MATHEMATICAL MODELS OF DUAL TRANSMISSIVITY AND EXAMPLES OF THEIR APPLICATION IN INTERPRETING PIEZOMETRIC TESTS CONDUCTED IN THE BEŁCHATÓW LIGNITE MINE

Piezometric tests such as the slug test or PARAMEX test usually result in observing damped oscillations or exponential movement of the water level. However, during some tests, a bi-exponential response of the water table has been recorded. Bi-exponential movement may indicate the presence of a dual-permeability medium around the piezometer screen. Such medium is composed of two subdomains, each characterized by different hydraulic properties (including transmissivity, T). The paper aims to present two mathematical models – the piecewise exponential model and the bi-exponential model – which were applied in order to interpret the results of slug test conducted in heterogeneous sediments of the Bełchatów Lignite Mine. Theoretical background, interpretation algorithms and examples of dual transmissivity estimation for several chosen piezometers are presented. All necessary calculations were performed using Paramex 4 and MATLAB software. Furthermore, the limitations of the interpretation algorithms are discussed.

Noninvasive estimation of microvascular O2 provision during exercise on-transients in healthy young males

Two methods for estimating changes in microvascular O2 delivery during the on-transient of exercise were evaluated. They were tested to assess the role of the adjustment of the estimated microvascular O2 delivery in the speeding of V̇o2 kinetics during a Mod1-Hvy-Mod2 protocol (Mod, moderate-intensity exercise; Hvy, heavy-intensity “priming” exercise), in which Mod2 is preceded by a bout of Hvy. Mod pulmonary V̇o2 (V̇o2p) and deoxy-hemoglobin [HHb] data were collected in 12 males (23 ± 3 yr); response profiles were fit with a monoexponential. Signals were also 1) scaled to a relative % of the response (0–100%) to calculate the [HHb]/V̇o2 ratio for each individual and 2) rearranged in the Fick equation for estimation of capillary blood flow (Qcap). A transient [HHb]/V̇o2 “overshoot” observed in Mod1 (1.06 ± 0.05; P < 0.05) was absent during Mod2 (1.01 ± 0.06; P > 0.05); reductions in the [HHb]/V̇o2 ratio (Mod1 − Mod2) were related to reductions in phase II τV̇o2p ( r = 0.82; P < 0.05). For Qcap, a near-exponential response was observed in 8/12 subjects in Mod1 and only in 4/12 subjects in Mod2. The Qcap profile was shown to be highly dependent on the [HHb] baseline-to-amplitude ratio. Thus, accurate and physiologically consistent estimations of Qcap were not possible in most cases. This study confirmed that priming exercise results in an improved O2 delivery as shown by the decreased [HHb]/V̇o2 ratio that was related to the smaller τV̇o2 in Mod2. Additionally, this study suggested that Qcap analysis may not be valid and should be interpreted with caution when assessing microvascular delivery of O2.