Lactate after exercise in man: II. Mathematical model
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Summary
- 1.
The total lactate distribution space is composed of two compartments, i.e., (M) the previously working muscles and (S) the remaining lactate space;
- 2.
The rates of lactate release and utilization in (M) and (S) are proportional to the lactate contents of these compartments;
- 3.
The post-exercise lactate production rates in (M) and (S) are constants;
- 4.
Arterial lactate concentration can represent the average lactate concentration in (S).
Consideration of experimental facts reported in the literature shows these assumptions to be reasonable. The relationships obtained express the compatibility of parameters and time functions concerning lactate concentrations, as well as rates of production, uptake, release, and utilization. They open the way to various applications, especially those involving numerical fits to observed time courses of lactate concentrations.
Key words
Two-compartment model Lactate kinetics, uptake, release, utilizationList of Abbreviations and Symbols
- α12, α21
Coefficients denoting efficiency in lactate transfer from (M) to (S) and (S) to (M), respectively (min−1)
- a, a0
Coefficients of linear fits to observed lactate removal rates
- b0, b1, b2
Coefficients of linear fits to observed lactate releases
- (BS)
Blood space
- c2, d2
Coefficients denoting efficiency in lactate utilization by (M) and (S) (min−1)
- C1, C2
Amplitudes of the exponential terms of L M (t) (mmol·l−1)
- D1, D2
Amplitudes of the exponential terms of L s (t) (mmol·l−1)
- L
Lactate concentration (mmol·l−1)
- La(t)
Lactate concentration in arterial blood at time t obtained by fits to experimental data (mmol·l−1)
- LM(t), LS(t)
Lactate concentrations in (M) and (S) at time t (mmol·l−1)
- (LU), (LR)
Lactate uptake and lactate release rates (mmol·l−1)
- (LU)M, (LR)M
Simultaneous muscular lactate uptake and lactate release rates (mmol·min−1)
- LV(t)
Lactate concentration in blood leaving (M) at time t (mmol·l−1)
- (M), (S)
Worked muscle space and remaining lactate space
- (MRR)
Metabolic removal rate of lactate (mmol·min−1)
- (PR)
Lactate production rate (mmol·min−1)
- (PR)M=c1; (PR)S=d1
Lactate production rates in (M) and (S), respectively (mmol·min−1)
- q (t)
Blood flow perfusing (M) at time t (l·min−1)
- (REX)
Rate of lactate excretion (mmol·min−1)
- r1, r2
Roots of the characteristic equation (min−1)
- t
Time after the end of exercise (min)
- (TLS)
Total lactate distribution space
- V
Volume of a compartment (1)
- VM, VS
Volumes of (M) and (S) (1)
- VMS
V M to V S ratio
- VSM
V S to V M ratio
- γ1, γ2
Theoretical velocity constants of the time functions (min−1)
- ΦmM(t), ΦmS(t)
Lactate utilization rates in (M) and (S) (mmol·min−1)
- ΦMS(t)
Net muscular release rate of lactate (mmol·min−1)
- Μ
Net muscular release rate of lactate at t→∞ (mmol·min−1)
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References
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