Understanding M-Values by Erik C
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Understanding M-values By Erik C. Baker, P.E. In conjunction with an array of hypothetical "tissue" compartments, gas loading calculations and M-values compose the major elements of the dissolved gas or "Haldanian" decompression model. Through the use of widely-available desktop computer programs, technical divers rely on this model for their decompression safety. A good understanding of M-values can help divers to determine appropriate conservatism factors and evaluate the adequacy of various decompression profiles for a particular dive. hat are M-values? The term without experiencing symptoms of DCS. nitrogen and helium for each "M-value" was coined by Because the ambient pressure at 33 fsw compartment at each depth as the "M- Robert D. Workman in the depth is twice that at sea level, Haldane value." Next, he made a "linear mid-1960's when he was doing concluded that a ratio of 2:1 for tolerated projection" of these M-values as a decompression research for the U.S. overpressure above ambient could be function of depth and found that it was a Navy Experimental Diving Unit used as the ascent limiting criteria. This reasonably close match to the actual data. (NEDU). Workman was a medical approximate ratio was used by Haldane to He made the observation that "a linear doctor with the rank of Captain in the develop the first decompression tables. projection of M-values is useful for Medical Corps of the U.S. Navy. In later years, and up until the 1960's, computer programming as well." The "M" in M-value stands for other ratios were used by various "Maximum." For a given ambient modelers for the different half-time THE WORKMAN M-VALUES pressure, an M-value is defined as the compartments. Most of the U.S. Navy maximum value of inert gas pressure decompression tables were calculated Workman's presentation of M-values in (absolute) that a hypothetical "tissue" using this supersaturation ratio method. the form of a linear equation was a compartment can "tolerate" without However, there was a problem. Many significant step in the evolution of the presenting overt symptoms of of the tables produced by this method dissolved gas decompression model. His decompression sickness (DCS). M- were deficient when it came to deeper M-values established the concept of a values are representative limits for the and longer dives. Robert Workman linear relationship between depth tolerated gradient between inert gas began a systematic review of the pressure [or ambient pressure] and the pressure and ambient pressure in each decompression model including previous tolerated inert gas pressure in each compartment. Other terms used for research that had been performed by the "tissue" compartment. This concept is an M-values are "limits for tolerated U.S. Navy. He arrived at some important element of the present-day overpressure," "critical tensions," and important conclusions. First of all, he dissolved gas model as applied by a "supersaturation limits." The term M- recognized that Haldane's original ratio variety of modelers. value is commonly used by of 2:1 (based on air) was really a ratio of Workman expressed his M-values in decompression modelers. 1.58:1 if you considered only the partial the slope-intercept form of a linear pressure of the inert gas in air - nitrogen. equation (see Figure 1). His surfacing HISTORICAL BACKGROUND [By that time in decompression research value was designated MO [pronounced it was known that oxygen was not a "M naught"]. This was the intercept In the dissolved gas or "Haldanian" significant factor in DCS; it was the inert value in the linear equation at zero depth decompression model, gas loading gases like nitrogen and helium that were pressure (gauge) at sea level. The slope calculations for each hypothetical "tissue" the culprits.] In his review of the research in the linear equation was designated compartment are compared against data, Workman found that the "tissue M [pronounced "delta M"] and "ascent limiting criteria" to determine the ratios" for tolerated overpressure varied represented the change in M-value with safe profile for ascent. In the early years by half-time compartment and by depth. change in depth pressure. of the model, including the method The data showed that the faster half-time developed by John S. Haldane in 1908, compartments tolerated a greater THE BÜHLMANN M-VALUES the ascent limiting criteria was in the overpressure ratio than the slower form of "supersaturation ratios." For compartments, and that for all Professor Albert A. Bühlmann, M.D., example, Haldane found that a diver compartments the tolerated ratios became began doing decompression research in whose "tissues" were saturated by less with increasing depth. Then, instead 1959 in the Laboratory of Hyperbaric breathing air at a depth of 33 fsw could of using ratios, Workman described the Physiology at the University Hospital in ascend directly to the surface (sea level) maximum tolerated partial pressure of Zürich, Switzerland. Bühlmann 1 continued his research for over thirty years and made a number of important Pressure Graph: Workman-style M-values contributions to decompression science. In 1983 he published the first edition (in versus Bühlmann-style M-values German) of a successful book entitled y l e Decompression - Decompression e e e n n n v i i i L L Sickness. An English translation of the e L L e e re u e u l u a l book was published in 1984. t a s a s e v u v - e l r S - M Bühlmann’s book was the first nearly P o t M n t s a n n complete reference on making n a e b a i e b r m a m l m decompression calculations that was u h , k A s r ü e widely-available to the diving public. As s o y B r y e W r a result, the "Bühlmann algorithm" u x s P x s became the basis for most of the world’s e slope = 1.0 e c r a in-water decompression computers and f P r u do-it-yourself desktop computer s S programs. Three more editions of the a Workman M = G t slope book were published in German in 1990, r 1993, and 1995 under the name e n I Workman M = intercept at Tauchmedizin or "Diving Medicine." [An t O n zero depth pressure (gauge) English translation of the 4th Edition of e y m x the book (1995) is in preparation for t r publication]. a p Bühlmann Coefficient b = Bühlmann’s method for m reciprocal of slope (1/b = slope) decompression calculations was similar o to the one that Workman had prescribed. C Bühlmann Coefficient a = intercept at This included M-values which expressed zero ambient pressure (absolute) a linear relationship between ambient 0 pressure and tolerated inert gas pressure 0 x in the hypothetical "tissue" Ambient Pressure, absolute compartments. The major difference between the two approaches was that Figure 1 Workman’s M-values were based on depth pressure (i.e. diving from sea level) decompression trials). The ZH-L16A set reciprocal of the slope. [Note: the and Bühlmann’s M-values were based on has sixteen pairs of coefficients for Coefficient a does not imply that humans absolute pressure (i.e. for diving at sixteen half-time compartments and these can withstand zero absolute pressure! altitude). This makes sense, of course, M-values were mathematically-derived This is simply a mathematical since Workman was concerned with the from the half-times based on the tolerated requirement for the equation. The lower diving activities of the U.S. Navy surplus volumes and solubilities of the limit for ambient pressure in the (presumably performed at sea level) inert gases. The ZH-L16A set of M- application of the Bühlmann M-values is while Bühlmann was concerned with values for nitrogen is further divided into on the order of 0.5 atm/bar.] diving activities in the high mountain subsets B and C because the lakes of Switzerland. mathematically-derived set A was found DCAP AND DSAT M-VALUES Bühlmann published two sets of M- empirically not to be conservative enough values which have become well-known in in the middle compartments. The Many technical divers will recognize the diving circles; the ZH-L12 set from the modified set B (slightly more 11F6 set of M-values used by Hamilton 1983 book, and the ZH-L16 set(s) from conservative) is suggested for table Research’s Decompression Computation the 1990 book (and later editions). The calculations and the modified set C and Analysis Program (DCAP). This set "ZH" in these designations stands for (somewhat more conservative) is or "matrix" of M-values was determined "Zürich" (named after his hometown), suggested for use with in-water by Dr. Bill Hamilton and colleagues the "L" stands for "linear," and the "12" decompression computers which during development of new air or "16" represents the number of pairs of calculate in real-time. decompression tables for the Swedish coefficients (M-values) for the array of Similar to the Workman M-values, Navy. In addition to air diving, the 11F6 half-time compartments for helium and the Bühlmann M-values are expressed in M-values have worked well for trimix nitrogen. The ZH-L12 set has twelve the slope-intercept form of a linear diving and are the basis for many custom pairs of coefficients for sixteen half-time equation (see Figure 1). The Coefficient decompression tables in use by technical compartments and these M-values were a is the intercept at zero ambient pressure divers.