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. ratio was used by Haldane to develop the hat are M-values? The term "M-value" W first decompression tables. In later years, was coined by Robert D. Workman in the and up until the 1960's, other ratios were mid-1960's when he was doing used by various modelers for the different decompression research for the U.S. Navy half-time compartments. Most of the U.S. Experimental Diving Unit (NEDU). Navy decompression tables were Workman was a medical doctor with the calculated using this supersaturation ratio rank of Captain in the Medical Corps of the method. U.S. Navy. However, there was a problem. The "M" in M-value stands for Many of the tables produced by this "Maximum." For a given ambient method were deficient when it came to pressure, an M-value is defined as the deeper and longer dives. Robert maximum value of inert gas pressure Workman began a systematic review of (absolute) that a hypothetical "tissue" the decompression model including compartment can "tolerate" without previous research that had been presenting overt symptoms of performed by the U.S. Navy. He arrived at decompression sickness (DCS). M-values some important conclusions. First of all, are representative limits for the tolerated he recognized that Haldane's original ratio gradient between inert gas pressure and of 2:1 (based on air) was really a ratio of ambient pressure in each compartment. 1.58:1 if you considered only the partial Other terms used for M-values are "limits pressure of the inert gas in air - nitrogen. for tolerated overpressure," "critical [By that time in decompression research it tensions," and "supersaturation limits." was known that oxygen was not a The term M-value is commonly used by significant factor in DCS; it was the inert decompression modelers. gases like nitrogen and helium that were the culprits.] In his review of the HISTORICAL BACKGROUND research data, Workman found that the "tissue ratios" for tolerated overpressure In the dissolved gas or "Haldanian" varied by half-time compartment and by decompression model, gas loading depth. The data showed that the faster calculations for each hypothetical "tissue" half-time compartments tolerated a greater compartment are compared against overpressure ratio than the slower "ascent limiting criteria" to determine the compartments, and that for all safe profile for ascent. In the early years compartments the tolerated ratios became of the model, including the method less with increasing depth. Then, instead developed by John S. Haldane in 1908, of using ratios, Workman described the the ascent limiting criteria was in the form maximum tolerated partial pressure of of "supersaturation ratios." For example, nitrogen and helium for each compartment Haldane found that a diver whose at each depth as the "M-value." Next, he "tissues" were saturated by breathing air made a "linear projection" of these M- at a depth of 33 fsw could ascend directly values as a function of depth and found to the surface (sea level) without that it was a reasonably close match to the experiencing symptoms of DCS. Because actual data. He made the observation that the ambient pressure at 33 fsw depth is "a linear projection of M-values is useful twice that at sea level, Haldane for computer programming as well." concluded that a ratio of 2:1 for tolerated overpressure above ambient could be used as the ascent limiting criteria. This approximate THE WORKMAN M-VALUES This included M-values which expressed a linear relationship between ambient Workman's presentation of M-values in the pressure and tolerated inert gas pressure form of a linear equation was a significant in the hypothetical "tissue" compartments. step in the evolution of the dissolved gas The major difference between the two decompression model. His M-values approaches was that Workman's M-values established the concept of a linear were based on depth pressure (i.e. relationship between depth pressure [or diving from sea level) and Buhlmann's M- ambient pressure] and the tolerated inert values were based on absolute pressure gas pressure in each "tissue" (i.e. for diving at altitude). This makes compartment. This concept is an sense, of course, since Workman was important element of the present-day concerned with the diving activities of the dissolved gas model as applied by a U.S. Navy (presumably performed at sea variety of modelers. level) while Buhlmann was concerned with diving activities in the high mountain lakes Workman expressed his M-values of Switzerland. in the slope-intercept form of a linear equation (see Figure 1). His surfacing Buhlmann published two sets of value was M-values which have become well-known designated MO [pronounced "M naught"]. in diving circles; the ZH-L12 set from the This was the intercept value in the linear 1983 book, and the ZH-L16 set(s) from the equation at zero depth pressure (gauge) at 1990 book (and later editions). The "ZH" sea level. The slope in the linear equation in these designations stands for "Zurich" was designated M [pronounced "delta M"] (named after his hometown), the "L" and represented the change in M-value stands for "limits," and the "12" or "16" with represents the number of pairs of change in depth pressure. coefficients (M-values) for the array of half-time compartments for helium and THE BUHLMANN M-VALUES nitrogen. The ZH-L12 set has twelve pairs of coefficients for sixteen half-time Professor Albert A. Buhlmann, M.D., compartments and these M-values were began doing decompression research in determined empirically (i.e. with actual 1959 in the Laboratory of Hyperbaric decompression trials). The ZH-L16A set Physiology at the University Hospital in has sixteen pairs of coefficients for sixteen Zurich, Switzerland. Buhlmann continued half-time compartments and these M- his research for over thirty years and values were mathematically-derived from made a number of important contributions the half-times based to decompression science. In 1983 he on the tolerated surplus volumes and published the first edition (in German) of a solubilities of the inert gases. The ZH- successful book entitled Decompression - L16A set of M-values for nitrogen is further Decompression Sickness. An English divided into subsets B and C because the translation of the book was published in mathematically-derived set A was found 1984. Buhlmann's book was the first empirically not to be conservative enough nearly complete reference on making in the middle compartments. The modified decompression calculations that was set B (slightly more conservative) is widely-available to the diving public. As a suggested for table calculations and the result, the "Buhlmann algorithm" became modified set C (somewhat more the basis for most of the world's in-water conservative) is suggested for use with in- decompression computers and do-it- water decompression computers which yourself desktop computer programs. calculate in real-time. Three more editions of the book were published in German in 1990, 1993, and Similar to the Workman M-values, 1995 under the name Tauchmedizin or the Buhlmann M-values are expressed in "Diving Medicine." [An English translation the slope-intercept form of a linear of the 4th Edition of the book (1995) is in equation (see Figure 1). The Coefficient a preparation for publication]. is the intercept at zero ambient pressure (absolute) and the Coefficient b is the Buhlmann's method for reciprocal of the slope. [Note: the decompression calculations was similar to Coefficient a does not imply that humans the one that Workman had prescribed. can withstand zero absolute pressure! Buhlmann M-values is on the order of 0.5 This is simply a mathematical requirement atm/bar.] for the equation. The lower limit for ambient pressure in the application of the Pressure Graph: Workman-style M-values versus Bühlmann-style M-values y Ambient Pressure Line Bühlmann M-value Line y y Workman M-value Line x x slope = 1.0 Surface Pressure Pressure atSurface Sea Level Workman M = slope Workman M O = intercept at y zero depth pressure (gauge) x Bühlmann Coefficient b = reciprocal of slope (1/b = slope) Compartment Inert Gas Pressure, Gas absolute Inert Compartment Bühlmann Coefficient a = intercept at zero ambient pressure (absolute) 0 0 x Ambient Pressure, absolute Figure1 many custom decompression tables in use by technical divers. DCAP AND DSAT M-VALUES Many sport divers are familiar with Many technical divers will recognize the the Recreational Dive Planner (RDP) 11F6 set of M-values used by Hamilton distributed by the Professional Association Research's Decompression Computation of Diving Instructors (PADI). The M- and Analysis Program (DCAP). This set values used for the RDP were developed or "matrix" of M-values was determined by and tested by Dr. Raymond E. Rogers, Dr. Dr. Bill Hamilton and colleagues during Michael R. Powell, and colleagues with development of new air decompression Diving Science and Technology Corp. tables for the Swedish Navy. In addition to (DSAT), a corporate affiliate of PADI. The air diving, the 11F6 M-values have worked DSAT M-values were empirically verified well for trimix diving and are the basis for with extensive in-water diver testing and Doppler monitoring. been to become slightly more COMPARISON OF M-VALUES conservative.