Summary
Lactate movements during recovery following muscular exercise in man were studied by means of a two-compartment model. Mathematical discussion of the literal expressions obtained allows one to represent parameters concerning lactate exchange, utilization, and production in the previously working muscles and in the remaining lactate distribution space. It also shows that bi-exponential time courses predicted for muscular and blood lactate concentrations as well as for rates of lactate uptake, release, and utilization can denote several morphologies. All of the time evolutions for muscular and blood lactate concentrations found in the literature are consistent with these theoretical possibilities in the model. A numerical application confirms this concordance. Thus, this simple model, for which the basic assumptions were previously justified, appears to be qualitatively able to describe lactate exchanges and disappearance after exercise. A practical algorithm is put forward to display its possibilities and to test further its quantitative validity.
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Abbreviations
- α12, α21 :
-
Coefficients of efficiency in lactate transfer from (M) to (S) and (S) to (M), respectively (min−1)
- A 1, A 2 :
-
Amplitudes of the exponential terms of fits to L a (t) (mmol·l−1)
- (AS1), (AS2), (AS3), (AS4):
-
Assumptions on which the model is based
- “A-curves”:
-
Graphs of monotonic time functions
- “B-curves”:
-
Graphs of time functions showing an extremum and an inflexion point
- C 1, d 1 :
-
Lactate production rates in (M) and (S), respectively (mmol·min−1)
- c 2, d2 :
-
Coefficients of efficiency in lactate utilization by (M) and (S), respectively (min−1)
- C 1, C 2 :
-
Amplitudes of the exponential terms of L M (t) (mmol·l−1)
- D 1, D 2 :
-
Amplitudes of the exponential terms of L S (t) (mmol·l−1)
- (D 1), (D 2), (D 3):
-
Separating lines for definitions “(+)” and “(−)” of the parameters (Fig. 4)
- (F 1), (F 2):
-
Areas of validity of the model
- L a (t):
-
Lactate concentration in arterial blood at time t obtained by fits to experimental data (mmol·l−1)
- L M (t), L S (t):
-
Lactate concentrations in (M) and (S), respectively, at time t (mmol·l−1)
- L v (t):
-
Lactate concentration in blood leaving (M) at time t (mmol·l−1)
- L 1, L 2, L 3 :
-
Maximum allowable values for d 2 (Fig. 4) (min−1)
- (M), (S):
-
Worked muscle space and remaining lactate space
- ℳ1, ℳ2 :
-
Invariant points of (γ)
- (P 1), (P 2), (P 3):
-
Properties of the function y(t)
- q(t) :
-
Blood flow perfusing (M) at time t (l·min−1)
- t :
-
Time after the end of exercise (min)
- t 1, t 2 :
-
Instants at which y′ t (t) and y′' t (t) reduce to zero (min)
- V M , V S :
-
Volumes of (M) and (S), respectively (l)
- V MS :
-
V M to V S ratio
- V SM :
-
V S to V M ratio
- y t :
-
General form of time functions generated by the model (mmol·l−1 or mmol·min−1)
- α1, α2 :
-
Amplitudes of the transient terms of y(t) (mmol·l−1 or mmol·min−1)
- (γ):
-
Conics describing the relation between c 2 and d 2
- γ 1, γ 2 :
-
Velocity constants of the exponential fits to L a (t) (min−1)
- γ 1, γ 2 :
-
Theoretical velocity constants of the time functions (min−1)
- θ, θ :
-
Instants at which Φ MS (t) reduces to zero (min)
- Μ :
-
Net muscular release rate of lactate at t→∞ (mmol·min−1)
- Τ1, Τ1 :
-
Instants at which L M (t) crosses L S (t) (min)
- Φ mM (t), Φ mS (t):
-
Lactate utilization rates in (M) and (S), respectively (mmol·min−1)
- Φ MS (t):
-
Net muscular release rate of lactate (mmol·min−1)
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Zouloumian, P., Freund, H. Lactate after exercise in man: III. Properties of the compartment model. Europ. J. Appl. Physiol. 46, 149–160 (1981). https://doi.org/10.1007/BF00428867
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DOI: https://doi.org/10.1007/BF00428867