Understanding Mvalues By Erik C. Baker, P.E.


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1 Understanding values B Erik C. Baker, P.E. In conjunction with an arra of hpothetical "tissue" compartments, gas loading calculations and values compose the major elements of the dissolved gas or "Haldanian" decompression model. Through the use of widelavailable desktop computer programs, technical divers rel on this model for their decompression safet. A good understanding of values can help divers to determine appropriate conservatism factors and evaluate the adequac of various decompression profiles for a particular dive. hat are values? The term "value" was coined b Robert D. Workman in the mid0's when he was doing decompression research for the U.S. Nav Eperimental Diving Unit (NEDU). Workman was a medical doctor with the rank of Captain in the edical Corps of the U.S. Nav. The "" in value stands for "aimum." For a given ambient pressure, an value is defined as the maimum value of inert gas pressure (absolute) that a hpothetical "tissue" compartment can "tolerate" without presenting overt smptoms of decompression sickness (DCS).  values are representative limits for the tolerated gradient between inert gas pressure and ambient pressure in each compartment. Other terms used for values are "limits for tolerated overpressure," "critical tensions," and "supersaturation limits." The term  value is commonl used b decompression modelers. HISTORICAL BACKGROUND In the dissolved gas or "Haldanian" decompression model, gas loading calculations for each hpothetical "tissue" compartment are compared against "ascent limiting criteria" to determine the safe profile for ascent. In the earl ears of the model, including the method developed b John S. Haldane in 0, the ascent limiting criteria was in the form of "supersaturation ratios." For eample, Haldane found that a diver whose "tissues" were saturated b breathing air at a depth of fsw could ascend directl to the surface (sea level) without eperiencing smptoms of DCS. Because the ambient pressure at fsw depth is twice that at sea level, Haldane concluded that a ratio of : for tolerated overpressure above ambient could be used as the ascent limiting criteria. This approimate ratio was used b Haldane to develop the first decompression tables. In later ears, and up until the 0's, other ratios were used b various modelers for the different halftime compartments. ost of the U.S. Nav decompression tables were calculated using this supersaturation ratio method. However, there was a problem. an of the tables produced b this method were deficient when it came to deeper and longer dives. Robert Workman began a sstematic review of the decompression model including previous research that had been performed b the U.S. Nav. He arrived at some important conclusions. First of all, he recognized that Haldane's original ratio of : (based on air) was reall a ratio of.: if ou considered onl the partial pressure of the inert gas in air  nitrogen. [B that time in decompression research it was known that ogen was not a significant factor in DCS; it was the inert gases like nitrogen and helium that were the culprits.] In his review of the research data, Workman found that the "tissue ratios" for tolerated overpressure varied b halftime compartment and b depth. The data showed that the faster halftime compartments tolerated a greater overpressure ratio than the slower compartments, and that for all compartments the tolerated ratios became less with increasing depth. Then, instead of using ratios, Workman described the maimum tolerated partial pressure of nitrogen and helium for each compartment at each depth as the "value." Net, he made a "linear projection" of these values as a function of depth and found that it was a reasonabl close match to the actual data. He made the observation that "a linear projection of values is useful for computer programming as well." THE WORKAN VALUES Workman's presentation of values in the form of a linear equation was a significant step in the evolution of the dissolved gas decompression model. His values established the concept of a linear relationship between depth pressure [or ambient pressure] and the tolerated inert gas pressure in each "tissue" compartment. This concept is an important element of the presentda dissolved gas model as applied b a variet of modelers. Workman epressed his values in the intercept form of a linear equation (see Figure ). His surfacing value was designated O [pronounced " naught"]. This was the intercept value in the linear equation at zero depth pressure (gauge) at sea level. The in the linear equation was designated [pronounced "delta "] and represented the change in value with change in depth pressure. THE BÜHLANN VALUES Professor Albert A. Bühlmann,.D., began doing decompression research in in the Laborator of Hperbaric Phsiolog at the Universit Hospital in Zürich, Switzerland. Bühlmann
2 continued his research for over thirt ears and made a number of important contributions to decompression science. In he published the first edition (in German) of a successful book entitled Decompression  Decompression Sickness. An English translation of the book was published in. Bühlmann s book was the first nearl complete reference on making decompression calculations that was widelavailable to the diving public. As a result, the "Bühlmann algorithm" became the basis for most of the world s inwater decompression computers and doitourself desktop computer programs. Three more editions of the book were published in German in 0,, and under the name Tauchmedizin or "Diving edicine." [An English translation of the th Edition of the book () is in preparation for publication]. Bühlmann s method for decompression calculations was similar to the one that Workman had prescribed. This included values which epressed a linear relationship between ambient pressure and tolerated inert gas pressure in the hpothetical "tissue" compartments. The major difference between the two approaches was that Workman s values were based on depth pressure (i.e. diving from sea level) and Bühlmann s values were based on absolute pressure (i.e. for diving at altitude). This makes sense, of course, since Workman was concerned with the diving activities of the U.S. Nav (presumabl performed at sea level) while Bühlmann was concerned with diving activities in the high mountain lakes of Switzerland. Bühlmann published two sets of  values which have become wellknown in diving circles; the ZHL set from the book, and the ZHL set(s) from the 0 book (and later editions). The "ZH" in these designations stands for "Zürich" (named after his hometown), the "L" stands for "linear," and the "" or "" represents the number of pairs of coefficients (values) for the arra of halftime compartments for helium and nitrogen. The ZHL set has twelve pairs of coefficients for siteen halftime compartments and these values were determined empiricall (i.e. with actual Compartment Inert Gas Pressure, absolute 0 0 Figure Pressure Graph: Workmanstle values versus Bühlmannstle values Surface Pressure at Sea Level Workman value Line decompression trials). The ZHLA set has siteen pairs of coefficients for siteen halftime compartments and these values were mathematicallderived from the halftimes based on the tolerated surplus volumes and solubilities of the inert gases. The ZHLA set of  values for nitrogen is further divided into subsets B and C because the mathematicallderived set A was found empiricall not to be conservative enough in the middle compartments. The modified set B (slightl more conservative) is suggested for table calculations and the modified set C (somewhat more conservative) is suggested for use with inwater decompression computers which calculate in realtime. Similar to the Workman values, the Bühlmann values are epressed in the intercept form of a linear equation (see Figure ). The Coefficient a is the intercept at zero ambient pressure (absolute) and the Coefficient b is the Bühlmann value Line Bühlmann Coefficient b = reciprocal of (/b = ) Bühlmann Coefficient a = intercept at zero ambient pressure (absolute) Ambient Pressure Line Workman = Workman O = intercept at zero depth pressure (gauge) Ambient Pressure, absolute = reciprocal of the. [Note: the Coefficient a does not impl that humans can withstand zero absolute pressure! This is simpl a mathematical requirement for the equation. The lower limit for ambient pressure in the application of the Bühlmann values is on the order of 0. atm/bar.] DCAP AND DSAT VALUES an technical divers will recognize the F set of values used b Hamilton Research s Decompression Computation and Analsis Program (DCAP). This set or "matri" of values was determined b Dr. Bill Hamilton and colleagues during development of new air decompression tables for the Swedish Nav. In addition to air diving, the F values have worked well for trimi diving and are the basis for man custom decompression tables in use b technical divers. an sport divers are familiar with
3 the Recreational Dive Planner (RDP) distributed b the Professional Association of Diving Instructors (PADI). The values used for the RDP were developed and tested b Dr. Ramond E. Rogers, Dr. ichael R. Powell, and colleagues with Diving Science and Technolog Corp. (DSAT), a corporate affiliate of PADI. The DSAT values were empiricall verified with etensive inwater diver testing and Doppler monitoring. COPARISON OF VALUES Tables thru present a comparison of values for nitrogen and helium between the various Haldanian decompression algorithms discussed in this article. All values are presented in Workmanstle format. An evolution or refinement in the values is evident from Workman () to Bühlmann (0). The general trend has been to become slightl more conservative. This trend reflects a more intensive validation process (empirical testing) and includes the use of Doppler ultrasound monitoring for the presence and quantit of "silent bubbles" (bubbles which are detectable in the circulation but are not associated with overt smptoms of decompression sickness). CONSISTENCY OF VALUES One observation that can be made about the comparison between the values of the various algorithms is that there is not a great difference between them. In other words, there appears to be a certain consistenc between the values determined b various independent researchers around the globe. This is a good sign as it indicates that the science has determined a relativel consistent threshold for smptoms of decompression sickness across the human population. FORAT FOR VALUES values are often epressed in the form of a linear equation as in the Workmanstle or the Bühlmannstle. This format is ideal for computer programming since it allows the values to be calculated "onthefl" as the are needed. The linear format permits the displa of  value lines on the pressure graph as well. values can also be epressed in the form of a "matri" or table. This is simpl where the values for each halftime compartment and each stop depth are precalculated and arranged in columns and rows. This format is useful for detailed comparisons and analsis. Some of the earl dive computers and desktop computer programs used the table format to "look up" values for each stop during the calculation process. VALUE CHARACTERISTICS value sets can be classified into two categories, nodecompression sets and decompression sets. Nodecompression values are surfacing values onl. The DSAT RDP values are an eample. Nostop dive profiles are designed so that the calculated gas loadings in the compartments do not eceed the surfacing values. This allows for direct ascent to the surface at an time during the dive. Some nodecompression Workman Definitions: = tolerated inert gas pressure (absolute) in hpothetical "tissue" compartment Depth = depth pressure (gauge) measured from surface at sea level Tolerated Depth = tolerated depth pressure (gauge) measured from surface at sea level O = intercept at zero depth pressure (gauge); surfacing value = of value line Bühlmann Definitions: P t.tol. i.g. = tolerated inert gas pressure (absolute) in hpothetical "tissue" compartment P t. i.g. = inert gas pressure (absolute) in hpothetical "tissue" compartment P amb. = ambient pressure (absolute) P amb.tol. = tolerated ambient pressure (absolute) a = intercept at zero ambient pressure (absolute) b = reciprocal of of value line algorithms account for ascent and descent rates in the calculations.
4 Cpt No. Table : Comparison of values for Nitrogen Between Various Haldanian Decompression Algorithms American Sstem of Pressure Units  feet of sea water (fsw) Workman values () HT min fsw O Cpt HT No. min. Bühlmann ZHL values () fsw O DSAT RDP values () Cpt No. HT min fsw O Cpt HT No. min DCAP FF values () 00 0 fsw O Cpt No. b HT min Bühlmann ZHL values (0) A fsw O B fsw O C O fsw Cpt = Compartment HT = Halftime O = Surfacing value (sea level = atm = fsw = bar) = of value line Table : Comparison of values for Nitrogen Between Various Haldanian Decompression Algorithms European Sstem of Pressure Units  meters of sea water (msw) Workman Bühlmann ZHL DSAT RDP DCAP F Bühlmann ZHL values () values () values () values () values (0) A B C Cpt HT O Cpt HT O Cpt HT O Cpt HT O Cpt HT O O O No. min msw No. min msw No. min msw No. min msw No. min msw msw msw b Cpt = Compartment HT = Halftime = Surfacing value (sea level = msw = bar) = of value line O
5 Table : Comparison of values for Helium Between Various Haldanian Decompression Algorithms American Sstem of Pressure Units  feet of sea water (fsw) Workman Bühlmann ZHL Bühlmann ZHLA values () values () values (0) Cpt HT No. min fsw O Cpt HT No. min fsw O Cpt HT No. min fsw O b Cpt = Compartment HT = Halftime = of value line O = Surfacing value (sea level = atm = fsw = bar) Table : Comparison of values for Helium Between Various Haldanian Decompression Algorithms European Sstem of Pressure Units  meters of sea water (msw) Workman Bühlmann ZHL Bühlmann ZHLA values () values () values (0) Cpt HT O Cpt HT O Cpt HT O No. min msw No. min msw No. min msw.. b Cpt = Compartment HT = Halftime = of value line = Surfacing value (sea level = msw = bar) O Decompression values are characterized b having a parameter which determines the change in value with change in ambient pressure. The value of the parameter will var depending on the halftime of the hpothetical "tissue" compartment. Generall, faster halftime compartments will have a greater than slower halftime compartments. This reflects the observation that faster compartments tolerate greater overpressure than slower compartments. If the is greater than then the value line "epands" on the pressure graph and that compartment will tolerate greater overpressure gradients with increasing depth. A fied of means that the compartment will tolerate the same overpressure gradient regardless of depth. In all cases, the value of the can never be less than. Otherwise, the value line would cross under the ambient pressure line at some point and this would represent an "illogical" situation whereb the compartment could not tolerate even the ambient pressure. THE ABIENT PRESSURE LINE The ambient pressure line is an allimportant reference line on the pressure graph. Passing through the origin, it has a of and simpl represents the collection of points where the compartment inert gas loading will be equal to ambient pressure. This is important because when the inert gas loading in a compartment goes above the ambient pressure line, an overpressure gradient is created. An value line represents the established limit for tolerated overpressure gradient above the ambient pressure line. THE DECOPRESSION ZONE The "decompression zone" is the region on the pressure graph between the ambient pressure line and the value line (see Figure ). Within the contet of the dissolved gas model, this zone represents the functional area in which decompression takes place. In theor, a positive gradient above ambient pressure is desireable in order for a compartment to "offgas" or "decompress." In some
6 instances, such as with a high fraction of ogen in the mi, a compartment will be able to offgas even though the total inert gas partial pressure is less than ambient pressure. An "efficient" decompression profile is characterized b leading compartment gas loadings which plot within the decompression zone. The gas loadings for various halftime compartments will cross into and then out of the decompression zone during the decompression profile depending upon which compartment is "leading" or "controlling" at the time. Generall, the faster compartments will cross into the decompression zone first and be leading (gas loadings closest to value lines) and then the rest of the decompression profile will be controlled b the slower compartments in sequence. ULTIPLE INERT GASES Presentda dissolved gas models emplo a concept for multiple inert gases which states that the total inert gas pressure in a hpothetical "tissue" compartment is the sum of the partial pressures of the inert gases present in the compartment, even though the various inert gases each have a different halftime for that compartment. ied gas decompression algorithms must deal with more than one inert gas in the breathing mi, such as helium and nitrogen in trimi. values for this situation are handled differentl b the various algorithms. Some methodologies use the same values for both nitrogen and helium; usuall the are based on the values for nitrogen. In the Bühlmann algorithm, an intermediate value is calculated which is an adjustment between the separate values for nitrogen and helium based on the proportion of these inert gases present in the compartment. In the value linear equation, the Coefficient a (He+N ) and the Coefficient b (He+N ) are computed in accordance with the partial pressures of helium (PHe) and nitrogen (PN ) as follows: a (He+N ) = [a (He))PHe + a (N ))PN ] / [PHe + PN ]; b (He+N ) = [b (He))PHe + b (N ))PN ] / [PHe + PN ]. An value Concept: A solid line drawn through a fuzz, gra area; a representative threshold beond which a high frequenc of smptoms of decompression sickness (DCS) can be epected in a majorit of divers value Line Safet argin* Actual Profile Figure Ambient Pressure Line DCS Bubbles Smptoms Smptomatic Bubbles "Silent" Bubbles assive Smptoms Limited Smptoms No Smptoms Less Deco ore Deco Risk ore Risk Less Risk * varies according to individual disposition, phsical condition, acceptable risk, etc. WHAT DO VALUES REPRESENT? A misconception among some divers is that values represent a hard line between "getting the bends" and "not getting the bends." This might eplain wh some divers routinel push the limits of their tables or dive computer. The eperience of diving medicine has shown that the established limits (values) are sometimes inadequate. The degree of inadequac is seen to var with the individual and the situation. Accordingl, it ma be more appropriate to describe an value as "a solid line drawn through a fuzz, gra area" (see Figure ). The reasons for this lack of definitude involve comple human phsiolog, variations among individuals, and predisposing factors for decompression sickness. Overall, the dissolved gas model has worked well for divers and the knowledge base has continued to grow. For eample, it was originall presumed that all inert gas had to remain dissolved in solution and that an bubbles were indicative of DCS. However, we now know that silent bubbles are present even during smptomfree dives. Thus, the realit is that there is a combination of two conditions during a dive  most of the inert gas presumabl in solution and some of the inert gas out of solution as bubbles. An value, therefore, represents not onl a tolerable overpressure gradient, but a tolerable amount of bubbles as well. values are empiricall verified, meaning that actual decompression trials are carried out with human subjects. These tests are conducted with a relativel small number of subjects intended to represent the much larger population of divers. Even though good data is obtained about the approimate threshold for smptoms of decompression sickness (values), this process cannot accuratel predict or guarantee an absolute threshold for everone. Also, we know from eperience that certain factors are predisposing for decompression sickness: lack of phsical conditioning, fattiness, fatigue, drugs/alcohol, dehdration, overeertion, ver cold water, open patent foramen ovale (PFO), etc. Individual susceptibilit can var on a dail basis as well. VALUES AND CONSERVATIS Limited smptoms, if an, and a reasonabl low level of risk are associated with values. This criteria,
7 however, ma not be entirel acceptable to all divers. an divers would like to be in the range of "no smptoms" and "ver low level of risk" when it comes to their decompression profiles. Fortunatel, it is well understood among decompression modelers and programmers that calculations based on the established values alone cannot produce sufficientl reliable decompression tables for all individuals and all scenarios. This is wh decompression programs provide for a means of introducing conservatism into the calculations. Some of the methodologies include increasing the inert gas fractions used in the calculations, appling a depth safet factor which calculates for a deeperthanactual dive depth, calculating for a longerthanactual bottom time, and adjusting the halftimes to be asmmetrical during offgassing (slower). Some programs use more than one of these methods combined. These methodologies for conservatism are effective when properl applied. The degree of "effectiveness" is usuall gauged b divers in terms of how much longer and deeper the decompression profiles become, and through individual eperience with the outcome of the profiles. VALUE RELATIONSHIPS Some fundamental relationships involving values and decompression calculations are indicated on the pressure graph in Figure. The Percent value calculation has been used b various decompression modelers over the ears. Professor Bühlmann, for eample, evaluated man of his decompression trials on a Percent value basis and reported the data as such in his book(s). The Percent value calculation is a measure of how far a decompression profile has entered into the "decompression zone." 0% value is at the ambient pressure line and represents the bottom of the decompression zone. 0% value is at the value line and represents the top of the decompression zone. ANALYSIS OF PROFILES Compartment Inert Gas Pressure, absolute 0 0 Figure Pressure Graph: value Relationships Safet argin Surface Pressure "Decompression Zone" is between lines value value Inert Gas Pressure an divers would like to know precisel what the effect is of the conservatism factors in their desktop decompression program(s). The realize that longer and deeper profiles are generated with increasing conservatism factors, but more fundamental information is desired. Both the Percent value and Percent value relationships are useful for the analsis and evaluation of decompression profiles. Using a standard set of reference values, different profiles can be evaluated on a consistent basis. This includes comparison of profiles generated b entirel different programs, algorithms, and decompression models. UNIVERSAL REFERENCE VALUES The Bühlmann ZHL values are emploed in most, if not all, of the desktop decompression programs in use b technical divers. These values were developed and tested for a broad value Line Inert Gas Pressure Ambient Pressure, absolute Ambient Pressure Line inert gas loading for tpical deco profile Inert Gas % value = Pressure value 0 % value = Inert Gas Pressure value 0 range of ambient pressure eposures; from high altitude diving to deep sea diving. When used with appropriate conservatism, the have proven to be "reliable" for technical diving (to the etent that something can be reliable in an ineact science). The have become the de facto worldwide standard that can serve as universal reference values for the comparison and evaluation of decompression profiles. It is a relativel eas task for programmers to include Percent value and Percent value calculations in summar form with the decompression profiles. Table is an eample of this and shows the effect of conservatism factors used in a commerciallavailable desktop decompression program. At 0% Conservatism Factor, the decompression profile is in the 0% value range and has entered approimatel 0% into the decompression zone (0% value ). It is evident that this program emplos a level of baseline conservatism
8 Table : Effect of Conservatism Factors in a CommerciallAvailable Program on Decompression Profiles Referenced to Bühlmann ZHL values (ZHLA Helium, ZHLB Nitrogen) Deco Stop (fsw) /0 Trimi Dive (% O / 0% He) to 0 fsw for 0 min. Deco mies  Nitro % at fsw, 0% O at 0 fsw 0% Conservatism Factor Run (min) aimum * % value.% () 0.0% () 0.% () 0.% () 0.% () 0.% () 0 0.% () 0 0.% () 0 0.% ().% () 0 0.% () * Upon Arrival at the Stop aimum * % value.% ().% ().% ().% ().% ().% ().% () 0.% () 0.% ().% () 0.% () Deco Stop (fsw) 0% Conservatism Factor 0% Conservatism Factor Run (min) aimum * % value.% ().% ().0% ().% ().% ().% ().% ().% ().% ().% ().% ().% ().% () aimum * % value.0% ().% ().% ().0% ().% ().% ().% ().% ().% ().0% ().% ().% ().% () aimum * Deco Run aimum * % value Stop (fsw) (min) % value 0.% ().% () % ().% () % ().% ().% ().% () 0.% ().% () 0.% ().% () 0.% () 0.% () 0.0% ().% () 0.% ().% () 0.% ().% () 0.% ().% () 0 0.% ().% ().% ().% ().% ().% () 0 0.% ().% () since none of the values reaches 0%. At 0% Conservatism Factor (which is recommended in the user s manual), the profile is in the % value range and has entered approimatel 00% into the decompression zone. At 0% Conservatism Factor, the profile is in the % value range and has entered approimatel 0% into the decompression zone. Note that the values given in Table are upon arrival the respective stops which is the worstcase condition. This correlates with the edges of the "stairsteps" in the gas loading profile on the pressure graph (see eample in Figure ). The highest values across all profiles are calculated upon arrival at the surface which illustrates wh a ver slow final ascent from the last decompression stop to the surface is alwas prudent. ARGIN OF SAFETY Using the value relationships and a standard set of reference values, divers can determine personal decompression limits which are both welldefined and transportable. The margin of safet selected will depend on individual disposition and prior eperience with profiles. An honest assessment of one s fitness for decompression diving is alwas in order. For eample, this author/diver (an office worker) has chosen a personal limit of % value and 00% value for tpical trimi dives. To ensure a fied margin of safet, a decompression profile can be calculated directl to a predetermined percentage of the value. The advantage of this approach is complete consistenc across the entire ambient pressure range and precise control over the resultant profile. Z About the Author Erik C. Baker is an electrical engineer with a consulting engineering firm in Florida. He pursues research into decompression and diving phsiolog as a hobb, and has developed several FORTRAN computer programs for decompression calculation and analsis. Erik is a certified cave diver and trimi diver. Decompression References: Bennett PB, Elliott DH, eds.. The Phsiolog and edicine of Diving. London: WB Saunders. Bocott AE, Damant GCC, Haldane JS. 0. The prevention of compressed air illness. J Hg (London) :. Bühlmann, AA.. DecompressionDecompression Sickness. Berlin: SpringerVerlag. Bühlmann, AA.. Tauchmedizin. Berlin: SpringerVerlag. Hamilton RW, uren A, Röckert H, Örnhagen H.. Proposed new Swedish air decompression tables. In: Shields TG, ed. XIVth Annual eeting of the EUBS. European Undersea Biomedical Societ. Aberdeen: National Hperbaric Center. Hamilton RW, Rogers RE, Powell R, Vann RD.. Development and validation of nostop decompression procedures for recreational diving: The DSAT Recreational Dive Planner. Santa Ana, CA: Diving Science and Technolog Corp. Schreiner HR, Kelle PL.. A pragmatic view of decompression. In: Lambertsen CJ, ed. Underwater
9 Phsiolog IV. New York: Academic Press. Wienke BR.. Basic decompression theor and application. Flagstaff, AZ: Best. Wienke BR.. Basic diving phsics and applications. Flagstaff, AZ: Best. Workman RD.. Calculation of decompression schedules for nitrogenogen and heliumogen dives. Research Report . Washington: Nav Eperimental Diving Unit. Workman RD.. American decompression theor and practice. In: Bennett PB, Elliott DH, eds. The phsiolog and medicine of diving and compressed air work. London: Baillière, Tindall & Cassell.
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