The coefficients of variables for simultaneous differential equations as adopted in this work. The calculation results are theoretical estimations of the timedependent quantity of iodine in various compartments for a typical body. Additionally, the decay constant for physical halflife of ^{131}
1. Introduction
This chapter quantitatively analyzed the biokinetic models of iodine thyroid and the gastrointestinal tract (GI tract) using MATLAB software. Biokinetic models are widely used to analyze the internally absorbed dose of radiation in patients who have undergone a nuclear medical examination, or to estimate the dose of I131 radionuclide that is absorbed by a critical organ in patients who have undergone radiotherapy (ICRP30, 1978). In the specific biokinetic model, human organs or tissues are grouped into many compartments to perform calculations. The defined compartments vary considerably among models, because each model is developed to elucidate a unique function of the human metabolic system.
The solutions to the timedependent simultaneous differential equations that are associated with both the iodine and the GI tract model, obtained using the MATLAB default programming feature, yield much medical information, because the calculations that are made using these equations provide not only the precise timedependent quantities of the radionuclides in each compartment in the biokinetic model but also a theoretical basis for estimating the dose absorbed by each compartment. The results obtained using both biokinetic models can help a medical physicist adjust the settings of the measuring instrumentation in the radioactive therapy protocol or the radiosensitivity of the dose monitoring to increase the accuracy of detection and reduce the uncertainty in practical measurement.
In this chapter, MATLAB algorithms are utilized to solve the timedependent simultaneous differential equations that are associated with two biokinetic models and to define the correlated uncertainties that are related to the calculation. MATLAB is seldom used in the medical field, because the engineeringbased definition of the MATLAB parameters reduces its ease of use by unfamiliar researchers. Nevertheless, using MATLAB can greatly accelerate analysis in a practical study. Some firm recommendations concerning future studies on similar topics are presented and a brief conclusion is drawn.
2. Iodine thyroid model
2.1. Biokinetic model
The iodine model simulates the effectiveness of healing by patients following the postsurgical administering of ^{131}
According to the ICRP30 report in the biokinetic model of iodine, a typical human body can be divided into five major compartments. They are
stomach,
body fluid,
thyroid,
whole body, and
excretion as shown in Fig. 1.
Equations 14 are the simultaneous differential equations for the timedependent correlation among iodine nuclides in the compartments
The terms q_{i} andλ_{i} are the timedependent quantity of ^{131}I in all compartments and the decay constants between pairs of compartment, respectively (R: physical half life, ST: stomach, BF: body fluid, Th: thyroid, WB: whole body). Accordingly, the quantity of iodine nuclide in the stomach decreases regularly, whereas the quantity change inside the body fluid is complicated because the iodine can be transported from either stomach or whole body into the body fluid and then removed outwardly also from two channels (to thyroid or to excretion directly). The quantity change of iodine nuclides in either thyroid or whole body is comparatively direct since only one channel is defined for inside or outside [Fig. 1]. Since the biological halflives of iodine, as recommended by ICRP30 for the stomach, body fluid, thyroid and whole body, are 0.029d, 0.25d, 80d and 12d, respectively, the corresponding decay constants for each variable can be calculated [Tab. 1]. Additionally, the timedependent quantity of iodine in each compartment is depicted in Fig. 2, and the initial time is the time when the ^{131}I is administered to the patient.
λ  coeff.  Derivation 
λ_{R}  0.0862 
ln2 / 8.0 
λ_{ST}  24 
ln2 / 0.029 
λ_{BF1}  0.832 
0.3xln2 / 0.25 
λ_{BF2}  1.940 
0.7xln2 / 0.25 
λ_{Th}  0.0058 
ln2 / 120 
λ_{WB2}  0.052 
0.9xln2 / 12 
λ_{WB1}  0.0052 
0.1xln2 / 12 
2.2. MATLAB algorithms
Eqs 14 can be reorganized as below and solved by the MATLAB program.
The MATLAB program is depicted as below;
###########################################################
A=[24.086 0 0 0;24 2.859 0 0.052; 0 0.832 0.0922 0; 0 0 0.0058 0.144];
x0 = [1 0 0 0]';
B = [0 0 0 0]';
C = [1 0 0 0];
D = 0;
for i = 1:101,
u(i) = 0;
t(i) = (i1)*0.1;
end;
sys=ss(A,B,C,D);
[y,t,x] = lsim(sys,u,t,x0);
plot(t,x(:,1),'',t,x(:,2),'.',t,x(:,3),'',t,x(:,4),'',t,x(:,2)+x(:,4),':')
semilogx(t,x(:,1),'',t,x(:,2),'.',t,x(:,3),'',t,x(:,4),'',t,x(:,2)+x(:,4),':')
legend('ST','BF','Th','WB','BF+WB')
% save data
n = length(t);
fid = fopen('44chaineq.txt','w'); % Open a file to be written
for i = 1:n,
fprintf(fid,'%20.16f %20.16f %20.16f %20.16f %20.16f %20.16f\n',t(i),x(i,1),x(i,2),x(i,3),x(i,4),x(i,2)+x(i,4)); % Saving data
end
fclose(fid);
save 44chaineq.dat ascii t,x
###########################################################
Figure 2 plots the derived timedependent quantities of iodine in various compartments in the biokinetic model. The solid dots represent either the sum of quantities in the body fluid and the whole body, or the thyroid gland. The practical measurement made regarding body fluid and whole body cannot be separated out, whereas the data concerning the thyroid gland are easily identified data collection.
2.3. Experiment
2.3.1. Characteristics of patients
Five patients (4F/1M) aged 37~46 years underwent one to four consecutive weeks of whole body scanning using a gamma camera following the postsurgical administration of ^{131}I for ablation of the residual thyroid. An iodine clearance measurement was made on all five patients before scanning to suppress interference with the data.
2.3.2. Gamma camera
The gamma camera (SIEMENS ECAM) was located at ChungShan Medical University Hospital (CSMUH). The gamma camera's two NaI 48×33×0.5 cm^{3} plate detectors were positioned 5 cm above and 6 cm below the patient's body during scanning. Each plate was connected to a 2"diameter 59 Photo Multiplier Tube (PMT) to record the data. Ideally, the two detectors captured ~70% of the emitted gamma ray. Each patient scanned was given a 1.11GBq (30 mCi) ^{131}I capsule for thyroid gland remnant ablation. The ^{131}I capsule was carrierfree with a radionuclide purity that exceeded 99.9% and radiochemical purity that exceeded 95.0%. All radio pharmaceutical capsules were fabricated by Syncor Int., Corp. The coefficient of variance (%CV) of the activity of all capsules from a single batch was less than 1.0%, as verified by spot checks (Chen et al., 2003). Therefore, the positionsensitive gamma ray emitted from the ^{131}I that was administered to patient could be analyzed and plotted.
2.3.3. Whole body scanning of patients
Each patient was treated with 1.11 GBq ^{131}I once weekly for four consecutive weeks, to ensure ablation of the residual thyroid gland. This treatment suppressed the rapid absorption of ultra high doses by normal organs. Post treatment ^{131}I was typically administered six weeks after the thyroidectomy operation. However, thyroid medication was discontinued during the sixth week to reduce the complexity of any side effects. Care was taken to ensure that drugs that were administrated one week before scanning contained no iodine or radiographic contrast agent. Table 2 presents the measured data and the scanning schedule for the first subject for the first week. The schedules for other patients were similar, with only minor modifications. The final column in Tab. 2 presents data obtained from the thigh as ROI. This area was used to determine the pure background for the NaI counting system. Additionally, the body fluid and whole body compartments were treated as a single compartment and redefined as "remainder" in the empirical evaluation since
2.4. Data analysis
Data for each patient are analyzed and normalized to provide initial array in MATLAB output format to fit the optimal data for Eqs. 14. Additionally, to distinguish between the results fitted in MATLAB and the practical data from each subject, a value, Agreement (AT), is defined as
where Y_{n}(nor. iten.) and Y_{n}(MATLAB) are the normalized intensity that were practically obtained from each subject in the n_{th} acquisition, and that data computed using MATLAB, respectively. N is defined to be between 11 and 17, corresponding to the different counting schedules of the subjects herein.
An AT value of zero indicates perfect agreement between analytical and empirical results. Generally, an AT value of less than 5.00 can be regarded as indicating excellent consistency between computational and practical data, whereas an AT within the range 10.0015.00 may still offer reliable confidence in the consistency between analytical and empirical results (Pan et al., 2000; 2001). Table 3 shows the calculated data for five subjects over four weeks of whole body scanning. As shown in Tab. 3, the T_{1/2}(thy.) and T_{1/2}(BF) are changed from 80d and 0.25d to 0.66±0.50d and 0.52±0.23d, respectively. Yet, the branching ratio from the body fluid compartment to either the thyroid compartment (I_{thy.}) or the excretion compartment (I_{exc.}) is changed from 30% or; 70%, respectively to 11.4±14.6% or; 88.4±14.6%, respectively. A shorter biological halflife (80d→0.66d) and a smaller branching ratio from body fluid to remnant thyroid gland (30%→11.4%) also reveal the rapid excretion of the iodine nuclides by the metabolic mechanism in thyroidectomy patients.
Figure 3 presents the results computed using MATLAB along with practical measurement for various subjects, to clarify the evaluation of the ^{131}I nuclides of either the thyroid compartment or the remainder. As clearly shown in Fig. 3, the consistency between each calculated curve and practical data for various subjects reveals not only the accuracy of calculation but also the different characteristics of patients’ biokinetic mechanism, reflecting the real status of remnant thyroid glands.
2.5. Discussion
Defining the biological halflife of iodine in the thyroid compartment without considering the effects of other compartments in the biokinetic model remains controversial. For healthy people, the thyroid compartment dominates the biokinetic model of iodine. In contrast, based on the analytical results, for (near) total thyroidectomy patients, both the body fluid and the thyroid dominate the revised biokinetic model. Additionally, the biological halflife of iodine in the thyroid of a healthy person can be evaluated directly using the timedependent curve. The timedependent curve for thyroidectomy patients degrades rapidly because of iodine has a short biological halflife in the remnant thyroid gland. Withholding iodine from the body fluid compartment of thyroidectomy patients rapidly increases the percentage of iodine nuclides detected in subsequent
counting No.  elapsed time(hrs)  whole body  thyroid  thigh 
1  0.05  21504618  355224  101133 
2  0.25  19894586  434947  219306 
3  0.5  22896468  754599  308951 
4  0.75  23417836  834463  298034 
5  1.00  23645836  944563  316862 
6  2.00  21987448  1014885  311113 
7  3.00  18901178  1124704  260065 
8  4.00  18997956  1329043  245960 
9  5.00  19006712  1297005  242498 
10  6.00  16861720  1247396  204844 
11  7.00  16178016  1334864  191212 
12  8.00  14884935  1222750  175766 
13  32.00  7810032  1080369  70999 
14  56.00  3709699  949135  17926 
15  80.00  2100217  673606  7377 
16  104.00  1639266  540182  4627 
17  128.00  1477639  429230  5457 
In a further examination of the theoretical biokinetic model, since 90% of the administered ^{131}I to the whole body (compartment 4) feeds back to the body fluid (compartment 2) and only 30% of the administered ^{131}I in the body fluid flows directly into the thyroid (compartment 3) [Fig. 1], the crosslinks between compartments make obtaining solutions to Eqs. 14 extremely difficult. Just a small change in the biological halflife of iodine in the thyroid compartment significantly affects the outcomes for all compartments in the biokinetic model. Moreover, the effect of the stomach (compartment 1) on all compartments is negligible in this calculation because the biological halflife of iodine in the stomach is a mere 0.029 day (~40min). The scanned gamma camera counts from the stomach yield no useful data two hours after I131 is administered, since almost 90% of all of the iodine nuclides are transferred to other compartments. Therefore, analysis of the calculated ^{131}I nuclides in the biokinetic model remains in either the remainder or the thyroid compartment only (Chen et al., 2007).
Case No.  week  T_{1/2}(thy.) (d)  T_{1/2}(BF)(d)  I_{thy }(%)  I_{exc }(%)  AT_{thy}  AT_{BF} 
ICRP30  80  0.25  30  70  
1  1  1.10  0.65  12.5  87.5  1.74  31.22. 
2  0.50  0.50  5.0  95.0  0.60  12.58  
3  0.50  0.50  5.0  95.0  0.60  12.10  
4  0.50  0.50  5.0  95.0  0.55  6.23  
2  1  1.70  1.20  55.0  45.0  4.34  7.56 
2  1.25  0.80  32.5  67.5  5.24  25.38  
3  1.10  0.55  12.5  87.5  3.21  30.13  
4  0.50  0.30  5.0  95.0  1.20  35.90  
3  1  0.15  0.40  5.0  95.0  0.53  8.93 
2  0.15  0.40  5.0  95.0  0.22  2.07  
3  0.15  0.40  5.0  95.0  0.10  3.64  
4  0.15  0.40  5.0  95.0  0.70  7.56  
4  1  0.25  0.25  5.0  95.0  0.62  27.65 
5  1  1.25  0.50  5.0  95.0  1.74  5.79 
Average  0.66±0.50  0.52±0.23  11.4±14.6  88.4±14.6  1.52±1.54  14.05±11.01 
3. Gastrointestinal tract model
The gastric emptying half time (GET) of solid food in 24 healthy volunteers is evaluated using the gamma camera method. The GET of solids is used to screen for gastric motor disorders and can be determined using many approaches, among which the gamma camera survey is simple and reliable. Additionally, scintigraphic gastric emptying tests are used extensively in both academic research and clinical practice, and are regarded as the goldstandard for evaluating gastric emptying (Minderhoud et al., 2004; Kim et al., 2000). The GET can also be estimated by monitoring the change in the concentration of an ingested tracer in the blood, urine, or breath, since the tracer is rapidly absorbed only after it leaves the stomach. The tracer, the paracetamol absorption approach and the ^{13}Coctanoate breath test (OBT), all support convenient means of evaluating GET. However, the breath test yields only a convolution index of GE, although it requires no gamma camera and can be performed at the bedside (Sanaka et al., 1998; 2006).
The use of a gamma camera to survey the absorption by subjects of Tc99m radionuclidelabeled products satisfies the criteria for the application of the GI tract biokinetic model, because the short physical half life of Tc99m is such that a limited dose is delivered. In this study, the revised GET of solids is determined from several
3.1. Biokinetic model
According to the ICRP30 report, the biokinetic model of the GI tract divides a typical human body into five major compartments, which are
stomach (ST),
small intestine (SI),
upper large intestine (ULI),
lower large intestine (LLI), and
body fluid (BF), as shown in Fig. 4.
Equations 69 are the simultaneous differential equations that specify the timedependent correlation among the quantities of the radioactivated Tc99m nuclides in the compartments.
The terms q_{i} and λ_{i} are defined as the timedependent quantities of radionuclide, Tc99m, and the biological halfemptying constants, respectively, for the compartments. λ_{R} is the physical decay constant of the Tc99m radionuclide.
Since the biological half lives of Tc99m, given by ICRP30, in the stomach, small intestine, upper large intestine and lower large intestine are 0.029d, 0.116d, 0.385d and 0.693d, respectively, the corresponding halfemptying constants can be calculated, and are presented in Fig. 4. Additionally, λ_{b} is the metabolic removal rate and equals [f_{1}×λ_{SI}/(1f_{1})]. This term varies with the chemical compound and is 0.143 for Tc99m nuclides.
λ  Halfemptying constant  Derivation 
λ_{R}  2.77 d^{1}  (ln2 / 6.0058) × 24 
λ_{ST}  24 d^{1}  ln 2 / 0.029 
λ_{SI}  6 d^{1}  ln 2 / 0.116 
λ_{ULI}  1.8 d^{1}  ln 2 / 0.385 
λ_{LLI}  1 d^{1}  ln 2 / 0.693 
λ_{b}  1 d^{1}  0.143×6 / (10.143) 
3.2. MATLAB algorithms
Eqs 69 can be reorganized again as below and solved by the MATLAB program.
The MATLAB program is depicted as below;
###########################################################
A=[26.77 0 0 0;24 9.77 0 0; 0 6 4.57 0; 0 0 1.8 3.77];
x0 = [1 0 0 0]';
B = [0 0 0 0]';
C = [1 0 0 0];
D = 0;
for i = 1:101,
u(i) = 0;
t(i) = (i1)*0.01;
end;
sys=ss(A,B,C,D);
[y,t,x] = lsim(sys,u,t,x0);
plot(t,x(:,1),'',t,x(:,2),'.',t,x(:,3),'',t,x(:,4),'',t,x(:,2)+x(:,3)+x(:,4),':')
semilogx(t,x(:,1),'',t,x(:,2),'.',t,x(:,3),'',t,x(:,4),'',t,x(:,2)+x(:,3)+x(:,4),':')
legend('ST','SI','ULI','LLI','SI+ULI+LLI')
% save data
n = length(t);
fid = fopen('gi44chaineq.txt','w'); % Open a file to be written
for i = 1:n,
fprintf(fid,'%10.8f %20.16f %20.16f %20.16f %20.16f %20.16f\n',t(i),x(i,1),x(i,2),x(i,3),x(i,4),x(i,2)+x(i,3)+x(i,4)); % Saving data
end
fclose(fid);
save gi44chaineq.dat ascii t,x
###########################################################
Figure 5 shows the timedependent amount of Tc99m in each compartment, and the initial time is defined as the time when a Tc99m dose is administered to the volunteer. The results can be calculated and plotted using a program in MATLAB.
3.3. Experiment
3.3.1. Characteristics of volunteers
Twentyfour healthy volunteers (13F/11M) aged 19~75 years underwent six continuous hours of whole body scanning using a gamma camera after they had ingested Tc99m labeled phytate with solid food.
3.3.2. Tc99mlabeled phytate solid food
The test meal comprised solid food and a cup of 150 ml water that contained 5% dextrose. The solid food was two pieces of toast and a twoeggomelet. The two eggs were broken, stirred and mixed with 18.5 MBq (0.5 mCi) Tc99mlabeled phytate. Each omelet was baked in an oven for 20 min at 250 ^{0}C, and then served to a volunteer. Each volunteer had fasted for at least eight hours before eating the meal and finished it in 20 minutes, to avoid interference with the data.
3.3.3. Gamma camera
The gamma camera (SIEMENS ECAM) was located at the Department of Nuclear Medicine, TaiChung Veterans General Hospital (TVGH). The camera's two NaI (48×33×0.5 cm^{3}) plate detectors were positioned 5 cm above and 6 cm below the volunteer's body during scanning. Each plate was connected to a 2"diameter 59 Photo Multiplier Tube (PMT) to record data. The two detectors captured ~70% of the emitted gamma rays.
3.3.4. Whole body scanning of volunteers
Each volunteer underwent his/her first gamma camera scan immediately after finishing the meal. The scan protocol was as follows; supine position, energy peak of 140 keV (window: 20%), LEHS collimator, 128×128 matrix, and scan speed of 30 cm/min. over a distance of 150 cm (~5 min. scan from neck to knee) for 5 min. every half hour. The complete scan took six hours. Thirteen sets of data were recorded for every volunteer for analysis. The regions of interest (ROIs) of the images in the subsequent analysis were
whole body, WB,
stomach, ST, and
small intestine, upper large intestine and lower large intestine, SI+ULI+LLI.
The data that were obtained from SI could not be separated from those obtained from ULI or LLI, whereas the data for ST were easily distinguished during the collection of data. Therefore, the SI, ULI, and LLI data were summed in the data analysis.
3.4. Data analysis
Table 5 shows the results that were obtained for 24 healthy volunteers. The first row includes theoretical recommendations in the ICRP30 report for comparison. The results are grouped into male and female, and each volunteer is indicated. The GET is the effective half life of Tc99m in the stomach. It equals the reciprocal of the sum of the reciprocal of the biological half life and that of the radiological half life (GET^{1}= T_{1/2eff}(ST)^{1}= [T_{1/2}(Tc99m)^{1} + T_{1/2}(ST)^{1}]). The biological half lives in the stomach T_{1/2}(ST) and small intestine T_{1/2}(SI) in
Case No. 
Sex  T_{1/2}(ST) Min. 
T_{1/2}(SI) Min. 
T_{1/2}(ULI) Min. 
T_{1/2}(LLI) Min. 
T_{1/2}(b) Min. 
ATST % 
ATLSI % 
ICRP30  41.8  167.0  554.5  998.0  998.0  
1  F  166.4  199.6  554.5  998.0  1.0E+05  8.4  7.5 
2  F  142.6  199.6  554.5  998.0  1.0E+05  10.5  7.3 
3  F  110.9  166.4  554.5  998.0  1.0E+05  5.9  7.6 
4  F  142.6  199.6  554.5  998.0  1.0E+05  5.9  3.6 
5  F  124.8  199.6  554.5  998.0  1.2E+04  11.3  6.9 
6  F  166.4  199.6  554.5  998.0  1.0E+05  9.8  8.5 
7  F  99.8  332.7  554.5  998.0  1.0E+05  12.7  17.0 
8  F  142.6  249.5  554.5  998.0  1.0E+05  14.5  10.6 
9  F  99.8  249.5  554.5  998.0  1.0E+05  10.9  14.9 
10  F  199.6  166.4  554.5  998.0  1.0E+05  11.9  10.1 
11  F  99.8  166.4  554.5  998.0  1.0E+05  8.2  7.6 
12  F  124.8  166.4  554.5  998.0  1.0E+05  14.2  9.6 
13  F  166.4  199.6  554.5  998.0  1.0E+05  15.8  8.6 
Average (1~13) 
137.4 ±31.3 
207.3 ±46.9 
554.5  998.0  9.3E+04± 2.4E+04 
10.8± 3.1 
9.2 ±3.5 

14  M  83.2  199.6  554.5  998.0  1.0E+05  12.1  13.3 
15  M  99.8  249.5  554.5  998.0  1.0E+05  11.4  16.3 
16  M  99.8  166.4  554.5  998.0  1.0E+05  7.6  8.6 
17  M  99.8  249.5  554.5  998.0  1.0E+05  8.1  15.7 
18  M  62.4  166.4  554.5  998.0  3.3E+04  3.3  6.5 
19  M  142.6  124.8  554.5  998.0  1.0E+05  11.5  6.9 
20  M  76.8  166.4  554.5  998.0  1.0E+05  3.7  5.1 
21  M  45.4  166.4  554.5  998.0  5.0E+04  10.9  9.6 
22  M  62.4  166.4  554.5  998.0  1.0E+05  10.3  9.7 
23  M  90.7  166.4  554.5  998.0  1.0E+05  13.8  13.9 
24  M  52.5  998.1  554.5  998.0  1.0E+05  10.9  14.4 
Average (14~24) 
76.7 ±23.0 
256.3 ±248.9 
554.5  998.0  8.9E+04± 2.4E+04 
9.3 ±3.4 
10.5 ±4.0 
males are 76.7± 23.0 min. and 256.3± 248.9 min. respectively, and in females are 137.4± 31.3 min., 207.3± 46.9 min, respectively. Therefore, the GET and T_{1/2eff}(SI) for males are 63.2±18.9 min. and 149.8±145.1 min. and those for females are 99.5±22.6 min. and 131.6±29.8 min., respectively. The values of both T_{1/2}(ULI) and T_{1/2}(LLI) that were used in the program calculation were those suggested in the ICRP30 report. The calculated T_{1/2}(b) 10,000, is greatly higher that that, 998, recommended by the original ICRP30 report. The increased half life, associated with metabolic removal (around an order of magnitude greater than its suggested value), indicates that only a negligible amount of Tc99m phytate is transported to the body fluid (BF).
Both AT_{ST} and AT_{LSI} reveal consistency between the measured and estimated fitted curves for ST and SI+ULI+LLI [Eq. 5]. The ATs are around 3.6~16.3; the average ATs for males are 9.3± 3.4 and 10.5± 4.0 and those for females are 10.8± 3.1 and 9.2± 3.5 [Tab. 5, last two columns]. Twentysix correlated data are used in the program in MATLAB to find an optimal value of Tc99m quantities for each volunteer (13×2=26, ST and SI+ULI+LLI). Equations 69 must be solved simultaneously and include all four compartments of the GI tract biokinetic model [cf. Fig. 4]. Figure 6 plots the timedependent curves of ST and SI+ULI+LLI for males and females. The inconsistency between the theoretical and empirical values is significant.
3.5. Discussion
Unlike the thyroid biokinetic model, which includes a feedback loop between the body fluid compartment and the whole body compartment, the GI Tract biokinetic model applies exactly the direct chain emptying principle, and assumes that no equilibrium exists between the parent and daughter compartments, because the parent’s (ST) biological half emptying time is shorter than the daughter’s (SI+ULI+LLI) biological half emptying time. The unique integration of parent’s and daughter’s biological half emptying times also reflects the unpredictability of the real GET of the gastrointestinal system. Therefore, a total of 13 groups of data were obtained for each volunteer over six continuous hours of scanning and input to the program in MATLAB to determine the complete correlation between ST and SI+ULI+LLI. Simplifying either the biokinetic model or the calculation may generate errors in the output and conclusion. Very few studies have addressed the timedependent curve for SI+ULI+LLI, because this curve is not a straight line that is associated with a particular emptying constant (slope) [Fig. 6]. Any two or three sets of discrete measurements cannot provide enough data to yield a conclusive result. The optimal fitted timedependent SI+ULI+LLI curve is a polynomial function of fourth or fifth order. Therefore, the data must be measured discretely in five or six trials to draw conclusions with a satisfactory confidence level.
The biological half emptying time of SI dominates the timedependent curve of SI+ULI+LLI, since the SI biological half emptying time, T_{1/2}(SI), fluctuates markedly, whereas the values of both T_{1/2}(ULI) and T_{1/2}(LLI) contribute inconsiderably to solve the simultaneous differential equations in the program in MATLAB [cf. Tab. 5]. Additionally, a close examination of the timedependent SI+ULI+LLI curve of either males or females reveals that quantities of Tc99m radionuclides in the SI compartment for males more rapidly approaches saturation than does that for the females, and so the biological half emptying time is shorter in males [cf. Fig. 6]. However, the analyzed results concerning GETs herein do not support this claim (female: 207.3±46.9 min.; male: 256.3±248.9 min.) because the extent of changes of the SI (daughter compartment) is governed by the chain emptying rate from the ST (parent compartment), and the T_{1/2}(ST) for males (76.7±23.0 min.) is shorter than that for females (137.4±31.3 min.). Restated, the correct interpretation of the results must be based on the GI Tract biokinetic model and satisfy the simultaneous differential equations, Eqs. 69.
4. Recommendation and conclusion
Both the effective halflife of iodine in either the thyroid or the body fluid compartment of (near) total thyroidectomy patients and the gastric emptying half time of solid food in 24 healthy volunteers (11M/13F) were determined using the
MATLAB is rarely used in the medical field because of its complicated demanding programming. However, its powerful ability to define timedependent simultaneous differential equations and to derive optimal numerical solutions can accelerate correlative analyses in most practical studies. Notably, only an appropriate definition at the beginning of study can ensure a reliable outcome that is consistent with practical measurements. The application of a simplistic or excessively direct hypothesis about any radiological topic can yield very erroneous results.
4.1. Iodine thyroid model
The revised values of T_{eff} of iodine in the thyroid compartment were initially obtained from computations made for each subject using the iodine biokinetic model and averaged over all five subjects. The T_{eff} of iodine in the thyroid compartment was revised from the original 7.3d to 0.61d, while that of iodine in the body fluid compartment was increased from 0.24d to 0.49d. The I_{thy.} and I_{exc.} were revised from the original 30% and 70% to 11.4% and 88.4%, respectively following
4.2. Gastrointestinal tract model
The results obtained using the program in MATLAB were based on four timedependent simultaneous differential equations that were derived to be consistent with the measured gamma ray counts in different compartments in the GI Tract biokinetic model. The GET and T_{1/2eff}(SI) for males thus obtained were 63.2±18.9 min. and 149.8±145.1 min. and those for females were 99.5±22.6 min. and 131.6±29.8 min. The calculated T_{1/2}(b), 10,000 was greatly higher that that, 998, recommended by the original ICRP30 report. The fact that the half life associated with metabolic removal, T_{1/2}(b), was around ten times the original value implied that a negligible amount of Tc99m phytate was transported to the body fluid.
Acknowledgments
The authors would like to thank the National Science Council of the Republic of China for financially supporting this research under Contract No. NSC~932213E166004. Ted Knoy is appreciated for his editorial assistance.
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