A preliminary model of serum growth hormone response to hypoglycemia in man

A Preliminary Model of Serum Response to Hypoglycemia

A

and human

linearized

simplified.

response damped

model

of

the

to hypoglycemia is reviewed. response to intravenous insulin regulatory

parameters

regulatory

well with direct trations following is simulated

into

system.

and

number

Iresponses

of blood ;ldministration.

implications

relating

This model. administration,

smaller

Computed

measurements inxilin their

a

system

Growth Hormone in Man

glucose The

based and effect

serum which

growth

which LIPOII

hormone

predicts a criticall! lumps several kinetic characterizes the

model

growth hormone of parameter

the conform concenvariation\

discussed.

Growth hormone is considered to be an important regulatory factor in carbohydrate metabolism, particularly during stressful conditions which tend tc> deplete the body carbohydrate reserves. For example. the level of serum growth hormone is elevated (a) during physical cxcrcise.‘~‘~‘.~’(b) by diminished lcvcls of the blood glucose followin? insulin administration.” and (c) by prolongcd fasting.” The effect of growth hormone on carbohydrate metabolism apparently is twofold, in that (a) it increases the level of blood glucose and ultimately triggers the release of insulin. which in turn increases glucose utilization.‘, and (b) it tends to decrease the effectiveness of insulin in the enhancement of glu case utilization.7,‘.” This latter characteristic is considered a specific diabetopenic property of growth hormone. Our interest is centered upon energy metabolism. In an earlier publication.“, we reported that a depressedsteady-state level of the blood glucose is maintained 7-l

REGULATION

OF BLOOD GROWTH

HORMONE

II

for several hours during prolonged exercise. Under those conditions, glucose oxidation as well as the rate of blood glucose replacement tends to increase.” Since the body’s ability to maintain blood glucose at a relatively constant level results from complex interactions between carbohydrate, precursors of carbohydrate. and various hormones.” we have extended our investigations to include an evaluation of the quantitative and kinetic aspects of the interactions between blood glucose and growth hormone, one of a group of hormones having the opposite effect of insulin. Our proposed model ” did not attempt to include all possible details. but rather to describe observed blood glucose and growth hormone concentrations with a minimum number of constants. The simplified model proved successful in characterizing the serum growth hormone responses of healthy individuals under two different physiological states (resting and exercising). The present paper documents the physiological basis of the proposctl model. cites the results of additional studies to test the limits of validity of the simplified model, and summarizes the physiological sensitivity coeficients which appear to dominate the mathematical characteristics of the serum growth hormone rcsponsc to hypoglycemia. Since. to our knowledge. this is the first atempt to predict quantitativelc the serum growth hormone curve, considerable detail regarding assumptions, methodology. and physiologic response is presunted. METHODS PROCEUURF-s AND ANALYSES

The data have been drawn from experiments conducted with I3 male postabsorptive subjects who were selected on the basis of their physical fitness, motivation, and general health. Each subject was fully advised as to the nature and extent of the study before giving consent and being accepted. All subjects participated in two separate tests (exercising or resting). For studies of the resting state, the subjects rested quietly on a reclining couch. Studies of physical exercise followed a common plan of aerobic work on a treadmill. Speed and grade were adjusted for each subject to provide a work load which was approximately 33% of the maximal work capacity. Each period of exercise consisted of 1 h and 20 min of walking followed by 10 min of rest. In order to avoid important dehydration, each subject consumed 300 ml of water every 1.5 h and took 1 g of NaCl every 4 hours. Oxygen consumption was determined from expired air samples collected through low-resistance connections in chain-compensated gasometers. After X!,j hr of testing, insulin (E. R. Squibb and Sons) was administered to 7 subjects in a dosage equal to 0.05 unit/kg, iv; adrenalin (Parke, Davis and Co. j was administered to 6 subjects in a dosage equal to 0.1 mg/kg, im. Throughout the entire test, periodic blood samples were drawn from an in-

p II

‘1OL’kCv.

II<)\\

\ltl).

I I
\\I)

(s\li(

I \

dwelling pvlyethylcnc catheter inserted into one of the ;inlecuhital \c,ins. Sc,rum \:imple4 \\ crc dt-a\\,n Ott anal t’r~~n for ~II~~~~c~~cI~~ ;tnal! ~;i’\ (;Illcchc \\ iI’ nic;l\urccI by an en/c matic 111~~~cc’clurc.! Insulin \\;i\ mc:r\ur~4 !I! i.~idiclirnnilill~l assay using the rloublc antihotlJ, technique. Iodin~rtctl I I 1 insulin aiiil instilii! binding rcagcnt \\cI-c 0ht;rinccl tram the h’rlclc~ll--C’hic~r~o C‘orp ( Irnmunc~~ assay Kit I M-3Y ). Insulin ~tanclards were prclxlrccl l’ronl ;I \inglc h:ltch 01 bovine insulin (Cal Biochem. Gr;ldc I3 ), Prccipitatc\ wcrc collcctcd 13~ micI.oliltration through cellular acutatc liltcr disc\. lixlioacti\~ity ot’ the‘ prccipit:lt~

wa5 measured in

;I

well-tvpe crystal scintillation? ci~untcr.

Growth hormone W;IS mcasurcd hq’ radioi~nn~un~)-~lss~l~ using the d~uhlc antibody technique as dcscrihcd prcvivusly.’ ’ Hriclly. r:thbitx acre immunized with human growth hormone (I\inrll~ suppliccl I,! Dr. C‘. H. 1.i. Ilnivcrsit\ c)t (‘alifornia Medic:11 <‘enter. Sun I:r;lncisco 1, Imnlunorcactive anti-rabbit gamma globulin was prepared in goat\. Human growth hormone standards ( LAJ~ Ivo. HS503A ) \\‘cre obtaintxl through the hind coopcr:ltion of Dr. A. E. Wilhelmi. Emory lini\,crsit>. Atlanta.
The

principal

features

of our

analyses

are as follows:

(a)

the development

of an equation that relates level of serum growth hormone to dcpresscd levels of the intluencc of variations in the of serum glucose. and (b) an evaluation major parameters on the predicted response. Our general model for blood glucose regulation involving only growth hormone and consistent with current findings is as follows: A decrease in blood glucose is a primary stimulus for hormone releasing factor apparadditional growth hormone secretion.” Growth ently is secreted by the hypothalamus and transported to the anterior pituitary via the micro-circulation of the brain.l;‘ Growth hormone released by the pituitary (growth hormone production) is transported in the systemic circulation to certain tissues such as liver and kidneys which arc known to have a high rate of glucose production.“‘,” Preliminary evidence suggeststhat the level of hlood _growth hormone tends to regulate the secretion rate from the pituitary;‘. consequently, we have included an autoregulatory loop for pituitary growth hormone release which is related to growth hormone metabolism. Similar autoregulation is assumed for glucose production.‘!’ Our model for blood glucose regulation is shown in Fig. 1 as a conventional feedback system block diagram.

REGULATION

OF

BLOOD

GROWTH

-------_

77

HORMONE -----

CONTROLLINGSYSTEM ’

r - -iOiittED

1 CONTROLLING1

SYSTEM

1

1

. DISTlJRBlhG SIGNAL GLUCDlEDtRTUGN

dl dt

Pig.

I.

hrodel

for

the

evaluation

of

glttcose

regttlalion

in postahsorptive

subjects.

In Fig. I. G is the serum glucose concentration, PC: is an inherent production rate of glucose by tissues, A, is a tissue parameter which represents a stimulatory influence of H (serum growth hormone concentration) on glucose production, L, is the removal rate of serum glucose, tll/tlf ih any rate of perturbation in the level of serum glucose, A, is a parameter which represents a stimulatory influence of G on growth hormone production. and L, is the removal rate of serum growth hormone. Since in vitro studies show glucose production by kidney and liver”” and growth hormone production by pituitary cxplants.2’ the assumption of I’,: and I’,, seemsjustified. The major assumptions for this largely inductive process of modeling are as follows: ( 1 ) Each regulatory organ system (hypothalamus-anterior pituitary or liver-l\idncy) functions as a reservoir for growth hormone or glucose and as a detector for the respective compounds; (3) growth hormone and glucose arc lost from the plasma at various rates, depending upon the physiologic state of other tissues, and such losses are interpreted as loads upon the controller and controlled system; (3) operating regulatory function of growth hormone is to maintain a constant level of plasma glucose; (4) irregularities in plasma mixing dynamics are ignored; (5) reserves and precursor materials for growth hormone or glucose biosynthesis are not rate limiting factors in normal regulation. When the relationships in Fig. I are expressed in mathematical form. two first-order differential equations are obtained. These arc as follows: VidG dt) = PC; $ AZH - L,G + Vidl dt,.

111

V(dH dt) = P,, - AlG - L,H.

(21

It is assumed that the above relationship applies to the whole body, but our determinations are constrained to measurementsof blood concentrations. If Eqs. ( I ) and (2) are divided throughout by a constant compartmental volume, V,

7s

kOI~X(,.

and the regulak~r\ the following.

IlOU

coclficients

\I
TRIMI.

\SI)

(, \I<(

;II’C replaced bq lower

r/c; l/l’

I’,

!..Ci + +/i

t/H

I’,,

I,H

cir

I\

C:IW ~~nlbol~.

the\ ;14sunic

t (!I (II a.

11,(1’

4’

Solving these equations for LI yields the following linear second order diikrentiai equation for the system:

The responsesof postabsorptivc subjects to exercise and to the adminstration of either insulin or adrenalin are shown in Fig. 3. For the sake of complctcnes.\, RESTING

EXERC;S;;v;

02 UPTAKE = .280 2.037

O2 UPTAKE = 1.13 It .G9

l~ters/mln

liters/mln

0 l

-

PREINJECTION INSULIN ADRENALIN

$j EL,A K

‘5

2

4

6

810120

2 TIME,

4

6

810

12

hr

Fig. 2. Response of resting and exercising subjects to insulin or adrenalin administration. Serum constituents are shown on the ordinate: time in hours is shown on the abscissa. Response to insulin is shown with closed symbols (0); response to adrenalin is shown with open symbols (0).

REGULATION

OF

BLOOD

GROWTH

HORMONE

79

all the data are shown; however, since our modeling attempts have been limited exclusively to the glucose-growth hormone system. discussion and statistical comparisons of only those variables are presented. During X-l/a h of exercise, the level of serum glucose declined from 84t I I .2 mg/’ IO0 ml to 68 t 8.2 mg/ IO0 ml; the level of growth hormone kcreased from 0.70 z-1 0.60 mkg/ml to 2.9 5: I.2 mpg/ml. Following the administration of insulin. the serum glucose declined to 38 mg/lOO ml and then returned slowly to preinjection levels; after a slight delay, the level of serum growth hormone rose to 14.4 mhLg/ml and then returned toward preinjection levels. Paired comparisons of individual responses measured initially and after 8-V: hours of exercise indicate that the increased level of growth hormone observed during exercise is statistically significant 1.-1 3.85. p. < < 0.01 ). During rest, the level of serum glucose declined from 89 t 6.6 mg/lOO ml to 76 z 7.2 mg/ 100 ml, The level of serum growth hormone was relatively constant, 0.60 c 0.44 mpg/ml. Subsequent to the administration of insulin, the level of serum glucose declined to 39 mg/ 100 ml and then returned to preinjection levels; the level of serum growth hormone rose to 18.3 mpg/ml and then declined. The nature of the observed results suggests that the growth hormone response to major perturbation of blood glucose is critically damped, The equation for such :i system is as follows:

and 1 /,I,

+

1/1U!!

=

(I”.

18’

Equation (6) was solved in terms of the Laplace transform, The forcing function. perturbation of blood glucose, was assumed to be a modified triangular pulse. By successive approximation and digital computation, values were obtained for N and u, which when substituted in Eq. (6) gave good agreement between the observed and computed response of serum growth hormone. Symbols, definitions. ;md values are listed in the appendix, Reference will be made to these throughout the body of this text. The serum growth hormone response of resting subjects is shown in Fig. 3. In general, the observed and computed values agree well over the period of time studied. The response of exercising subjects is shown in Fig. 4. Again, good agreement was found between observed and computed values. Computed values for the parameter c1 are 0.0045 and 0.0078 for exercising and resting subiects, respectively. The computed value for a, is 2.3 for both

so

\OCN(,.

IlOW’,\RI).

I~RI’X,.

\\I)

(z.ZRCIi\

Fig. 3. Serum growth hormone response to insulin administration in resting subjects. Serum growth hormone level in mpg/ml is shown on the ordinate: time in minutes is shown on the abscissa. Observed values are shown with the open circles Cc::1: predicted values with the parameter 0.007X are shown with the open squares ( 0).

conditions of exercise and rest. Consequently. this latter value is considered to be a physiologic constant under our experimental conditions. EFFECT

of: PARAMETER

VARIATIONS

The effect of controlled variations in the parameters was studied systematically for conditions of exercise. For values of less than our nominal value of 0.0045, the amplitude of the response is increased and the rate of return to normal levels is decreased. Conversely. for values of greater than the nominal value, the amplitude of the responsediminished and the rate of return to normal levels is accelerated.

”

Fig. Serum shown values

J PREDICTED OBSERVED

VALUE WITH il :.1X45 vALIJES

4. Serum growth hormone response to insulin administration in exercising subjects. growth hormone level in mpg/ml is shown on the ordinate; time in minutes is on the abscissa. Observed values are shown with the open circles (0); predicted with the parameter 0.0045 are shown with the open squares (0).

REGULATION

OF BLOOD GROWTH

HORMONE

Xl

Our resting subjects showed a higher value of (I than did the exercising subjects (0.0078 as compared with 0.0045 ), yet the amplitude of their response was greater and rate of return to normal levels was faster. This was due partly to the greater magnitude of the glucose pulse (0.37 mg/ml serum at rest compared with 0.30 m&ml serum during exercise ). and the different time history of the glucose pulse during rest (see Appendix A). The effect of variation in rr,/ was also examined. In our exercising subjects. a,1 is 0.675; as I is increased the amplitude of the growth hormone responseis incrcasrd, but tinal values are unaffected. Preliminary studies were conducted to evaluate the effect of variations in the parameter (I,/I,, - u,pn ). As shown in Appendix A, that term is related to the tinal value. H,:. of the level of serum growth hormone. In general, variations in t I,p,, - L/,/)~;) do not modify the amplitude of the growth hormone response: only the final steady-state value is affected. Since p,, ad 11~are important determinants of the steady-state level, it is likely that they may vary slightly and thus produce minor fluctuations in the tinal value of serum growth hormone. Esrtnr~r~s OF OTHERPARAMETERS In order to describe more adequately steady-state blood glucose regulation, additional model parameters have been determined. Numerical values for POand A 2 were obtained as follows: (a) the average serum glucose replacement rate determined in our similar earlier study of prolonged rest and exercise I’ was plotted against the level of serum growth hormone determined in the present studies. (b ) the slope of that line represents A,, and (c) the JJintercept is taken as P,;. The general relationship is shown in Fig. 5. Here we assumedthe serum volume to be 3 liters; accordingly, the values shown on the ordinate are applicable to total serum. From Fig. 5, PC,is 15.1 mg glucose/min and A, is 1.27 mg glucose/min/m~g growth hormone/ml. The steady-state relationship for glucose may be obtained by substitution of these values along with blood glucose turnover rate into Eq. ( I ) and setting both rlG/clt and (/l/dt equal to zero. DISCUSSiON

AND CONCLUSIONS

The present research was undertaken to develop preliminary information regarding the dynamic response of the growth hormone system. In order to provide data of value for physiological investigations of hypophyseal responses to well-defined stresses,our approach has been to draw upon the results of both experimental and simulation studies. In general style, our model resembles the various simplified, linearized models proposed by others on the related subject .>, ,,, of blood glucose regulation. _-. _.,.2,. 2:1Also. assumptions made from our data are in accord with Belie’s “2 conclusion that certain glucose-hormonal regulatory systemsoperate in or near the region of critical damping.

1

2

SERUM

GROWTH

HORMONE,

mpLg/ml

Fig. 5. Steady-state relationship between serum glucose production and level of serum growth hormone. Serum glucose replacement rate in mg/min is shown on the ordinate: level of serum growth hormone in mpg/ml is shown on the abscissa.

Although the analytical treatment presented here deals only with a restricted time scale and contains simplifying assumptions, the conformation between observed and computed responsesof growth hormone to glucose perturbation supports our premises and indicates that we have arrived at a good first order approximation of the regulatory system. Thus, despite the limitations of knowledge, our model defines the gross dynamic behavior of growth hormone and. consequently, we feel that there are physiological counterparts to the model parameters which should be sought experimentally. First, our model identities the requirement for a functional glucose sensor. In theory, we can postulate two types of glucose sensors.For example, the rapid disappearance of glucose from the serum after insulin adminstration probably results in a transitory accumulation of glucose in insulin sensitive tisues. Those tissues may have receptors which are excited by increased levels of glucose. On the other hand, in tissue such as the central nervous system which is relatively insensitive to insulin, a reduction of blood glucose must cause a prompt fall in tissue glucose content. Hence. if receptors exist in the central nervous system or in the vascular or extravascular compartment, they must be sensitive to a reduced level of glucose. In any event, the receptor signal is amplified by u’ (i.e., a factor of 2.3). Figure 6 is useful for speculations concerning certain properties of a theoretical glucose receptor. Here we have plotted the time history of the serum glucose perturbation in resting subjects along with critical time values, b, determined by computer simulation (see Appendix A ) These latter values were required to reproduce the growth hormone response. Grossly, three rates of change are apparent in the experimntal data, i.e., the rates between O-

REGULATION

OF

BLOOD

GROWTfi

83

HORMONI-

.

OBSERVED THEORETICAL I 0

50

100 TIME. m,n

VALUES MODEL L 150

VALUES

200

Fig. 6. Time history of the glucose perturbation in resting subjects. Level of serum glucose in mg/lOO ml is shown on the ordinate; time in minutes is shown on the abscissa. Observed values are shown with closed smybols (0); theoretical model values are shown with open symbols (0).

30 min. 30-45 min, and 45-180 min. Computed values for b show different rates of change and the complex pulse is contracted. This suggeststo us that the pituitary gland does not respond to the actual level of serum glucose, but rather may respond to rates of change of glucose in some portion of the vascular system.

Second, our model serves a heuristic function as a means for reappraisal of research findings and for indicating future areas of research. On the one hand, it would seem a safe procedure to design new physiological experiments on the theory which suggests several new parameters and regulatory coefficients (PG, L,. A, P,,, L,, A,) of significance. One such experiment would be to measure steady-state levels of serum growth hormone during infusions of insulin or glucose at known rates. Other experiments might be designed to further elaborate the control of glucogenesisin isolated tissuesby growth hormone. Overall, we can identify three major areas where further research is needed as follows: (a ) studies of the mechanismsby which the pituitary gland receives and processes serum glucose information, (b) studies of the influence of administration of immunologically-specific growth hormone on blood glucose, and (c) studies of the exact effects of disrupted connections between the pituitary gland and a prevailing blood glucose deficiency. On the other hand, our model may serve as a point of reference for other studies. For example, Ackerman and co-workers L’4postulated a model with constant coefficients to describe blood glucose regulation. One term, 11, was used to represent the effects of combined concentrations of insulin and its antag-

Third. WC ha\,c made fc\+ assumptions regarding the forcing t’uncticjn ()li: approach has been to induct hypoglycemia by phy4oloic I~GIIIS. I‘htl\. it1 GUI opinion. cvcn the modified triangular ~uluc~w pulp probably rcprcacnta to (I greater extent the true htatc ()I’ affair\ in the IxK~\ instead of cjthcr I’orcins I’UIIC-;\ scc~lnclarq tions which wc might II;I\c’ c1~ow1l for anatytical con\cnicncc. advantage of the present cspperiments lies in the !‘act that WC ha\,c obr:lined data from which WC can dra\c certain inl’crcncca regarding the relatic~n4ip\ between blood gluco~ and insulin. This. however. will hc ~hc 4ubjcct ot ;I iatc‘l report. Finally, in its present form, our model i\ uwful t’or ii preliminary control system analysis in order to shed light on the mechanisms controlling hypophyscal responses. SUMMARY A simplified model of the growth hormone-glucose regulatory system ha\ been conformed to data from studies of induced hypoglycemia in healthy subjects measured by intermittent sampling after intravenous administration of insulin. In order to maintain simplicity without sacriticing accuracy, our equation for the serum growth hormone response was reduced to two unknowns. The unknowns, representing physiologic sensitivity coeficients. were evaluated by successive approximation and digital computer simulation. Further digital simulations were performed to test approximations made in formulating the model. and to determine the relative importance of the coefficients in home ol’ the mechanisms involved in blood growth hormone regulation. In our studies, simulations of the basic model were performed with only one forcing function which conformed closely to observed experimental data. A1so. whereas our general equation might describe ;I variety of nonoscillatory rcsponses of the serum growth hormone (depending upon the magnitude of the sensitivity coefficients ), we have constrained our analysis to the critically dampccl region in response to a representative negative serum glucose pulse induced by insulin. The results of our computer studies suggest the following: (a) under conditions of rest as well as prolonged physical work, the sensitivity of serum growth hormone production to serum glucose concentration is constant. (b) the parameter (based upon the fractional removal rates of serum growth hormone ;IS well as glucose) which determines the growth and decay of the serum growth hormone response is larger in resting subjects than in exercising subjects, (c J there is a lag or time delay between the onset of hypoglycemia and increase in

REGULATION

OF

BLOOD

GROWTH

HORMONE

level of blood growth hormone, and (d) the response of the pituitary to rate of change of blood glucose.

85

is related

ACKNOWLEDGMEN’J

We express our thanks to Mrs. Patricia Smith for her technical assistance in the grouth h~~rmone assays. REFERENCES

I. HLNI~K, W. M., FONSEKA, C. C., AND PASSMORL. R. Growth hormone: important role in muscular exercise in adults. Sc,ic~nce 150, 105 I-1053 (1965). 2. ROTH. J., GLICK. S. M., YAI.OW. R. S.. AND BLRSON. S. A. Secretion of human growth hormone: physiologic and experimental modification. Metrrholism 12. 577-570 llY63l. 3. ROIH. J., GLICK. S. M.. Y,u ow, R. S.. AND BtHSON. S. A. The inHuence of blood glucose on the plasma concentration of growth hormone. tlitrhr~rcs 13, 355-361 ( 1964). 4. SCIIAI cit. D. S. The influence of physical stress and exercise on growth hormone and insulin secretion in man. J. Ltrh. C/in. hlvd. 69. 256-269 (1967). 5. R~JI‘H, J., GUCK. S. M., YAIOW. R. S., AND BERSON, S. A. Hypoglycemia: :I potent stimulus IO secretion of growth hormone. Scir~c 140, 9X7-Y88 (1963). 6. AI ‘ISZL’LER. N., STEELE. R.. WALL. J. S.. DUNN, n., ,~ND 11t Bouo, R. C. Efl’ect of growth hormone on carbohydrate metabolism in normal and hypophysectomized dogs: studies with Cl’ gluco\e. .3n1c~r. J. Ph.v.~i~~/. 196, 121-124 (1959). 7. Hist1oP. J. S., STttLE. R.. AI I-ZIXCR, N.. RATtjbI a, 1.. B.ltRKNbs. C., AND DE Bo~o, K. ( Diminished responsiveness to insulin in the growth hormone-treated normal dog.

,-fmcr.

J. Physid.

212,

272--27X

(1967).

X. FKOH~I~N. I.. A., MAC GILLIVRA~, M. H., ANI) ACTTO. T. JR. Acute effects of human qowth hormone on insulin secretion and glucose utilization in normal and growth hormone deficient subjects. J. Clirr. Endwrirtot. crud kfrt. 27, 561-567 ( 1967). 9. IKKOS. D. AND Luf-r. R. Effects of short-term administration of large doses of human growth hormone on carbohydrate metabolism in adult, non-diabetic. hypophysectomired women; studieh with 1‘C-labelled glucose. .l&r E~tl~rir~ol 39, 567-583 ( I Y62). 10. YOUNG. D. R., P~LLIGRA, R.. AND ADACHI. R. R. Serum glucose and free fatty acids in man during prolonged exercise. .l. il[~pl. Phy.rio/. 21, 1047-1052, (1966). 1 I. YouN(,, D. R., PELLICX~. Ii., SHAPIRA. J., ADA~HI, R. R., ANLI SKRETTINGLAND, K. Glucose oxidation and replacement during prolonged exercise in man. 1. App/. t’try.siol. 23, 734-741 (1967). I?. \~‘ouNc,. D. R. AND HOWARI). J. C. Determination of parameters which relate growth hormone response to serum glucose perturbation. Proc. Irztevr~nf’l. Ulrliojz of Phy.t;ot. Sci.. 7, p 478, 24th Internat’l. Gong. Washington, D. C. (196X). 17. HILI , J. B. ANI) I(tS55Lt.R.
18.

‘2.

‘> -. i

REGULATION

OF BLOOD GROWTH APPENDIX

SYMBOLS,

DIMENSIONS,

BEHAVIOR

SL Inbol I. 2. 3. 1. 5. 6. 7. X. 9 IO. II. 12. 13. 14. IS. 16. 17.

AND

OF SERUM

VALUES GROWTH

A

OF PAKAMET~RS HORMONE

87

HORMONE

THAT

TO GLWOSE

RELATE

THE

DYNAMIC

PCRTURBATION

Detinition

Dimensions

Parameter which determines the rate of grouth and decay of the serum growth hormone response Sensitivity of serum growth hormone production to serum glucose concentration Sensitivity of serum glucose production to serum growth hormone concentration Time Time Time Time Serum glucose concentration Serum growth hormone concentration Initial value of serum growth hormone concentration Initial rate of change of serum growth hormone concentration Final value of serum growth hormone concentration Amplitude of serum glucose perturbation Amplitude of serum glucose perturbation Amplitude of serum glucose perturbation Fractional removal rate of serum growth hormone Fractional removal rate of serum glucose Parameter which determines final steadystate values of serum growth hormone concentration Production rate of glucose per unit volume of serum Production rate of growth hormone per unit volume of serum Time Serum volume

I min mpgH/ml/min mg G/ml nig G/ml/min mpg H ‘ml min min min min mg/nil nirglml ni@giml

Parameter values Rest Exercise 0.0078

0.004s

2.3

2.3

0 48 52 63

5 33 35

0.5

2.9

0.05

0

m&ml

0.50

2.9

mg/ml mg/ml mg/ml I fmin

0.37 0.10

0.30 0

0.5

2.9

mpgiml /min

I /min m,g;ml

mg~mlimin m~g/ml!mui min ml