Thyroid hormone production rates in rat liver and intestine in vivo: a novel graph theory and experimental solution

Thuvan T. Nguyen, Koen A. Mol, and Joseph J. DiStefano, III

Biocybernetics Laboratory, Departments of Computer Science and Medicine, University of California Los Angeles, Los Angeles, California 90095-1596

Submitted 31 May 2002 ; accepted in final form 10 March 2003


    ABSTRACT
 TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
We develop a novel method for finding sufficient experimental conditions for discriminating and quantifying individual biomolecule production sources in distributed, inhomogeneous multisource systems in vivo, and we apply it experimentally to a complex, unsolved problem in endocrinology. The majority of hormonal triiodothyronine (T3) is produced from prohormone thyroxine (T4) in numerous nonthyroidal organs and, with one exception, the T3 production rate has not been fully resolved in any single extrathyroidal organ of any species. Using a readily generalized graphic method called cut-set analysis, we show here that measured steady-state responses in several organs to three independent tracer infusions, two into blood and one directly into the organ(s) of interest, are sufficient to resolve this problem for organs fully accessible to direct infusion in vivo. We evaluated local T3 production in rat liver and intestine, which also required T3 bile flux measurements, and we found that liver produces ~31% and whole intestine ~6% of whole body T3 from T4. With thyroidal production included, liver contributes ~15% and intestine ~3% of whole rat T3 production. This new methodology is broadly applicable, especially to biosystems that include molecular interconversions at multiple sites.

multisource triiodothyronine production; cut-set analysis; local organ hormone production rates; thyroid hormone interconversion; intraduodenal-intraileal infusion; bile hormone flux; steady-state kinetics; inhomogeneous multisource biosystems


BESIDES THE NUMEROUS MOLECULAR COMPONENTS common to all cells, many less ubiquitous endogenous substances are produced at multiple and often widely distributed anatomic sites. Many are products of local interconversion processes, thyroid and steroidal hormones, lipoproteins, and D vitamins, for example. For primarily technical reasons, quantification of these distributed sources at individual production sites in vivo remains a very difficult problem, with no general solution yet available. Thyroid hormone (TH), for example, is produced in virtually all mammalian organs, and data-sufficient experimental designs and results on its rate of production in a single organ have been reported only for developing rat brain (46) and for human (38), mammalian (22), fasting trout (44), and adult rat (18) thyroid glands.

It is well established that thyroxine (T4) is the main secretory product of the thyroid gland and that triiodothyronine (T3), the main metabolically active TH, is also secreted by the gland, at least in mammals. However, a substantial fraction of whole body T3, but not T4, is produced extrathyroidally and enzymatically from exchangeable T4 in tissues. Notably, the T3-producing (activating) enzymes, the iodothyronine 5'-deiodinases called D1 and D2, are distributed quite differently among different tissues (47). Indeed, from a regulation viewpoint, intracellular T3 production appears to be under local control in many organs, e.g., in rat brain and others containing primarily D2 (19, 32), as well as via hypothalamo-pituitary-thyroid feedback "axis" control (23). Quantification of local T3 production takes on its primary import in this local regulation context, a problem whose solution has thus far eluded all. For the liver, estimates reported from in vivo kinetic studies vary from substantial extrathyroidal T3 produced by liver (3, 51) to nearly none at all (17).

Both T3 and T4 are exchangeable between blood and cells; thus the T3 typically found in any tissue has many sources, indistinguishable without appropriate experimental intervention, problems shared by all distributed-source biomolecules. For practical purposes, the T3 typically found in the cell has been classified by thyroidologists as having two sources. The first is that provided indirectly via circulating T3 of unknown origin, via capillary uptake, lumped into one and commonly called "plasma-derived T3." The second is the unique T3 produced enzymatically from T4 locally, via D1 or D2, called "local T3." The source identification problems in this field have thus been simplified to that of distinguishing and quantifying the contributions of each of these two sources in a given cell type or organ, most notably in Refs. 45 and 4951, where local T3 derived from local T4 was designated "LcT3(T4)," and this pool size parameter was estimated in as many as 34 different tissues by use of a dual-isotope T3/T4 kinetic experiment design. Others have used the same approach, e.g., Ref. 43. As we will show, the steady-state pool size estimates provided by the dual-isotope design do not reflect local production rates per se, because this design does not fully distinguish locally derived tracer T3 from that produced in any or all other organs and then transported there via blood, at least not without additional independent data. Although we have shown this indirectly in previous work (9, 10, 2022), this lack of complete information from dual-tracer kinetics was noted explicitly earlier, in Ref. 46, where dual-tracer data were supplemented by additional tracer kinetic study data eliciting the fractional rate of removal of T3 from brain tissues. This additional independent data, when combined and analyzed together with the dual-tracer kinetic results, permitted computation of T3 production rates in developing rat brain (46).

In the present studies, we use graph theory and cut-set analysis to show that at least a triple-tracer approach is needed. We found that measured steady-state responses in several organs to three independent tracer infusions of T3 and/or T4, two into blood and one directly into the organ of interest, are together sufficient to resolve this local conversion rate problem for organs fully accessible to direct infusion. Enterohepatic system (EHS) organs, although they fulfill this requirement, present an unusual experimental challenge because of their special interconnectivity. We apply these new experimental design models and evaluate local T3 production rates in the EHS organs, liver and intestine, separately and together. The separation was achieved by reapplying cut-set analysis and using an additional measurement, the steady-state T3 bile flux.

This new graph theory-based approach is generalizable and readily applicable to critical design of experiments for quantifying distributed sources in many other complex, inhomogeneous biosystems in vivo. These include other interconverting biomolecules, such as steroidal androgens and estrogens, vitamins and lipoproteins, and possibly even more ubiquitously distributed molecular pathways.


    METHODS
 TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
New Experimental Design Models Via Cut-Set Analysis

We take advantage of the special physioanatomic interconnections and exchanges among liver, intestine, and blood, and we use the two TH steady-state pool model structures in Figs. 1 and 2 to find solutions for local T3 production in both liver and intestine. Both structures and solutions were obtained by extending several new theoretical experimental design results in cut-set analysis of compartmental (and nonhomogeneous) pool models (2022). We present the models and a summary of new results here. Detailed derivations and an explanation of the cut-set analysis are given in the APPENDIX, and our nomenclature is summarized in Table 1.



View larger version (22K):
[in this window]
[in a new window]
 
Fig. 1. Eight-pool model explicitly representing conversion of thyroxine (T4) to iodothyronine (T3) in intestine and liver separately. The kij values are rate constants (time-1 units).

 


View larger version (19K):
[in this window]
[in a new window]
 
Fig. 2. Six-pool model explicitly representing T4-to-T3 conversion in enterohepatic organ system (EHS), i.e., liver+intestine together. Summed rate constants k21+k31 and k65+k75 correspond to EHS = liver + intestinal thyroid hormone (TH) influx from blood, as in Fig. 1, but EHS efflux arrows kx and ky satisfy mass-balance equations (kx+ky)Q3EHS = (k56 + k06) Q3LIV + k07 Q3INT, where the Q values are the corresponding pool masses.

 

View this table:
[in this window]
[in a new window]
 
Table 1. Special nomenclature

 

In Fig. 1, enterohepatic T4-> T3 conversion is separated into liver and intestinal conversions, in separate organ pools. In Fig. 2, it is depicted in combined liver and intestinal EHS pools. Figure 1 has eight and Fig. 2 has six measurable T4 and T3 pools, with vascular or biliary pathways among them and sinks within them. These pools represent steady-state nonhomogeneous hormone pool sizes (labeled or unlabeled mass units) in blood (BLD), residual carcass (RESTO), and either the liver (LIV) and intestine (INT = tissue + contents) separately, or combined in the EHS, measured in steady state. The several Q4ORG and Q3ORG values, shown as measurements from each pool (dashed lines), represent the respective T4 and T3 measurable masses in these same organs, i.e., ORG {equiv} EHS, LIV, or INT, or measurements in BLD or in RESTO (in ng or cpm). We remark that ORG can be any other organ that is fully accessible and directly infusible, e.g., brain or kidney, which renders the method and Fig. 2 more generally applicable. The kij parameters (h-1) represent fractional rates of transfer of T4 or T3 between pools, by arterial, venous, or biliary pathways and within or from pools by degradation or excretion. Numbering of the pools in Fig. 2 is consistent with corresponding separate or combined pools in Fig. 1, and relationships among kij in the two figures have been noted in Fig. 2. Note that these models incorporate all production, metabolism, and other elimination pathways separately and distinctly. Thus the fractional T3 production rates, shown by the bolder arrows k4-3EHS, k4-3LIV, and k4-3INT, are the distinct measures only of these T4-to-T3 conversions. They are not encumbered by, nor do they include, alternate or subsequent metabolism pathways. We show in the APPENDIX that we can solve for these three k values by superimposing three tracer-input infusions in Fig. 1, as shown in Fig. 3.



View larger version (28K):
[in this window]
[in a new window]
 
Fig. 3. Experiment design models for T3 production in the EHS, with cut-sets A1, B1, and C1 surrounding the T3 EHS pools, and in intestine with cut-sets A2, B2, and C2 enclosing only the intestinal T3 pool (see APPENDIX).

 

In Fig. 3, tracer [125I]T4 (T* 4) in experiment A (Expt A), and [131I]T3 (T**3)in experiment B (Expt B), are infused into blood simultaneously, at rates IR4BLD A and IR3BLD B (group 1). The additional experiment C (Expt C) requires a direct infusion of tracer T3 into the intestine, for practical purposes [125I]T3 in a separate group of rats (group 2). Expt C is done with two separate pumps, each filled with [125I]T3 (T*3), one directed intraluminally into the duodenum (IR3duodenum Cint), the other intraluminally into the distal ileum (IR3ileumCint), as noted earlier. This is to simulate approximately the natural influx of endogenous T3 into intestine from bile and from blood (14).

The primary measurements include the tracer masses of T3 and T4 in all organs depicted in Fig. 3, i.e., the Q3ORGA,B,Cint and Q4ORGA (in cpm), IR3INTCint = IR3duodenumCint + IR3ileumCint (in cpm/h), and plasma specific activities (SA). Mass fluxes are obtained as products of k and Q values, with tracer converted to endogenous masses by dividing by SA. As shown in the APPENDIX, the first cut-set analysis of Fig. 3 yields the conversion rate of T4 to T3 in the EHS

(1)
where SA4plasmaA is the measured specific activity in plasma of [125I]T4 in Expt A.

The second cut-set analysis in the APPENDIX yields the result for whole intestine. In this case, the solution also requires direct measurement of the T3 bile flux, in Expt C only, as shown in Fig. 3, where . Intestinal mass-flux conversion of T4 to T3 is

(2)
The percentage of whole body T4 converted to T3 (CR4-3TOTAL) attributed to EHS is thus calculated as

(3)
where TOTAL = liver + intestine + blood + residual carcass, and

(4)
is the fraction of T4 production (secretion) converted to T3 (34, 35). Similarly, the percentage of whole body T4 converted to T3 attributed to intestine is

(5)
Finally, T4 converted to T3 in liver is computed as the difference between EHS and intestinal conversion. From Eqs. 1 and 2:CR4-3LIVER = CR4-3EHS - CR4-3INT (ng/h). From Eqs. 3 and 5: %CR4-3LIVER = %CR4-3EHS - %CR4-3INT. Complete derivations of the equations are given in the APPENDIX.

Animal Experiments

Animals were prepared and cared for, and outer ring-labeled 3,5,3'-[131I]T3 (T**3, ~3.7 mCi/µg) and [125I]T4 (T*4, ~3 mCi/µg) were synthesized from 3,5-T2 and 3,5,3'-T3, respectively, and purified on HPLC, all as described in Ref. 34. Tracer 99mTc was obtained from the UCLA Department of Nuclear Medicine and was used to label rat donor red blood cells with the Ultratag 99mTc-RBC Labeling Kit (Malinckrodt, St. Louis, MO). {beta}-Glucuronidase (Escherichia coli type VII), aryl-sulfatase (type V), and other reagents were purchased from Sigma; Alzet Osmotic Minipumps (model 2001) were purchased from Alza (Palo Alto, CA). HPLC analyses were done using a gradient system (LKB/Pharmacia), as in Ref. 34, with mobile phase 20:80–40:60 acetonitrile-H2O (0.1% phosphoric acid) for analytic samples and 50:50 MeOH-H2O (0.1% phosphoric acid) isocratic mobile phase for tracer purification. These were run at 1 ml/min, all on a C8 reverse-phase 5-µm ChromPack analytic column.

Pump preparation, study groups, and implantation. Purified tracer infusates [125I]T4 (T*4) and [131I]T3 (T**3) were prepared and tested as in Ref. 34. Alzet pumps were filled with the labeled T4 or T3 and implanted subcutaneously for 7 days, also as in Ref. 34, in two rat groups. In group 1 (n = 8), [125I]T4 and [131I]T3 were infused subcutaneously and simultaneously from separate pumps. In group 2 (n = 5), [125I]T3 in two pumps was infused simultaneously into the duodenum and the distal ileum of the intestine by use of two PE-60 catheters placed in a hole in the duodenum and one in the distal ileum. The holes were sealed with animal glue, and the tubing was sutured to the intestinal wall, as in Ref. 15. To prevent catheter clogging, tip openings were heated and stretched to reduce tubing diameter, thereby increasing efflux velocity, and several pinholes were made near the tip to assure continuous flow (15). The tubing was filled with [125I]T3 tracer and attached to two T*3 pumps implanted subcutaneously between the shoulders by running it under the skin. On day 0, 0.5 ml of blood was drawn from the vena cava for hematocrit and endogenous plasma T3 and T4 measurements. Rats were housed in individual metabolic cages for the duration of the study.

Day 7 operations. Both groups were treated as in Refs. 13, 34, and 35, with one exception. Labeled 99mTc-RBC was injected intravenously 5 min before termination to correct for hormone trapped in blood in tissues. Blood was collected by cardiac puncture to provide 99mTc concentrations, final hematocrits, sera for radioimmunoassays, steady-state concentrations of total 125I or 131I in plasma, and T*4 or T*3 or T**3 plasma concentrations and their metabolites after chromatography. Intestine and liver were collected and rinsed in ice water. Residual carcass and liver, and rinsed intestinal tissue after separation from contents (13, 35), were quickly frozen in liquid N2 and processed as described below. Small and large intestinal contents were premixed in a single vessel and left for 2 h at room temperature. This assured nearly complete hydrolysis of small intestine conjugates by large intestinal bacteria, with minimal deiodination of tracer, as measured in chromatography and demonstrated earlier in Refs. 13 and 35. In group 2 rats, the common bile duct was also cannulated with PE-10 tubing, and bile was collected for 1 h before termination, weighed, and counted for total 125I.

Homogenization, extraction, and chromatography. Individual organ and residual carcass samples were pulverized and homogenized in a threefold dilution of ice-cold extractant, as in Ref. 34. Premixed intestinal content samples were combined with frozen, crushed intestinal tissue samples and homogenized together. Up to six ~1-g aliquots of each tissue homogenate were weighed and counted, and total organ 99mTc, 125I, and 131I radioactivity (QmORG* or **) was calculated as the measured 99mTc, 125I, and 131I concentrations (CmORG* or **) times the organ weight (MORG), as in Refs. 34 and 35. Extracts, including untreated and hydrolyzed bile (see Bile hydrolysis), were chromatographed on Sephadex G25 and by HPLC (34, 35).

Blood and tissue T3 and T4. Total blood and tissue T**3 and T*4 were measured as in Refs. 34 and 35. Briefly, labeled fractions of T3 and T4 in tissues on day 7 (f3 or f4), multiplied by the concentration of 125I and 131I activity in the tissue sample, provided the concentrations of T*4, T*3, or T**3 in that sample. The latter multiplied by organ weight (MORG) provided the total T*4, T*3, or T**3 in that organ, including activity in residual blood trapped in the organ. Total tissue T*4 and T**3 pool sizes (Q4or3ORG* or **) were corrected for residual trapped blood radioactivity in dissected tissues and the residual carcass (35). Plasma samples were radioimmunoassayed in triplicate for unlabeled T3 and T4 concentrations, as in Ref. 34.

Bile hydrolysis. We used a minor modification of the method described in Ref. 13. Six hundred microliters of bile were added to 500 µlof {beta}-glucuronidase (10 units/µl bile) and 500 µl of aryl-sulfatase (11 units/µl bile) in 0.2 M sodium acetate, pH 5.0 buffer. Samples were incubated for 4 h at 37°C and stopped by freezing on dry ice for 2 h. Completeness of hydrolysis was verified by comparing total T**3 recovered in treated and untreated bile samples.


    RESULTS
 TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
On day 7, neither hematocrits nor plasma hormone concentrations were significantly different in the two rat groups. Hematocrits were 0.48 ± 0.012 (SD) for group 1 (n = 8) rats and 0.47 ± 0.061 for group 2 (n = 5) rats [not significant (NS)]. Endogenous plasma hormone concentrations for T4 were 32.9 ± 3.47 ng/ml in group 1 and 39.4 ± 7.09 ng/ml in group 2 (NS), and for T3, 0.69 ± 0.019 ng/ml in group 1 and 0.68 ± 0.016 ng/ml in group 2 (NS).

Steady-State T3 Production Rates from T4 in Liver, Intestine, and Whole Body

Table 2 provides mass fluxes, fractional rates of conversion, and relative values based on our measurement of the percentage of whole body T4 converted to T3, 23.7 ± 1.7% (SE).


View this table:
[in this window]
[in a new window]
 
Table 2. T3 production rates from T4 in liver, intestine, and whole body

 

Bile Flux of T3 and Steady-State Kinetic Parameters and Distribution Pools of T3 and T4

The steady-state biliary influx of total T3 into the intestine was 2.37 ± 0.201 (SE) ng·h-1·100 g body wt-1 (fractional influx rate = 0.265 ± 0.0098 h-1). T3 and T4 kinetic parameters are given in Table 3. Organ tracer pool size data for Expts A, B, and C, normalized by the different T4 or T3 tracer infusion rates in each rat studied, are given with their variabilities in Table 4. Finally, absolute and relative organ pool sizes and concentrations of endogenous T3 and T4 are given in Table 5, based on organ and plasma specific activity measurements. In steady state, blood contained very little T3 (~3.5%), but 27% of the T4; liver had only 6–9% of total body T3 or T4; and intestines contained about as much T3 as residual carcass and somewhat less T4.


View this table:
[in this window]
[in a new window]
 
Table 3. T3 and T4 kinetic parameters

 

View this table:
[in this window]
[in a new window]
 
Table 4. Normalized organ tracer pool sizes for Expt A, Expt B, and Expt C rat groups

 

View this table:
[in this window]
[in a new window]
 
Table 5. Absolute and relative organ pool sizes and concentrations of endogenous T3 and T4

 


    DISCUSSION
 TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
General Considerations

Discriminating among distributed sources in biosystems is difficult, and the literature on distributed source localization is sparse. Quantification is even more difficult, because measurements are typically, of necessity, indirect. The problems are invariably methodological and depend on the measured signal types and experimental design models used. In biomagnetic and bioelectric systems, including imaging modalities like MRI and computed tomography, pattern recognition, signal processing, and localization algorithms have been applied successfully to reconstruct equivalent source patterns (52). Problems are exacerbated when only tracer signals are available. For example, with tracer imaging processes, like functional positron emission tomography, the imaging mechanism does not distinguish between precursor and product of the tracer. Even blood-borne data, when collected from biosystems with more than one endogenous source, typically can provide only indirect, minimum source rate estimates, unless all sources enter blood directly. Otherwise, a more complex experiment involving multiple tracers is required (6, 37).

The multisource quantification problem for thyroid hormone shares some of the structural complexities of other biosystems with unidirectional precursor-product mechanisms and has been addressed using various methods and models, for example, in pharmacokinetics Refs. 4 and 41 and in metabolism studies Refs. 23 and 28. Several studies by our own group (12, 2022) and others (26, 31, 38, 39) have also addressed this problem for thyroid hormone, utilizing unidirectionally linked submodels of iodothyronine distribution and metabolism to establish T3 or reverse-T3 (rT3) production from T4 in lumped slow- and lumped fast-exchanging tissue groups. The different approaches to quantifying or distinguishing the multiple sources share the same difficulty: information is limited by the number and kinds of probes available for obtaining independent data about individual or collective sources, with more such probes needed for more complex biosystems. On the basis of our results, we conjecture that the number of such probes needed is roughly proportional to the number of sources to be quantified.

Local T3 Production

Consider quantifying the rate at which T3 is produced in an organ of interest, or the local T3 contribution relative to that in other organs in vivo. In this open and exchanging system, the problem is that T3 (or tracer T*3) derived from T4 (or tracer T*4) and found in that organ in steady state could have been produced either in that organ or transferred from other organs. As noted above, the key to resolving the ambiguities is multiple tracer probes and measurements that provide sufficient independent information. We have shown earlier that two tracers, when the conventional dual-isotopic T**3/T*4 injection or infusion design is used, do not provide enough data for local source quantification, not even for collective tissue groupings (9, 10, 2022). Two tracers do, however, provide ranges for "slow" and "fast" tissue groupings (8, 12) and for the thyroidal T3 secretion rate in mammals when multicompartmental analysis of sufficient tracer kinetic data is used (2022, 38, 44). In the current work, we have established that direct infusion of tracer T3 into a T3-producing organ, a third probe in addition to the conventional dual T3/T4 tracer infusion, plus appropriate measurements of the three different tracer responses in blood and tissues (and bile, when liver or intestinal T3 production is of interest), is a sufficient condition for quantifying that organ T3 source.

This is not the only additional probe capable (in principle) of providing the needed additional information, along with the dual T3/T4 blood infusion study; indeed, there are undoubtedly other possibilities, e.g., T4 instead of T3 infusion in the organ of interest, or independent measurement of T3 degradation rates in that organ (46). However, as a corollary, we have shown again that the dual-tracer infusion study data alone do not provide enough information for source rate quantification, in particular the independent information needed to isolate and quantify the local source. The key is Eq. A3 in the APPENDIX, which has one unknown on the right-hand side, k65+k75, the fractional transfer rate of T3 from blood to EHS (via hepatic and mesenteric arterial pathways). This is in addition to the unknown of interest, the fractional T4-to-T3 conversion rate in the EHS, k4-3EHS, on the left-hand side of Eq. A3. Thus there are two unknowns, with only one equation to resolve them, and k65+k75 clearly cannot be established from Expt A and Expt B, the dual-tracer study, on the basis of analysis of Fig. 3 (with notation defined in Fig. 1) developed in the first several lines of the APPENDIX and Eqs. A1 and A2.

Early estimates of the origins of the T3 found in liver were based on T3 receptor kinetic studies. Theoretical analyses of tracer T3 kinetics across plasma, cytoplasm, and nuclear compartments indicated that maximum nuclear T3 occupancy occurs when specific activities of nuclear T3 and plasma T3 are equal, suggesting that nuclear T3 in liver depends primarily on the plasma T3 concentration (36, 45). The contribution of intracellular (local) T4 to T3 conversion to nuclear (not whole cell) T3 was reported to be ~30% relative to plasma-derived T3 also found in the liver nucleus (45). However, nuclear T3 represents <10% of intracellular T3 in rat liver (36), so it is difficult to glean the relative contributions for the whole cell, an important factor given that D1 mono-deiodination occurs in the plasma membrane (40, 48) and D2 in the endoplasmic reticulum (33). In any case, these values represent relative steady-state pool sizes, not production rates.

In situ liver perfusion studies, in contrast, address the production rate question more directly and are capable in principle of providing data on actual rates of local T3 production from T4 in liver, as well as effects of experimental interventions on this T3 source. Also, this approach obviates many of the problems associated with the far more numerous in vitro liver homogenate studies, which do not retain the metabolic control systems associated with intact cellular and organ structure. T3 production was shown to be a direct function of liver size, T4 uptake, and 5'D activity in one liver perfusate preparation, indicating that this organ has a large capacity for T4 uptake and T3 production from T4 via 5'D (30). Unfortunately, the nonphysiological perfusates used in these studies did not provide realistic estimates of the in vivo contribution of liver to T3 production. In two other perfused rat liver studies, local T4 conversion to T3 was estimated as 10% (29) and 4% (25), disparate values that, again, probably can be attributed to (intentional) nonphysiological perfusates.

With use of the dual-isotope steady-state approach, local T3 produced from T4, denoted LcT3(T4), was estimated in 34 rat tissues (49). To establish relative measures, this group defined %LcT3(T4) as the percent contribution of the locally derived T3 from local T4 relative to the total T3 resident in a given tissue, the remainder being the plasma-derived T3 pool. At face value, these data suggest that both liver and intestine contribute significantly to the total circulating T3 pool: %LcT3(T4) was ~40% for liver and ~29% for all intestinal tissues combined (43, 4951). It is important to note, however, that these important data represent pool size measures, not production rates, i.e., these estimates are not the same as, nor are they proportional to, local conversion rates, or even local conversion rates relative to those in other tissues.

Normal human liver appeared to produce no T3 of its own, on the basis of interpretations of kinetic studies using simultaneously intravenously injected [125I]T4, -T3, -rT3, and 131I in normal human volunteers, and Eng et al. (17) remarked that slowly equilibrating tissue sites are thus primarily responsible for peripheral T4-to-T3 conversion and regulation of circulating T3 levels in humans. The literature supports the significance of slow pools, like muscle, in overall T3 production (7, 12, 42), but there is also reasonable evidence that liver is an important site of T3 production in humans (27, 38) and in the rat, as we have shown here by specific quantification.

Liver and Intestinal T3 Production vs. Thyroidal Secretion

We estimate T3 secretion (SR3) from our data as 50% of total body T3 production (PR3), as follows. PR3 = SR3 + CR3-4 > PR3min = PAR3 (9), where CR3-4 is the measured total rate of production of T3 from T4, 6.2 ng·h-1·100 g body wt-1, and PAR3, 12.4 ng/h, is the measured plasma appearance rate (Table 2). This yields a lower bound on SR3, with SR3min = 12.4 - 6.2 = 6.2 ng/h. Then %SR3 is estimated as 100 SR3min/PR3min = 100 x 6.2/12.4 = 50%. No upper limit on SR3 is available from our data, but this ratio of minima is likely to be a reasonable best estimate. It is about the same as two reported estimates, ~50% in Ref. 5, and 50% calculated from the data in Ref. 18, the latter obtained by achieving complete tissue euthyroidism in T3+T4-replaced female adult rats, the T3 component being 6.25 ng/h, i.e., 100 x 6.25/(6.25+6.2) = 50%. It is also comparable to the 43% computable from whole body study data for PAR3 (=SR3min + CR3-4) reported in Table 1 of Ref. 43. Thus, from our data, liver T3 production is estimated as 15% and intestinal T3 production as 3% of total body T3 production. This leaves 32% to be accounted for in other organs.

Plasma-Derived T3 and the Elusive Liver

It is of interest to compare the liver T3 production rate from local T4, 2.18 ng·h-1·100 g body wt-1, with other computed or computable T3 mass influxes and effluxes in liver. The influx of T3 from peripheral plasma, T3 uptake via the hepatic artery, is ≥119 ng/h, with use of the values of liver fractional uptake rate (kuptake = 40/h) and plasma T3 pool size (3 ng) we measured (14, 35). We more recently obtained a more precise estimate of kuptake for liver, 46.2/h, using the same database, plus additional early kinetic data: another 6 rats at t = 1.5 min, thereby yielding a T3 arterial influx of 139 ng/h. Thus plasma-derived T3 is ≥64 (=139/2.18) times greater than locally derived T3 from T4. Inclusion of the unmeasured influx of T3 from portal vein would render plasma-derived T3 about two orders of magnitude greater than locally derived T3 from T4.

Liver T3 efflux/elimination occurs along the hepatic vein and via the biliary and local hepatic degradative pathways. We measured the T3 biliary efflux directly, as 2.37 ng/h. The venous efflux also has been roughly estimated from our same transient kinetic database (14) and is of the same order of magnitude as the arterial influx, >100 ng/h. The degradative pathway is more difficult to quantify, but it cannot amount to more than total body T3 production, ~12 ng/h, minus fecal excretion, ~3.6 ng/h (13), and therefore it too is of the order of magnitude of local T3 production.

These comparisons explain why liver kinetic processes are so difficult to quantify in the intact biosystem. Arteriovenous T3 fluxes exceed local production and degradation rates by two orders of magnitude, swamping local metabolic processes overall, thereby rendering the liver kinetically indistinct from the plasma pool, relatively speaking. This, of course, does not diminish the major importance of liver as a T3 producer and metabolic processor, but it provides an explanation of why these processes are so elusive to experimental probes.

Graph Theory/Cut-Set Analysis

Our novel approach can be readily applied to design critical experiments for quantifying distributed, inhomogeneous biomolecular sources in many other biosystems with accessible organs or organelles, e.g., distributed sources of steroid hormones, vitamins, and lipoproteins (e.g., 1, 2, 16). It also can be used to exclude infeasible designs, on the basis of informationally insufficient probe site availability.


    APPENDIX
 TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Cut-set analysis of Fig. 3 provides the required individual pool T4-to-T3 conversion rates, from graphic and algebraic considerations, as follows. These are independent of the statistical properties of the data, treated separately. Two factors (18) govern the solution. First, in steady state, the sum of the mass influx arrows into a closed cut-set curve, in particular each of the two curves labeled A, B, C in Fig. 3, the first, A1,B1,C1, cutting the EHS organs (liver and intestine) together and the second, A2,B2,C2, cutting the intestine only, must be equal to the sum of the mass efflux arrows leaving the closed curve. Second, the curves must actually represent different experiments, three different input infusions, denoted A, B, and C, each capable of providing additional analytically independent information about parameters of the model graph or structure, and the inputs and measurements associated with each experiment must be clearly distinguished in the analysis. The only assumption made is that the model rate constants remain the same in each experiment, justified because they are small-perturbation tracer experiments.

To obtain the conversion rate in the EHS, we begin with Expt A data only, and thus cut-set A1 surrounding liver and intestine in Fig. 3. Expt B and Expt C do not play a role yet. By inspection, the steady-state mass-flux balance equation for cut-set curve A1 is

(A1a)
Now, with reference to Fig. 2, we note that CR4-3LIV A A + CR4-3INTA {equiv} k4-3EHSQ4EHSA. Similarly, (k56 + k06)Q3LIVA + k07Q3INTA {equiv} k3EHSQ3EHSA, where we have defined k3EHS as the total EHS T3 turnover rate constant, the sum of the two arrows kx+ky in Fig. 2. Thus Eq. A1a becomes

(A1b)
Then, solving for the key parameter of interest, k4-3EHS, we get

(A2)
Note that there is no term in Eqs. A1a or A1b for Expt B and Expt C inputs shown in Fig. 3, because only Expt A data are appropriate here.

Two rate constants still need to be resolved. To eliminate (solve for) k3EHS, we use the independent steady-state Expt B (cut-set B1), without influence of Expt A and Expt C. Summing influxes and effluxes yields (k65 + k75)Q3BLDB = k3EHSQ3EHSB. Therefore

Equation A2 then becomes

(A3)
To eliminate the factor (k65+k75), we apply cut-set analysis a third time to Fig. 3, in this case using Expt C and not A or B. The solution for k65+k75 is obtained, as above, from the mass-flux balance equation for the EHS (cut-set C1). After some algebra, this yields

(A4)
Substitution of Eq. A4 into Eq. A3 then gives

(A5)
Finally, CR4-3EHS = k4-3EHSQ4EHS (ng/h), as given in Eq. 1.

We remark here on the need for the additional information provided by the independent Expt C in solving the individual organ T3 production rate problem, information over and above that provided by the conventional dual-tracer infusion studies A and B. Equation A3, in particular, requires independent knowledge of k65k75 for solution, and this is not provided unless Expt C augments A and B. However, we hasten to add that our specific Expt C is not the only such third independent infusion study that can be used to solve the problem. For example, it can be shown that infusion of T*4, instead of T*3, directly into the organ (EHS in this case) would suffice. However, our derivation here clarifies why studies using data only from A/B dual-tracer experiments, like those reported in Refs. 43, 44, 4749, cannot by themselves provide local hormone production rates for this multisource system.

Evaluation of intestinal T3 production from T4 is a bit more involved algebraically. The steady-state mass-flux balance equation for pool 7 in the 8-pool model of Fig. 3, with Expt A data only (cut-set A2), is

(A6)
where k77 is the turnover rate of pool 7 (intestine): k77 = k07+k67 (see also Fig. 1). The key parameter of interest here is k4-3INT

(A7)
As above, Expt B data then yield a simpler pool 7 equation, from cut-set B2

and thus

(A8)
Then, from Eq. A7

(A9)
To eliminate k75 and k76 in Eq. A9, we first apply cut-set analysis a third time to Fig. 3, using Expt-C. Mass-flux balance for cut-set C2 gives

(A10)
We need an independent equation in k76 to complete the task, with k77 obtained from Eq. A8 and k75 from Eq. A10. From Figs. 1 and 3, let . Recall that is additionally measured. This provides the final unknown from measurements:

Then Eq. A10 becomes

Rearranging and gathering terms

and solving for k75 yields

(A11)
Then, substitution of k76 {equiv} k3bile and k75 from Eq. A11 into Eq. A9 yields the desired result for intestine:

(A12)
Finally, CR4-3INT = k4-3INTQ4INT (ng/h), as given in Eq. 2.


    ACKNOWLEDGMENTS
 
This research was supported by National Institute of Diabetes and Digestive and Kidney Diseases Grant DK-34839 and a TRAC grant from Knoll Pharmaceutical (now Abbott Laboratories).


    FOOTNOTES
 

Address for reprint requests and other correspondence: J. J. DiStefano III, UCLA, 4711 Boelter Hall, Los Angeles, CA 90095-1596 (E-mail: joed{at}cs.ucla.edu).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


    REFERENCES
 TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 

  1. Belisle S, Lehoux JG, and Brault J. The metabolism of androstenedione in human pregnancy: the use of constant infusion of unlabeled steroid to assess its metabolic clearance rate, its production rate, and its conversion into androgens and estrogens. Am J Obstet Gynecol 136: 1030–1035, 1980.[ISI][Medline]
  2. Berman M. Kinetic analysis of turnover data. In: Progress in Biochemical Pharmacology, edited by Paoletti R and Larger S. Basel: Karger, 1979, p. 67–108.
  3. Boonnamsiri V, Kermode JC, and Thompson BD. Prolonged intravenous infusion of labelled iodocompounds in the rat: [125I]thyroxine and [125I]tri-iodothyronine metabolism and extrathyroidal conversion of thyroxine to tri-iodothyronine. J Endocrinol 82: 235–241, 1979.[Abstract]
  4. Boxenbaum HG and Riegelman S. Pharmacokinetics of isoniazid and some metabolites in man. J Pharmacokinet Biopharm 4: 287–325, 1976.[ISI][Medline]
  5. Chanoine JP, Braverman LE, Farwell AP, and Safran M. The thyroid gland is a major source of circulating T3 in the rat. J Clin Invest 91: 2709 2713, 1993.[ISI][Medline]
  6. DiStefano JJ. Concepts, properties, measurement and computation of clearance rates of hormones and other substances in biological systems. Ann Biomed Eng 4: 302–319, 1976.[ISI][Medline]
  7. DiStefano JJ. Skeletal muscle is the largest pool of T3 and the major site of its in vivo production from thyroxine in the rat (Abstract). Clin Res 29: 026A, 1981.
  8. DiStefano JJ. Modeling approaches and models of the distribution and disposal of thyroid hormones. In: Thyroid Hormone Metabolism, edited by Hennemann G. New York: Dekker, 1986, chapt. 2, p. 39–76.
  9. DiStefano JJ. Hormone kinetic analysis. In: Endocrinology (2nd ed.), edited by DeGroot LJ. New York: Grune & Stratton, 1989, chapt. 160, p. 2726–2740.
  10. DiStefano JJ. Kinetic modeling methods in theory and practice. In: Thyroid Hormone Metabolism—Regulation and Clinical Implications, edited by Wu J. Oxford, UK: Blackwell Scientific Publications, 1990, chapt. 5, p. 65–89.
  11. DiStefano JJ and Feng D. Comparative aspects of the distribution, metabolism and excretion of 6 iodothyronines in the rat. Endocrinology 123: 2514–2525, 1988.[Abstract]
  12. DiStefano JJ, Jang M, Malone TK, and Broutman M. Comprehensive kinetics of triiodothyronine (T3) production, distribution and metabolism in blood and tissue pools of the rat using optimized blood sampling protocols. Endocrinology 110: 198–213, 1982.[Abstract]
  13. DiStefano JJ, Morris W, Nguyen TT, Van Herle A, and Florsheim W. Enterohepatic regulation and metabolism of triiodothyronine (T3) in hypothyroid rats. Endocrinology 132: 1665–1670, 1993.[Abstract]
  14. DiStefano JJ, Nguyen TT, and Yen YM. Transfer kinetics if 3,5,3'-triiodothyronine and thyroxine from rat blood to large and small intestines, liver and kidneys in vivo. Endocrinology 132: 1735–1744, 1993.[Abstract]
  15. DiStefano JJ, Sternlicht M, and Harris D. Rat enterohepatic circulation and intestinal distribution of enterally-infused thyroid hormones. Endocrinology 123: 2526–2539, 1988.[Abstract]
  16. Dupuy GM, Roberts KD, Bleau G, and Chapdelaine A. Sites of in vivo extraction and interconversion of estrone and estradiol in the dog. Steroids 39: 201–219, 1982.[ISI][Medline]
  17. Eng SJ, LoPresti JS, Liang H, and Nicoloff JT. Dynamics of T4 and T3 deiodination in man—dominant role of extrahepatic metabolism (Abstract). Thyroid 4: S–47, 1994.
  18. Esobar-Morreale HF, Escobar del Rey F, Obregon MJ, and Morreale de Escobar GM. Only the combined treatment with thyroxine and triiodothyronine ensures euthyroidism in all tissues of the thyroidectomized rat. Endocrinology 137: 2490–2502, 1996.[Abstract]
  19. Escobar-Morreale HF, Obregon MJ, Hernandez A, Escobar del Rey F, Morreale de Escobar GM. Regulation of iodothyronine deiodinase activity as studied in thyroidectomized rats infused with thyroxine or triiodothyronine. Endocrinology 138: 2559–2568, 1997.[Abstract/Free Full Text]
  20. Feng D and DiStefano JJ. Cut set analysis of compartmental models with applications to experiment design. Am J Physiol Endocrinol Metab 261: E269–E284, 1991.[Abstract/Free Full Text]
  21. Feng D and DiStefano JJ. Decomposition-based qualitative experiment design algorithms for compartmental models. Math Biosci 110: 27–43, 1992.[ISI][Medline]
  22. Feng D and DiStefano JJ. An algorithm for identifiable parameters and parameter bounds for a class of cascaded mamillary models. Math Biosci 129: 67–93, 1995.[ISI][Medline]
  23. Goresky CA, Bach GG, and Schwab AJ. Distributed-in-space product formation in vivo: enzymic kinetics. Am J Physiol Heart Circ Physiol 264: H2007–H2028, 1993.[Abstract/Free Full Text]
  24. Greer MA, Muakami M, and Tanaka K. Neuroendocrine relations in thyroid hormone metabolism. In: Thyroid Hormone Metabolism—Regulation and Clinical Implications, edited by Wu J. Oxford, UK: Blackwell Scientific Publications, 1990, p. 321–335.
  25. Hassan IM, Al-Ali AY, and Hassan M. Ultrastructural and hormonal metabolic studies of rat liver maintained in vitro by perfusion at 30 degrees C and 37 degrees C: a time course study by TEM, SEM and RIA. Histol Histopathol 4: 411–419, 1989.[ISI][Medline]
  26. Hays MT. Application of mathematical techniques to human thyroid hormone metabolism. In: Thyroid Hormone Metabolism—Regulation and Clinical Implications, edited by Wu J. Oxford, UK: Blackwell Scientific Publications, 1990, p. 91–121.
  27. Hershman J, Nademanee K, Sugawara A, Pekary AE, Ross R, Singh B, and DiStefano JJ. Thyroxine and triiodothyronine kinetics in cardiac patients taking amiodarone. Acta Endocrinol 111: 193–199, 1986.[ISI][Medline]
  28. Huang SC, Barrio JR, Yu DC, Chen B, Grafton S, Melega WP, Hoffman JM, Satyamurthy N, Mazziotta JC, and Phelps ME. Modelling approach for separating blood time-activity curves in positron emission tomographic studies. Phys Med Biol 36: 749–761, 1991.[ISI][Medline]
  29. Ikeda T, Takeuchi T, Ito Y, Murakami I, Mokuda O, Tominaga M, and Mashiba H. Effect of thyrotropin on conversion of T4 to T3 in perfused rat liver. Life Sci 38: 1801–1806, 1986.[ISI][Medline]
  30. Jennings AS, Ferguson DC, and Utiger RD. Regulation of the conversion of thyroxine to triiodothyronine in the perfused rat liver. J Clin Invest 64: 1614–1623, 1979.[ISI][Medline]
  31. Kaptein EM, Hoopes MT, Parise M, and Massrey SG. rT3 metabolism in patients with nephritic syndrome and normal GFR compared with normal subjects. Am J Physiol Endocrinol Metab 260: E641–E650, 1991.[Abstract/Free Full Text]
  32. Larsen PR. Physiologic signals regulating local activation of thyroid hormone. In: Thyroid Hormone Metabolism—Regulation and Clinical Implications, edited by Wu J. Oxford, UK: Black-well Scientific Publications, 1990, p. 167–180, 1990.
  33. Munira MA, Baqui BG, Harney JW, Larsen PR, and Bianco AC. Distinct subcellular localization of transiently expressed types 1 and 2 iodothyronine deiodinases as determined by immunofluorescence confocal microscopy. Endocrinology 141: 4309–4312, 2000.[Abstract/Free Full Text]
  34. Nguyen TT, Chapa F, and DiStefano JJ. Direct measurement of the contribution of type II 5'-deiodinase (D2) to steady state whole-body T3 production from T4 in the rat. Endocrinology 139: 4626–4633, 1998.[Abstract/Free Full Text]
  35. Nguyen TT, DiStefano JJ, Yamada H, and Yen YM. Steady state organ distribution and metabolism of thyroxine (T4) and 3,5,3'-triiodothyronine (T3) in intestines, liver, kidneys, blood and residual carcass of the rat in vivo. Endocrinology 133: 2973–2983, 1993.[Abstract]
  36. Oppenheimer JH, Schwartz HL, Koerner D, and Surks MI. Limited binding capacity sites for L-triiodothyronine in rat liver nuclei. Nuclear-cytoplasmic interrelation, binding constants, and cross-reactivity with L-thyroxine. J Clin Invest 53: 768–777, 1974.[ISI][Medline]
  37. Perl W, Effros M, and Chinard FB. Indicator equivalence theorem for input rates and regional masses in multi-inlet steady state systems with partially labelled input. J Theor Biol 25: 297–316, 1969.[ISI][Medline]
  38. Pilo A, Iervasi G, Vitek F, Ferdeghini M, Cazzuola F, and Bianchi R. Thyroidal and peripheral production of 3,5,3'-triiodothyronine in humans by multicompartmental analysis. Am J Physiol Endocrinol Metab 258: E715–E726, 1990.[Abstract/Free Full Text]
  39. Pilo A, Iervasi G, Vitek F, Turchi S, and Bianchi R. Disposal and distribution of rT3 in humans: a new double-tracer kinetic study. Am J Physiol Endocrinol Metab 264: E239–E249, 1993.[Abstract/Free Full Text]
  40. Prabakaran D, Rexford SA, Harney JW, Berry MJ, and Larsen PR. Polarized targeting of epithelial cell proteins in thyrocytes and MDCK cells. J Cell Sci 112: 1247–1256, 1999.[Abstract/Free Full Text]
  41. Rowland M, Benet LZ, and Riegelman S. Two-compartment model for a drug and its metabolite: application to acetylsalicylic acid pharmacokinetics. J Pharm Sci 59: 364–367, 1970.[Medline]
  42. Salvatore D, Barth T, Harney JW, and Larsen PR. Molecular biological and biochemical characterization of the human type 2 selenodeiodinase. Endocrinology 137: 3308–3315, 1996.[Abstract]
  43. Schröder-van der Elst JP and Van der Heide D. Thyroxine, 3,5,3'-triiodothyronine, and 3,3',5-triiodothyronine concentrations in several tissues of the rat: effects of amiodarone and desethylamiodarone on thyroid hormone metabolism. Endocrinology 127: 1656–1664, 1990.[Abstract]
  44. Sefkow AJ, DiStefano JJ III, Himichk BA, Brown SB, and Eales JG. Kinetic analysis of thyroid hormone secretion and interconversion in the 5-day-fasted rainbow trout, Oncorhynchus mykiss. Gen Comp Endocrinol 101: 123–138, 1996.[ISI][Medline]
  45. Silva JE, Dick TE, and Larsen PR. The contribution of local tissue thyroxine monodeiodination to the nuclear 3,5,3'-triiodothyronine in pitutitary, liver and kidney of euthyroid rats. Endocrinology 103: 1196–1207, 1978.[Abstract]
  46. Silva JE and Matthews PS. Production rates and turnover of triioidothyronine in rat developing cerebral cortex and cerebellum. J Clin Invest 74: 1035–1049, 1984.[ISI][Medline]
  47. St. Germain DL and Galton VA. The deiodinase family of selenoproteins. Thyroid 7: 655–668, 1997.[ISI][Medline]
  48. Toyoda N, Berry MJ, Harney JW, and Larsen PR. Topological analysis of the integral membrane protein, type 1 iodothyronine deiodinase (D1). J Biol Chem 270: 12310–12318, 1995.[Abstract/Free Full Text]
  49. Van Doorn J, Roelfsema F, and Van der Heide D. Concentrations of thyroxine and 3,5,3'-triiodothyronine at 34 different sites in euthyroid rats as determined by an isotopic equilibrium technique. Endocrinology 117: 1201–1208, 1985.[Abstract]
  50. Van Doorn J, Van der Heide D, and Roelfsema F. Sources and quantity of 3,5,3'-triiodothyronine in several tissues of the rat. J Clin Invest 72: 1778–1792, 1983.[ISI][Medline]
  51. Van Doorn J, Van der Heide D, and Roelfsema F. The contribution of local thyroxine monodeiodination to intracellular 3,5, 3'-triiodothyronine in several tissues of hyperthyroid rats at isotopic equilibrium. Endocrinology 115: 174–182, 1984.[Abstract]
  52. Wach P, Tilg B, Lafer G, and Rucker W. Magnetic source imaging in the human heart: estimating cardiac electrical sources from simulated and measured magnetocardiogram data. Med Biol Eng Comput 35: 157–166, 1997.[ISI][Medline]




This Article
Abstract
Full Text (PDF)
A corrigendum has been published
All Versions of this Article:
285/1/E171    most recent
00239.2002v1
Alert me when this article is cited
Alert me if a correction is posted
Citation Map
Services
Email this article to a friend
Similar articles in this journal
Similar articles in ISI Web of Science
Similar articles in PubMed
Alert me to new issues of the journal
Download to citation manager
Search for citing articles in:
ISI Web of Science (2)
Google Scholar
Articles by Nguyen, T. T.
Articles by DiStefano, J. J.
Articles citing this Article
PubMed
PubMed Citation
Articles by Nguyen, T. T.
Articles by DiStefano, J. J., III


HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
Visit Other APS Journals Online
Copyright © 2003 by the American Physiological Society.