An algebraic solution to dead space determination according to Fowler's graphical method

According to Fowler's method, anatomical dead space (VD) can be determined graphically or computer-aided by iteration procedures by which phase III of a fraction-volume expirogram F(V) is back-extrapolated by a straight line R(V). Whereas Fowler visually partitioned phase II into two equal areas bordered by F(V), R(V), and VD, in the present paper the area between F(V) and R(V) is set equal to the area of a trapezoid, one side of which is the unknown VD to be determined. We obtained two algebraic equations for both possible conditions, nonsloping and sloping alveolar plateau, and, as the main result, an even more general third equation that includes both Bohr's and Fowler's solution. The formulas exactly represent Fowler's graphical method and can be applied to all gases which are applicable in dead space determination. The derived equations were tested in experimental situations, showing equality between values of dead space determined by using the algebraic solution and the graphical method. Their major advantage is facilitating and speeding up computer-aided on-line determinations of VD.