Elimination Theory for Nonlinear Parameter Estimation

The work presented here exploits elimination theory (solving systems of polynomial equations in several variables) [1][2] to perform nonlinear parameter identification. In particular show how this technique can be used to estimate the rotor time constant and the stator resistance values of an induction machine. Although the example here is restricted to an induction machine, parameter estimation is applicable to many practical engineering problems. In [3], L. Ljung has outlined many of the challenges of nonlinear system identification as well as its particular importance for biological systems. In these types of problems, the model developed for analysis is typically a nonlinear state space model with unknown parameter values. The typical situation is that only a few of the state variables are measurable requiring that the system be reformulated as a nonlinear input-output model. In turn, resulting the nonlinear input-output model is almost always nonlinear in the parameters. Towards that end, differential algebra tools for analysis of nonlinear systems have been developed by Michel Fliess [4][5] and Diop [6]. Moreover, Ollivier [7] as well as Ljung and Glad [8] have developed the use of the characteristic set of an ideal as a tool for identification problems. The use of these differential algebraic methods for system identification have also been considered in [9], [10]. The focus of their research has been the determination of a priori identifiability of a given system model. However, as stated in [10], the development of an efficient algorithm using these differential algebraic techniques is still unknown. Here, in contrast, a method for which one can actually numerically obtain the numerical value of the parameters is presented. We also point out that [11] has also done work applying elimination theory to systems problems

Effect of insulin on system A amino acid transport in human skeletal muscle

Transmembrane transport of neutral amino acids in skeletal muscle is mediated by at least four different systems (system A, ASC, L, and Nm), and may be an important target for insulin's effects on amino acid and protein metabolism. We have measured net amino acid exchanges and fractional rates of inward (k(in), min-1) and outward (kout, min-1) transmembrane transport of 2-methylaminoisobutyric acid (MeAIB, a nonmetabolizable amino acid analogue, specific for system A amino acid transport) in forearm deep tissues (skeletal muscle), by combining the forearm perfusion technique and a novel dual tracer ([1-H3]-D-mannitol and 2-[1-14C]-methylaminoisobutyric acid) approach for measuring in vivo the activity of system A amino acid transport. Seven healthy lean subjects were studied. After a baseline period, insulin was infused into the brachial artery to achieve local physiologic hyperinsulinemia (76 +/- 8 microU/ml vs 6.4 +/- 1.6 microU/ml in the basal period, P < 0.01) without affecting systemic hormone and substrate concentrations. Insulin switched forearm amino acid exchange from a net output (-2,630 +/- 1,100 nmol/min per kig of forearm tissue) to a net uptake (1,610 +/- 600 nmol/min per kg, P < 0.01 vs baseline). Phenylalanine and tyrosine balances simultaneously shifted from a net output (-146 +/- 47 and -173 +/- 34 nmol/min per kg, respectively) to a zero balance (16.3 +/- 51 for phenylalanine and 15.5 +/- 14.3 nmol/min per kg for tyrosine, P < 0.01 vs baseline for both), showing that protein synthesis and breakdown were in equilibrium during hyperinsulinemia. Net negative balances of alanine, methionine, glycine, threonine and asparagine (typical substrates for system A amino acid transport) also were decreased by insulin, whereas serine (another substrate for system A transport) shifted from a zero balance to net uptake. Insulin increased k(in) of MeAIB from a basal value of 11.8.10(-2) +/- 1.7.10(-2).min-1 to 13.7.10(-2) +/- 2.2.10(-2).min-1 (P < 0.02 vs the postabsorptive value), whereas kout was unchanged. We conclude that physiologic hyperinsulinemia stimulates the activity of system A amino acid transport in human skeletal muscle, and that this effect may play a role in determining the overall concomitant response of muscle amino acid/protein metabolism to insulin

Role of tissue specific blood flow and tissue recruitment in insulin-mediated glucose uptake of human skeletal muscle

BACKGROUND: Conflicting evidence exists concerning whether insulin-induced vasodilation plays a mechanistic role in the regulation of limb glucose uptake. It can be predicted that if insulin augments blood flow by causing tissue recruitment, this mechanism would enhance limb glucose uptake. METHODS AND RESULTS: Twenty healthy subjects were studied with the forearm perfusion technique in combination with the euglycemic insulin clamp technique. Ten subjects were studied at physiological insulin concentrations (approximately 400 pmol/L) and the other 10 at supraphysiological insulin concentrations (approximately 5600 pmol/L). Four additional subjects underwent a saline control study. Pulse injections of a nonmetabolizable extracellular marker (1-[3H]-L-glucose) were administered into the brachial artery, and its washout curves were measured in one ipsilateral deep forearm vein and used to estimate the extracellular volume of distribution and hence the amount of muscle tissue drained by the deep forearm vein. Both during saline infusion and at physiological levels of hyperinsulinemia we observed no changes in blood flow and/or muscle tissue drained by the deep forearm vein. However, supraphysiological hyperinsulinemia accelerated total forearm blood flow (45.0+/-1.8 versus 36.5+/-1.3 mL x min(-1) x kg(-1), P<0.01) and increased the amount of muscle tissue drained by the deep forearm vein (305+/-46 versus 229+/-32 g, P<0.05). The amount of tissue newly recruited by insulin was strongly correlated to the concomitant increase in tissue glucose uptake (r=0.789, P<0.01). CONCLUSIONS: Acceleration of forearm blood flow mediated by supraphysiological hyperinsulinemia is accompanied by tissue recruitment, which may be a relevant determinant of forearm (muscle) glucose uptake

Glucose transport in human skeletal muscle: the in vivo response to insulin

Transmembrane glucose transport plays a key role in determining insulin sensitivity. We have measured in vivo WBGU, FGU, and K(in) and K(out) of 3-O-methyl-D-glucose in forearm skeletal muscle by combining the euglycemic clamp technique, the forearm-balance technique, and a novel dual-tracer (1-[3H]-L-glucose and 3-O-[14C]-methyl-D-glucose) technique for measuring in vivo transmembrane transport. Twenty-seven healthy, lean subjects were studied. During saline infusion, insulin concentration, FGU (n = 6), K(in), and K(out) (n = 4) were similar to baseline. During SRIF-induced hypoinsulinemia (insulin < 15 pM, n = 4) WBGU was close to 0, and FGU, K(in), and K(out) were unchanged from basal (insulin = 48 pM) values. During insulin clamps at plasma insulin levels of approximately 180 (n = 4), approximately 420 (n = 5), approximately 3000 (n = 4), and approximately 9500 pM (n = 4), WBGU was 14.2 +/- 1.3, 34.2 +/- 4.1 (P < 0.05 vs. previous step), 55.8 +/- 1.8 (P < 0.05 vs. previous step), and 56.1 +/- 6.3 mumol.min-1.kg-1 of body weight (NS vs. previous step), respectively. Graded hyperinsulinemia concomitantly increased FGU from a basal value of 4.7 +/- 0.5 mumol.min-1.kg-1 up to 10.9 +/- 2.3 (P < 0.05 vs. basal value), 26.6 +/- 4.5 (P < 0.05 vs. previous step), 54.8 +/- 4.3 (P < 0.05 vs. previous step), and 61.1 +/- 10.8 mumol.min-1.kg-1 of forearm tissues (NS vs. previous step), respectively.(ABSTRACT TRUNCATED AT 250 WORDS