scintigraphic images, the region of interest (stomach) was defined manually for each image on the basis of morphology, and all pixels within this region were counted automatically. Subsequently, the decay-corrected radioactivity counts were plotted against time. Gastric emptying times for different emptying stages (25%, 50%, and 75%) were determined by nonlinear regression analysis (Figure 1) with commercially available software.g The mathematical model was created with regard to the observation that after a lag phase, an approximately linear decrease of the radioactivity occurred (Appendix).
Data and statistical analysis—To assess intraassay (day-to-day) variation for each cat, the coefficient of variation was calculated for each method by means of a 2-way ANOVA with nested random factors. In addition, paired t tests were performed on scintigraphic data obtained on the 2 consecutive days (days 1 and 2) and on breath test data obtained on days 1 and 2 to test for systematic trends between the first and second replication. Because the intra-assay variation was found to be low (< 10%) and the paired t tests revealed no significant changes between day 1 and day 2 for either method (data not shown; all P values > 0.45), further analyses were performed on means of the data from days 1 and 2 (designated as global means).
Nonlinear mathematical model developed to estimate solid-phase gastric emptying times for various stages of emptying in cats via 99mTc-ACR. After the lag phase, decay was approximately linear. C0 = Radioactivity count at 0 minutes. C/2 = Radioactivity count at 0 minutes divided by 2 (half of the initial count). C(t) = Radioactivity count as a function of time. t50% = Time at which gastric emptying was 50%. TCE = Time at which gastric emptying was complete.
Citation: American Journal of Veterinary Research 75, 7; 10.2460/ajvr.75.7.648
Nonlinear mathematical model developed to estimate solid-phase gastric emptying times for various stages of emptying in cats via 99mTc-ACR. After the lag phase, decay was approximately linear. C0 = Radioactivity count at 0 minutes. C/2 = Radioactivity count at 0 minutes divided by 2 (half of the initial count). C(t) = Radioactivity count as a function of time. t50% = Time at which gastric emptying was 50%. TCE = Time at which gastric emptying was complete.
Citation: American Journal of Veterinary Research 75, 7; 10.2460/ajvr.75.7.648
Nonlinear mathematical model developed to estimate solid-phase gastric emptying times for various stages of emptying in cats via 99mTc-ACR. After the lag phase, decay was approximately linear. C0 = Radioactivity count at 0 minutes. C/2 = Radioactivity count at 0 minutes divided by 2 (half of the initial count). C(t) = Radioactivity count as a function of time. t50% = Time at which gastric emptying was 50%. TCE = Time at which gastric emptying was complete.
Citation: American Journal of Veterinary Research 75, 7; 10.2460/ajvr.75.7.648
Gastric emptying in 12 healthy cats assessed via 99mTc-ACR (A) and a [13C]-SABT (B) simultaneously after ingestion of a test meal containing 50 mg of [13C]sodium acetate and 250 MBq of 99mTc-albumin colloid on 2 consecutive days (averaged data). A baseline breath sample was obtained prior to meal ingestion, and a baseline scintigram was obtained immediately after meal ingestion (at 0 minutes). Breath samples and scintigrams were acquired for analysis at 30, 60, 90, 120, 150, 180, 210, 240, 300, 360, 480, and 600 minutes after meal ingestion. The y-axis depicts decay-corrected radioactivity counts and the delta-overbaseline 13C value (13C:12C ratio) in breath samples, respectively.
Citation: American Journal of Veterinary Research 75, 7; 10.2460/ajvr.75.7.648
Gastric emptying in 12 healthy cats assessed via 99mTc-ACR (A) and a [13C]-SABT (B) simultaneously after ingestion of a test meal containing 50 mg of [13C]sodium acetate and 250 MBq of 99mTc-albumin colloid on 2 consecutive days (averaged data). A baseline breath sample was obtained prior to meal ingestion, and a baseline scintigram was obtained immediately after meal ingestion (at 0 minutes). Breath samples and scintigrams were acquired for analysis at 30, 60, 90, 120, 150, 180, 210, 240, 300, 360, 480, and 600 minutes after meal ingestion. The y-axis depicts decay-corrected radioactivity counts and the delta-overbaseline 13C value (13C:12C ratio) in breath samples, respectively.
Citation: American Journal of Veterinary Research 75, 7; 10.2460/ajvr.75.7.648
Gastric emptying in 12 healthy cats assessed via 99mTc-ACR (A) and a [13C]-SABT (B) simultaneously after ingestion of a test meal containing 50 mg of [13C]sodium acetate and 250 MBq of 99mTc-albumin colloid on 2 consecutive days (averaged data). A baseline breath sample was obtained prior to meal ingestion, and a baseline scintigram was obtained immediately after meal ingestion (at 0 minutes). Breath samples and scintigrams were acquired for analysis at 30, 60, 90, 120, 150, 180, 210, 240, 300, 360, 480, and 600 minutes after meal ingestion. The y-axis depicts decay-corrected radioactivity counts and the delta-overbaseline 13C value (13C:12C ratio) in breath samples, respectively.
Citation: American Journal of Veterinary Research 75, 7; 10.2460/ajvr.75.7.648
Mean ± SD gastric emptying times for various stages of emptying (25%, 50%, and 75%) in the 12 healthy cats in Figure 2 assessed via [13C]-SABT (light gray bars) and 99mTc-ACR (dark gray bars).
Citation: American Journal of Veterinary Research 75, 7; 10.2460/ajvr.75.7.648
Mean ± SD gastric emptying times for various stages of emptying (25%, 50%, and 75%) in the 12 healthy cats in Figure 2 assessed via [13C]-SABT (light gray bars) and 99mTc-ACR (dark gray bars).
Citation: American Journal of Veterinary Research 75, 7; 10.2460/ajvr.75.7.648
Mean ± SD gastric emptying times for various stages of emptying (25%, 50%, and 75%) in the 12 healthy cats in Figure 2 assessed via [13C]-SABT (light gray bars) and 99mTc-ACR (dark gray bars).
Citation: American Journal of Veterinary Research 75, 7; 10.2460/ajvr.75.7.648
A 2-way repeated-measures ANOVA incorporating the effects of method and stage of gastric emptying was performed to compare values of [13C]-SABT and 99mTc-ACR for the 3 stages of gastric emptying (25%, 50%, and 75%). Additionally, the Pearson correlation coefficient between the 2 techniques was determined for each emptying stage. For all analyses, a value of P < 0.05 was considered significant.
Results
All cats accepted the test meal voluntarily and in its entirety (food was consumed within 1 to 3 minutes); hence, all measurements could be performed completely. There was no significant difference in time to complete consumption of test meals among cats or between days of performance of the experiments. The pattern of scintigraphic gastric emptying was approximately linear with a negligible lag phase in nearly all cats (Figure 2). Breath test analysis revealed a steady increase in 13CO2 concentration with a maximum value attained at approximately 150 minutes after ingestion of the test meal. The global means (mean values calculated from both days’ measurements) of gastric emptying times determined via the [13C]-SABT and 99mTc-ACR were significantly (P = 0.033) different (Figure 3). There was a significant (P < 0.001) interaction between method and stage of gastric emptying (25%, 50%, or 75%), indicating increasing differences between the means determined by the 2 methods with increasing degree of emptying. For the stages of gastric emptying, the correlation between the 2 methods was good at 25% (r = 0.655; P = 0.021) and weak at 50% (r = 0.588, P = 0.044) and 75% (r = 0.566, P = 0.055).
Discussion
Gastric radioscintigraphy is generally accepted as the gold standard method to assess gastric emptying in many species.20 Consequently, it has been recommended that all new methods should be compared against that technique. For humans, the Society of Nuclear Medicine has defined a standard protocol, and reference ranges derived from large study groups are available.21 This is not the case in veterinary medicine; no standard protocols are recognized, and species-specific reference ranges have not been determined. Nonetheless, radioscintigraphy has been used to assess gastric emptying in various animal species, including dogs, cats, horses, rats, monkeys, and pigs.20 Radioscintigraphy with 99mTc compounds (99mTc bound to pertechnetate,12 diethylene triamine pentacetic acid,22 sulfur colloid,23 tin,24 albumin colloid,20 disofenin,25 mebrofenin,26 or resin beads27) has been used most frequently in animals. Although some authors recommend the use of mebrofenin or disofenin in small animals on the basis of data from efficiency experiments,23 the present study indicated that 99mTc albumin colloid can be used in cats.
In humans, the [13C]-SABT has been used successfully to measure gastric emptying.28 In the present study, breath samples were collected from cats for 10 hours after feeding of a test meal because long periods of assessment have been shown to provide more accurate results.29 Sample collection intervals were short, especially at the beginning of gastric emptying, but they could be prolonged to make the test easier to perform. The use of gas chromatography to measure the 13C:12C ratio in breath samples was ideal because only small volumes of exhaled air could be collected from the cats. However, the fact that gas chromatography might not be readily available outside a research environment might limit clinical use of the breath test. There was little variation in [13C]-SABT results obtained from the cats in the present study between the 2 consecutive days on which experiments were conducted. This minor data variation between experiment days was consistent with findings for some companion animals (eg, horses18) but not for others (eg, dogs12). It is also interesting to note that overall, gastric emptying in cats is much slower than it is in dogs. Gastric half-emptying (50%) was achieved at approximately 4 hours after ingestion of a meal in the cats in the present study, whereas in another study12 involving the same test protocol in dogs, gastric half-emptying was achieved at approximately 2.5 hours after ingestion of a meal. The reasons for the time difference might be purely physiologic or species related. However, the good reproducibility of gastric emptying times with both methods in the present study could also be attributable to the fact that cats seem less affected by the procedure than are dogs, making feline gastric emptying more constant. It is difficult to compare the results of the breath test performed in the present study with data reported in the veterinary medical literature because methods of determining gastric emptying times vary. For example, in a study in cats by Peachey et al,14 peak CO2 production was determined without further calculation of gastric emptying times and the mean time after meal ingestion to peak CO2 production was approximately 60 minutes; in the present study, the mean time after meal ingestion to peak CO2 production was approximately 150 minutes. In the present and previous studies, it was evident that gastric emptying is not complete at 300 minutes after ingestion of a meal in cats and, as the present study findings indicated, CO2 concentration in breath samples starts to decrease between 300 and 600 minutes after meal ingestion.
To our knowledge, this is the first study in which direct and simultaneous comparison of gastric radioscintigraphy and a carbon C13 isotope–based breath test was performed in cats. It is interesting to note that the scintigraphic data indicated no clear lag phase for gastric emptying in most of the cats in the present study, as would be expected with solid-phase gastric emptying. This could be due to the type of food used in the study (the food had to be homogenized with the radioactive labels, and as a result was in a semisolid or paste-like form rather than chunks of food) or may be indicative of a species-specific pattern of gastric emptying. Technical difficulties related to the test meal seem less likely, considering that the same technique has been used in dogs, most of which had a demonstrable lag phase and a sigmoidal pattern of gastric emptying.12 The mean gastric half-emptying times (50%) in the present study were 238 minutes (approx 4 hours) for [13C]-SABT and 276 minutes (approx 4.5 hours) for 99mTc-ACR, which is longer than most published gastric emptying times for cats. Values at all examined time points did not differ significantly between methods. Correlation between methods (as determined by Pearson correlation coefficient) was good at the 25% stage of emptying and weak but acceptable at the 50% and 75% stages of emptying. These findings could be a result of the nature of the 2 methods: one (99mTc-ACR) is direct, whereas the other ([13C]-SABT) is indirect. Evidently, for eventual clinical use, slightly different reference ranges will be needed depending on the technique used. Correlation could also decrease with ongoing gastric emptying, given that the individual variation (SD) of gastric emptying times appeared to increase over time. Nonetheless, the results of the correlation analysis between the 2 methods in cats indicated that the [13C]-SABT can be a valid alternative to 99mTc-ACR, given that it was easy to perform and tolerated well by the cats in the present study. Findings of the present study also indicated that half-emptying times might not be the most appropriate time points to use as the only measure of gastric emptying in cats. Variation in half-emptying times among individual cats was detected and would have to be taken into account when interpreting gastric emptying results. Extrapolation of results of the present study to a clinical situation may be challenging, and further research in this field is necessary before the [13C]-SABT can be used in a wider clinical context to assess gastric emptying of individual cats with disorders that might be associated with delays in gastric emptying.
ABBREVIATIONS
| [13C]-SABT | [13C]Sodium acetate breath test |
| 99mTc-ACR | Technetium Tc 99m albumin colloid radioscintigraphy |
a/d, Hill's Pet Nutrition Inc, Hamburg, Germany.
Solco-Nanocoll, Sorin-Biomedica, Munich, Germany.
Non-evacuated Exetainer, Labco Ltd, High Wycombe, Buckinghamshire, England.
Philips Gamma Diagnost Tomo, Philips Medical Systems, Hamburg, Germany
IonVantage 1.1, GV Instruments Ltd, Wythenshawe, Cheshire, England.
BMDPAR, BMDP Statistical Software, version 8.1, Statistical Solutions, Cork, Ireland.
References
1. Steyn PF, Twedt DC. Gastric-emptying in the normal cat—a radiographic study. J Am Anim Hosp Assoc 1994; 30: 78–80.
2. Chandler ML, Guilford G, Lawoko CR. Radiopaque markers to evaluate gastric emptying and small intestinal transit time in healthy cats. J Vet Intern Med 1997; 11: 361–364.
3. Chandler ML, Guilford WG, Lawoko CR, et al. Gastric emptying and intestinal transit times of radiopaque markers in cats fed a high-fiber diet with and without low-dose intravenous diazepam. Vet Radiol Ultrasound 1999; 40: 3–8.
4. Sparkes AH, Papasouliotis K, Barr FJ, et al. Reference ranges for gastrointestinal transit of barium-impregnated polyethylene spheres in healthy cats. J Small Anim Pract 1997; 38: 340–343.
5. Steyn PF, Twedt D, Toombs W. The scintigraphic evaluation of solid-phase gastric-emptying in normal cats. Vet Radiol Ultrasound 1995; 36: 327–331.
6. Goggin JM, Hoskinson JJ, Butine MD, et al. Scintigraphic assessment of gastric emptying of canned and dry diets in healthy cats. Am J Vet Res 1998; 59: 388–392.
7. Gould RJ, Fioravanti C, Cook PG, et al. A model of gastric-emptying in cats shows solid emptying is promoted by MK-329—a CCK antagonist. J Nucl Med 1990; 31: 1494–1499.
8. Pearson H, Gaskell CJ, Gibbs C, et al. Pyloric and oesophageal dysfunction in the cat. J Small Anim Pract 1974; 15: 487–501.
9. Dennis R, Herrtage ME, Jefferies AR, et al. A case of hyperplastic gastropathy in a cat. J Small Anim Pract 1987; 28: 491–504.
10. Canton DD, Sharp NJH, Aguirre GD. Dysautonomia in a cat. J Am Vet Med Assoc 1988; 192: 1293–1296.
11. Ghoos YF, Maes BD, Geypens BJ, et al. Measurement of gastric-emptying rate of solids by means of a carbon-labeled octanoic-acid breath test. Gastroenterology 1993; 104: 1640–1647.
12. Schmitz S, Failing K, Neiger R. Solid phase gastric emptying times in the dog measured by C-13-sodium-acetate breath test and 99m technetium radioscintigraphy. Tierarztl Prax Ausg K Kleintiere Heimtiere 2010; 38: 211–216.
13. Sasaki N, Aiuchi H, Yamada H. Use of C-13-acetate breath test for assessment of gastric emptying in horses. J Vet Med Sci 2005; 67: 993–997.
14. Peachey SE, Dawson JM, Harper EJ. Gastrointestinal transit times in young and old cats. Comp Biochem Physiol A Mol Integr Physiol 2000; 126: 85–90.
15. Sanaka M, Urita Y, Sugimoto M, et al. Comparison between gastric scintigraphy and the [13C]-acetate breath test with Wagner-Nelson analysis in humans. Clin Exp Pharmacol Physiol 2006; 33: 1239–1243.
16. Punkkinen J, Konkka I, Punkkinen O, et al. Measuring gastric emptying: comparison of 13C-octanoic acid breath test and scintigraphy. Dig Dis Sci 2006; 51: 262–267.
17. Chew CG, Bartholomeusz FD, Bellon M, et al. Simultaneous 13C/14C dual isotope breath test measurement of gastric emptying of solid and liquid in normal subjects and patients: comparison with scintigraphy. Nucl Med Rev Cent East Eur 2003; 6: 29–33.
18. Sutton DGM, Bahr A, Preston T, et al. Validation of the C-13-octanoic acid breath test for measurement of equine gastric emptying rate of solids using radioscintigraphy. Equine Vet J 2003; 35: 27–33.
19. Craig H. Isotopic standards for carbon and oxygen and correction factors for mass-spectrometric analysis of carbon dioxide. Geochim Cosmochim Acta 1957; 245: G19–G28.
20. Wyse CA, McLellan J, Dickie AM, et al. A review of methods for assessment of the rate of gastric emptying in the dog and cat: 1898–2002. J Vet Intern Med 2003; 17: 609–621.
21. Donohoe KJ, Maurer AH, Ziessman HA, et al. Procedure guideline for gastric emptying and motility. Society of Nuclear Medicine. J Nucl Med 1999; 40: 1236–1239.
22. Chaudhuri TK. Use of 99mTc-DTPA for measuring gastric emptying time. J Nucl Med 1974; 15: 391–395.
23. Hoskinson JJ, Goggin JM, Butine MD. Evaluation of solid-phase labels for gastric emptying studies in cats. J Nucl Med 1997; 38: 495–499.
24. Dormehl IC, du Plessis M, Maree M, et al. A comparison of 111In-labelled polymer beads and 99mTc-Sn-colloid as solid food and semi-solid food tracers for scintigraphic gastric emptying studies. Nuklearmedizin 1986; 25: 50–54.
25. Goggin JM, Hoskinson JJ, Butine MD, et al. Scintigraphic assessment of gastric emptying of canned and dry diets in healthy cats. Am J Vet Res 1998; 59: 388–392.
26. Armbrust LJ, Hoskinson JJ, Lora-Michiels M, et al. Gastric emptying in cats using foods varying in fiber content and kibble shapes. Vet Radiol Ultrasound 2003; 44: 339–343.
27. Iwanaga Y, Wen J, Thollander MS, et al. Scintigraphic measurement of regional gastrointestinal transit in the dog. Am J Physiol 1998; 275: G904–G910.
28. Hellmig S, Von Schoning F, Gadow C, et al. Gastric emptying time of fluids and solids in healthy subjects determined by 13C breath tests: influence of age, sex and body mass index. J Gastroenterol Hepatol 2006; 21: 1832–1838.
29. Bluck LJ, Coward WA. Measurement of gastric emptying by the 13C-octanoate breath test—rationalization with scintigraphy. Physiol Meas 2006; 27: 279–289.
Appendix
Equations used to perform nonlinear curve fitting of scintigraphic data to estimate gastric emptying times at various emptying stages (25%, 50%, and 75%) in cats.
Different conditions were used depending on the section of the sigmoid emptying curve. The lag phase was defined as all time points (or x values; t) where no change or decreased radioactivity counts in relation to the initial count at 0 minutes (C0) were observed. The linear decay phase (between the lag phase and the time of complete stomach emptying) was described as a simple linear curve based on the following equation:
where C(t) is the count as a function of time, t is time (x values), b is the slope, and a is the fictitious y-axis intercept. Algebraic conversion of this equation provided the estimated gastric emptying times at the various stages (25%, 50%, and 75%) of emptying (ie, t25%, t50%, and t75%, respectively) as follows:
where min[C0;a] refers to the fact that in every case, the smaller of the 2 values of C0 or a was chosen to define the start of the linear emptying phase. In more detail, that means that in instances when no lag phase was present, C0 = a; however, in instances when a lag phase was present (a > C0), C0 was the starting point of linear decay.
