Handbook and Reference for SPINA

Preface

SPINA (structure parameter inference approach) is a cybernetic method for advanced interpretation of laboratory results. It allows for calculating constant structure parameters of endocrine feedback control systems in vivo from hormone or metabolite concentrations that have been obtained from serum or plasma specimens. The method is based on mathematical and cybernetic modelling of processing structures [1-3].

First successful implementations apply to the evaluation of thyroid function (SPINA Thyr) and insulin-glucose homeostasis (SPINA Carb). The methodology allows for calculating the thyroid’s maximum secretory capacity (GT or SPINA-GT) and the sum activity of peripheral 5’-deiodinases (GD or SPINA-GD) from levels of TSH, (F)T4 and (F)T3 that have been determined once only. A similar method delivers estimates for beta cell function (SPINA-GBeta) and insulin receptor gain (SPINA-GR) from fasting insulin and glucose concentrations. SPINA-GBeta and SPINA-GR provide the basis for an advanced disposition index (SPINA-DI).

SPINA Thyr has been evaluated in clinical trials covering more than 10 000 subjects with various disorders of thyroid homeostasis [4]. SPINA-GT has been demonstrated to correlate with thyroid function [5, 6] and gland volume as obtained via ultrasonography [7]. Its retest reliability is higher than that of TSH, FT4 or FT3 [8].

SPINA-GD is reduced in nonthyroidal illness syndrome (NTIS) [9-11] and increased in states of step-up hyperdeiodination [12], and it correlated in two large trials with TSH levels, thus mirroring intracellular cAMP levels [13, 14].

These structure parameters may therefore contribute to diagnosis of rare or at least less obvious thyroid disorders.

SPINA-GBeta and SPINA-GR could be demonstrated to correlate with more elaborate measures of insulin-glucose homeostasis including oral glucose tolerance testing and glucose clamp technique [3]. The disposition index SPINA-DI has advantages in diagnostic power over other methods for the diagnosis of diabetes mellitus or prediabetes [15].

In addition to SPINA-GT and SPINA-GD SPINA Thyr is able to calculate TTSI and Jostel’s TSH index, two static function tests for the assessment of pituitary function [16, 17]. SPINA Carb delivers HOMA and QUICKI estimates as well.

The functions described in this document can calculate structure parameters of thyroid and insulin-glucose homeostasis in statistical environments based on the statistical language S (e.g. the R® platform). As separate solutions stand-alone versions of SPINA are available for desktop computing platforms including macOS, Windows and Linux. These versions are not documented in this vignette.

Usage

library(SPINA);

TSH <- c(1, 3.24, 0.7);
FT4 <- c(16.5, 7.7, 9);
FT3 <- c(4.5, 28, 6.2);
lu <- 20;

estimated.GT(TSH, FT4);
#> [1] 4.696993 1.080631 3.367195

estimated.GD(FT4, FT3);
#> [1]  25.21762 336.22895  63.69687

estimated.TTSI(TSH, FT4, lu)
#> [1]  82.50 124.74  31.50

estimated.TSHI(TSH, FT4)
#> [1] 2.2192500 2.2112233 0.8538251

estimated.sTSHI(TSH, FT4, mean = 2.7, sd = 0.676)
#> [1] -0.7111686 -0.7230424 -2.7310280

estimated.sGD(FT4, FT3, mean = 30, sd = 5)
#> [1] -0.9564769 61.2457908  6.7393746

SPINA.GT(TSH, FT4)
#> [1] 4.696993 1.080631 3.367195

SPINA.GD(FT4, FT3)
#> [1]  25.21762 336.22895  63.69687

SPINA.sGD(FT4, FT3, mean = 30, sd = 5)
#> [1] -0.9564769 61.2457908  6.7393746

TSH <- 0.86;
T4 <- 163;
T3 <- 3.0;

estimated.GTT(TSH, T4)
#> [1] 7.52643

estimated.GDTT(T4, T3)
#> [1] 19.54035

SPINA.GTT(TSH, T4)
#> [1] 7.52643

SPINA.GDTT(T4, T3)
#> [1] 19.54035

Insulin <- 63.01;
Glucose <- 4.34;

SPINA.GBeta(Insulin, Glucose)
#> [1] 2.798864

SPINA.GR(Insulin, Glucose)
#> [1] 2.318659

SPINA.DI(Insulin, Glucose)
#> [1] 6.48961

HOMA.IR(Insulin, Glucose)
#> [1] 2.025655

HOMA.Beta(Insulin, Glucose)
#> [1] 250.0397

HOMA.IS(Insulin, Glucose)
#> [1] 0.4936675

QUICKI(Insulin, Glucose)
#> [1] 0.3431685

Arguments

Parameter	Explanation
TSH	Thyrotropin (TSH) concentration in mIU/L or µIU/mL, resp.
FT4	Free thyroxine (FT4) concentration in pmol/L. FT4 may be in an arbitrary unit for TTSI calculation, provided that it is in the same unit as lu.
FT3	Free triiodothyronine (FT3) concentration in pmol/L
T4	Total T4 (TT4) concentration in nmol/L
T3	Total T3 (TT3) concentration in nmol/L
lu	upper limit of FT4 reference range (should be in the same unit of measurement as the FT4 concentration)
mean	mean value of population sample for standardised (z-transformed) tests.
sd	standard deviation of population sample for standardised (z-transformed) tests.
Insulin	Plasma or serum insulin concentration in pmol/L
Glucose	Plasma or serum glucose concentration in mmol/L

Details

These functions deliver estimates for thyroid’s secretory capacity (SPINA-GT), total step-up deiodinase activity (SPINA-GD), Jostel’s TSH index (TSHI) and thyrotroph thyroid hormone sensitivity index (TTSI), and for the secretory capacity of pancreatic beta cells (SPINA-GBeta), insulin receptor gain (SPINA-GR), a static disposition index (SPINA-DI) as well as corresponding HOMA and QUICKI approaches (HOMA-Beta, HOMA-IR, HOMA-IS and QUICKI). The functions estimated.sGD and estimated.sTSHI return standardised (z-transformed) representations of SPINA-GD and Jostel’s TSH index, respectively.

Structure Parameter	S/R Function	Explanation	Reference Range
SPINA-GT	SPINA.GT or estimated.GT	Thyroid’s secretory capacity	1.41 – 8.67 pmol/s
SPINA-GD	SPINA.GD or estimated.GD	Sum activity of peripheral step-up deiodinases	20 – 40 nmol/s
SPINA-sGT	SPINA.SGD or estimated.sGD	z-transformed variant of SPINA-GD	–2 – +2
TSHI	estimated.TSHI	Jostel’s TSH index	1.3 – 4.1
sTSHI	estimated.sTSHI	Standardised TSH index	–2 – +2
TTSI	estimated.TTSI	Thyrotroph Thyroid Hormone Sensitivity Index	100 – 150
SPINA-GBeta	SPINA.GBeta	Secretory capacity of pancreatic beta-cells	0.64 – 3.73 pmol/s
SPINA-GR	SPINA.GR	Insulin receptor gain	1.41 – 9.00 mol/s
SPINA-DI	SPINA.DI	Static disposition index	4.01 – 7.65
HOMA-Beta	HOMA.Beta	Homeostasis model assessment – beta-cell function	45.4 – 179.4
HOMA-IR	HOMA.IR	Homeostasis model assessment – insulin resistance	< 2.5
HOMA-IS	HOMA.IS	Homeostasis model assessment – insulin sensitivity	> 0.4
QUICKI	QUICKI	Quantitativ insulin sensitivity check index	> 0.4

The functions estimated.GT, estimated.GD, estimated.sGD, estimated.TSHI, estimated.sTSHI and estimated.TTSI expect concentrations of free thyroid hormones. By contrast, the functions estimated.GTT and estimated.GDTT require total hormone concentrations.

SPINA.GT, SPINA.GD, SPINA.GTT, SPINA.GDTT and SPINA.sGD are alias function for estimated.GT, estimated.GD, estimated.GTT, estimated.GDTT and estimated.sGD, respectively.

All functions support vectorised calculations.

Value

Every function returns a numeric result representing a single “scalar” value or a vector, depending on the vector length of the arguments.

Examples

library(SPINA);

TSH <- c(1, 3.24, 0.7);
FT4 <- c(16.5, 7.7, 9);
FT3 <- c(4.5, 28, 6.2);

print(paste("GT^:", SPINA.GT(TSH, FT4)));
#> [1] "GT^: 4.696993125"      "GT^: 1.08063057191358" "GT^: 3.36719507142857"
print(paste("GD^:", SPINA.GD(FT4, FT3)));
#> [1] "GD^: 25.2176153706294" "GD^: 336.22895406993"  "GD^: 63.6968730188034"
print(paste("sGD^:", SPINA.sGD(FT4, FT3)));
#> [1] "sGD^: -0.956476925874126" "sGD^: 61.245790813986"   
#> [3] "sGD^: 6.73937460376069"

# Source:
# Pilo A, Iervasi G, Vitek F, Ferdeghini M, Cazzuola F,
# Bianchi R. Thyroidal and peripheral production of 
# 3,5,3'-triiodothyronine in humans by multicompartmental 
# analysis. Am J Physiol. 1990 Apr;258(4 Pt 1):E715-26. 
# PMID 2333963.

# BSA: body surface area in m^2
# IDV: initial distribution volume
# TT4: total T4 in mcg/dl
# TT3: total T3 in ng/ml
# FT4: free T4 in pg/ml
# FT3: free T3 in pg/ml
# TT4.SI: total T4 in nmol/l
# TT3.SI: total T3 in nmol/l
# FT4.SI: free T4 in pmol/l
# FT3.SI: free T3 in pmol/l
# SR: secretion rate
# CR.F, CR.S and CR.T: conversion rate (fast pool, slow pool and total)
# PAR: plasma apperance rate
# PR: production rate
# CR.6, CR.2, CR.0: conversion ratio from 6-compartment, 2-compartment and noncompartmental model

t3.mc <- data.frame(Sex = c("m", "f", "m", "m", "m", "m", "m", "m", "f", "m", "f", "m", "f", "f"), 
Age = c(54, 43, 31, 65, 44, 26, 27, 19, 53, 36, 48, 20, 44, 59),
Body.Mass = c(83, 68.5, 83, 69, 75, 73, 82, 63, 66.5, 72, 53, 65.5, 63, 60),
BSA = c(2.02, 1.7, 2.02, 1.73, 1.8, 1.9, 1.98, 1.8, 1.69, 1.81, 1.49, 1.79, 1.75, 1.57),
IDV.T4 = c(3801, 2272, 2686, 2726, 2632, 2804, 2770, 3119, 2749, 2860, 2467, 3624, 2965, 2327),
TT4 = c(8, 10.4, 7.9, 8, 8.8, 6.5, 7.7, 7.2, 6.6, 8.3, 9.5, 6.5, 7.9, 9.6),
TT4.SI = c(8, 10.4, 7.9, 8, 8.8, 6.5, 7.7, 7.2, 6.6, 8.3, 9.5, 6.5, 7.9, 9.6) * 12.87,
TT3 = c(1.23, 1.1, 1.32, 1.03, 1.33, 1.07, 1.4, 1.2, 1.36, 1.08, 1.21, 1.26, 1.21, 1.02),
TT3.SI = c(1.23, 1.1, 1.32, 1.03, 1.33, 1.07, 1.4, 1.2, 1.36, 1.08, 1.21, 1.26, 1.21, 1.02) * 1.54,
FT4 = c(10.1, 10.5, 8.8, 13.1, 11.1, 8.8, 10.2, 8.9, 6.9, 9, 10.5, 10.4, 11.8, 8.4),
FT4.SI = c(10.1, 10.5, 8.8, 13.1, 11.1, 8.8, 10.2, 8.9, 6.9, 9, 10.5, 10.4, 11.8, 8.4) * 1.287,
FT3 = c(4.3, 5.7, 4.3, 4.4, 3.5, 3.4, 4.1, 4.1, 3.6, 2.6, 3.8, 4.1, 5, 4.3),
FT3.SI = c(4.3, 5.7, 4.3, 4.4, 3.5, 3.4, 4.1, 4.1, 3.6, 2.6, 3.8, 4.1, 5, 4.3) * 1.54,
TSH = c(1.2, 1.4, 1, 1.8, 1.5, 1.5, 2, 1.9, 1.4, 1.8, 1.1, 1.3, 2, 1.5),
SR.T4 = c(44.5, 55.5, 45.3, 59.3, 59.2, 41.5, 50.9, 57.7, 54.3, 51.8, 76.5, 61.1, 65.7, 62.9), 
SR.T3 = c(1.98, 4.45, 7.05, 3.14, 5.95, 5.31, 3.51, 4.15, 0.91, 1.4, 2.89, 2.47, 2.64, 0.88),
CR.F.mean = c(12.3, 6.71, 8.73, 9.32, 8.75, 9.14, 10.6, 9.35, 7.9, 12.6, 13.1, 17.3, 14.5, 9.07),
CR.S.mean = c(3.7, 1.11, 1.06, 0.18, 1.2, 0.52, 0.4, 6.74, 3.39, 0.38, 1.55, 2.02, 2.37, 3.64),
CR.T.mean = c(12.3, 6.71, 8.73, 9.32, 8.75, 9.14, 10.6, 9.35, 7.9, 12.6, 13.1, 17.3, 14.5, 9.07) + c(3.7, 1.11, 1.06, 0.18, 1.2, 0.52, 0.4, 6.74, 3.39, 0.38, 1.55, 2.02, 2.37, 3.64),
PAR.T3 = c(16.7, 11.8, 16.4, 12.4, 15.5, 14.7, 14.2, 18.8, 11.4, 14.1, 16.9, 21.1, 18.5, 12.6),
PR.T3.mean = c(18, 12.3, 16.8, 12.6, 15.9, 15, 14.5, 20.2, 12.2, 14.4, 17.5, 21.8, 19.5, 13.6),
PR.T3 = c(20, 14.4, 18.9, 15.2, 17.6, 17.3, 16.1, 21.2, 12.9, 16.3, 19.8, 24.1, 22.4, 14.6),
CR.S = c(12.3, 9.02, 11.7, 9.51, 10.6, 10.5, 9.5, 12.8, 7.74, 9.78, 12.2, 14.4, 13.9, 8.87),
CR.6 = c(42.9, 16.9, 25.8, 19.2, 20.1, 27.8, 25.8, 33.4, 24.8, 30, 22.8, 37.9, 30.7, 24.1),
CR.2 = c(41, 16.5, 25.7, 19.4, 19.9, 27.8, 25.8, 31.3, 23.9, 30.1, 22.7, 37.6, 30.2, 23.1),
CR.0 = c(39.3, 15.6, 24.2, 18.5, 19.1, 26.9, 25.2, 30.8, 22.5, 29.1, 21.5, 35, 28.5, 22.5),
QP = c(2.31, 1.47, 1.76, 1.62, 1.95, 1.58, 1.96, 2.08, 2.21, 1.71, 2, 2.55, 2.06, 1.51),
QF = c(3.22, 2.85, 2.86, 3.55, 2.55, 3.04, 2.87, 3.66, 3.31, 2.9, 3.18, 3.94, 4.35, 2.82),
QS = c(25.8, 18.3, 22.6, 19, 15.4, 14.2, 14.8, 19.4, 18, 18.7, 15.4, 30.1, 25.7, 17.8),
QT = c(31.3, 22.6, 27.3, 24, 19.9, 18.8, 19.6, 25.2, 23.5, 23.3, 20.6, 36.6, 32.2, 22.2)
)

t3.mc$GT <- SPINA.GT(t3.mc$TSH, t3.mc$FT4.SI);
t3.mc$GD <- SPINA.GD(t3.mc$FT4.SI, t3.mc$FT3.SI);

print(t3.mc$GT);
#>  [1] 3.248033 3.040833 3.224016 3.235143 3.072585 2.435923 2.366721 2.128005
#>  [9] 1.998262 2.222617 3.590382 3.165398 2.737971 2.325199
print(t3.mc$GD);
#>  [1] 47.10442 60.06211 54.06285 37.16202 34.88677 42.74737 44.47320 50.96911
#>  [9] 57.72506 31.96275 40.04141 43.61797 46.88182 56.63721

Insulin <- 63.01;
Glucose <- 4.34;

print(paste("GBeta^:", SPINA.GBeta(Insulin, Glucose)));
#> [1] "GBeta^: 2.7988635483871"
print(paste("GR^:", SPINA.GR(Insulin, Glucose)));
#> [1] "GR^: 2.31865876698364"
print(paste("DI:", SPINA.DI(Insulin, Glucose)));
#> [1] "DI: 6.48960950405869"

Important hints

The software functions described in this document are intended for research use only.

Concentrations of hormones and metabolites should have been obtained simultaneously in order to avoid bias by transition effects.

Calculating GT in patients who are treated with levothyroxine (L-T4) is of little if any value. Likewise, it is not recommended to calculate GD in patients who receive substitution therapy with liothyronine (L-T3) or triiodothyroacetate (TRIAC) or to calculate SPINA-GBeta (including its derivative SPINA-DI) in persons on insulin therapy. It may be interesting, however, to obtain a value for the unaffected structural parameter in affected cases, e.g. for SPINA-GD in patients on L-T4 substitution or for SPINA-GR in persons on insulin (provided a sufficient delay after administration of short-term insulin).

Usage of SPINA implies that you agree to its license and conditions with respect of the council directive 93/42/EEC of the European Union. This information is included with the license file that comes with SPINA Functions, and it is available online from https://spina.sourceforge.net.

References

Dietrich JW, Boehm BO: Equilibrium behaviour of feedback-coupled physiological saturation kinetics. In: Cybernetics and Systems 2006. Volume 1, edn. Edited by Trappl R. Vienna: Austrian Society for Cybernetic Studies; 2006: 269-274.
Dietrich JW, Tesche A, Pickardt CR, Mitzdorf U: Thyrotropic Feedback Control: Evidence for an Additional Ultrashort Feedback Loop from Fractal Analysis. Cybernetics and Systems 2004, 35(4):315-331.
Dietrich JW, Dasgupta R, Anoop S, Jebasingh F, Kurian ME, Inbakumari M, Boehm BO, Thomas N: SPINA Carb: a simple mathematical model supporting fast in-vivo estimation of insulin sensitivity and beta cell function. Sci Rep 2022, 12(1):17659.
Dietrich JW, Landgrafe-Mende G, Wiora E, Chatzitomaris A, Klein HH, Midgley JE, Hoermann R: Calculated Parameters of Thyroid Homeostasis: Emerging Tools for Differential Diagnosis and Clinical Research. Front Endocrinol (Lausanne) 2016, 7:57.
Dietrich JW: Thyreotoxische Krise [Thyroid storm]. Medizinische Klinik, Intensivmedizin und Notfallmedizin 2012, 107(6):448-453.
Midgley JE, Hoermann R, Larisch R, Dietrich JW: Physiological states and functional relation between thyrotropin and free thyroxine in thyroid health and disease: in vivo and in silico data suggest a hierarchical model. Journal of clinical pathology 2013.
Dietrich JW: Der Hypophysen-Schilddrüsen-Regelkreis. Entwicklung und klinische Anwendung eines nichtlinearen Modells, vol. 2. Berlin: Logos-Verlag; 2002.
Dietrich JW, Landgrafe G, Fotiadou EH: TSH and Thyrotropic Agonists: Key Actors in Thyroid Homeostasis. Journal of thyroid research 2012, 2012:351864.
Liu S, Ren J, Zhao Y, Han G, Hong Z, Yan D, Chen J, Gu G, Wang G, Wang X et al: Nonthyroidal illness syndrome: is it far away from Crohn’s disease? Journal of clinical gastroenterology 2013, 47(2):153-159.
Rosolowska-Huszcz D, Kozlowska L, Rydzewski A: Influence of low protein diet on nonthyroidal illness syndrome in chronic renal failure. Endocrine 2005, 27(3):283-288.
Han G, Ren J, Liu S, Gu G, Ren H, Yan D, Chen J, Wang G, Zhou B, Wu X et al: Nonthyroidal illness syndrome in enterocutaneous fistulas. American journal of surgery 2013, 206(3):386-392.
Chatzitomaris A, Hoermann R, Midgley JE, Hering S, Urban A, Dietrich B, Abood A, Klein HH, Dietrich JW: Thyroid Allostasis-Adaptive Responses of Thyrotropic Feedback Control to Conditions of Strain, Stress, and Developmental Programming. Front Endocrinol (Lausanne) 2017, 8:163.
Hoermann R, Midgley JE, Larisch R, Dietrich JW: Is pituitary TSH an adequate measure of thyroid hormone-controlled homoeostasis during thyroxine treatment? European journal of endocrinology / European Federation of Endocrine Societies 2013, 168(2):271-280.
Hoermann R, Midgley JE, Giacobino A, Eckl WA, Wahl HG, Dietrich JW, Larisch R: Homeostatic equilibria between free thyroid hormones and pituitary thyrotropin are modulated by various influences including age, body mass index and treatment. Clinical endocrinology 2014, 81(6):907-915.
Dietrich JW, Abood A, Dasgupta R, Anoop S, Jebasingh FK, Spurgeon R, Thomas N, Boehm BO: A novel simple disposition index (SPINA-DI) from fasting insulin and glucose concentration as a robust measure of carbohydrate homeostasis. J Diabetes 2024.
Jostel A, Ryder WD, Shalet SM: The use of thyroid function tests in the diagnosis of hypopituitarism: definition and evaluation of the TSH Index. Clinical endocrinology 2009, 71(4):529-534.
Pohlenz J, Weiss RE, Macchia PE, Pannain S, Lau IT, Ho H, Refetoff S: Five new families with resistance to thyroid hormone not caused by mutations in the thyroid hormone receptor beta gene. The Journal of clinical endocrinology and metabolism 1999, 84(11):3919-3928.
Pilo A, Iervasi G, Vitek F, Ferdeghini M, Cazzuola F, Bianchi R: Thyroidal and peripheral production of 3,5,3’-triiodothyronine in humans by multicompartmental analysis. Am J Physiol 1990, 258(4 Pt 1):E715-726.