Dry-Heat Destruction of Lipopolysaccharide: Mathematical

APPLIED AND ENVIRONMENTAL MICROBIOLOGY, Nov. 1978, p. 715-719 99-224/78/36-715$2./ Copyright 1978 American Society f Microbiology Vol. 36, No. 5 Printed in U.S.A. Dry-Heat Destruction of Lipopolysaccharide: Mathematical Approach to Process Evaluation KIYOSHI TSUJI'* AND A. R. LEWIS2 Control Analytical Research and Development' and Mathematical Services,2 The Upjohn Company, Kalamazoo, Michigan 491 Received f publication 21 August 1978 A mathematical model was developed to estimate the number of logarithmic cycles (LDec) of lipopolysaccharide concentration destroyed by a dry-heat sterilization process. The LDec values calculated from the mathematical model agreed well with those obtained from the destruction of lipopolysaccharide by a dry-heat treatment. A discussion of how the mathematical model may be used to evaluate a dry-heat sterilization cycle is presented. This mathematical model and the dryheat destruction curves indicated existence of a maximum LDec value at each temperature. The implications of this finding are discussed. Dry-heat sterilizers commercially available f bility and the implication of this equation f sterilization of components and materials may use in evaluating the dry-heat process cycles. be classified into the following two categies: continuous and static. A continuous dry-heat MATERIALS AND METHODS sterilizer generally uses high temperatures The heat penetration curves simulate those of the (above 3 C) f a sht time process. A hightemperature, sht-time (HTST) dry-heat sterpoules and those of the static dry-heat sterilizers. HTST dry-heat sterilizer used f sterilization of amilizer specifically designed f sterilization of ampoules is widely marketed in Europe (8; tunnel destroyed by exposure to the dry-heat treatments was The number of logarithmic cycles (LDec) of LPS drier and sterilizer type 35, 35-D-937, specifications received from Hans Gilowy, Berlin, Ger- with the z'(d') and zy(d2) values repted previously calculated from the heat penetration curves by using conventional thermal processing equations (1, 2, 9) many). These HTST sterilizers are equipped (1). The LDec values thus calculated were compared with laminar HEPA filters to achieve rapid heating and cooling of ampoules with particulate- an equation repted earlier (1). Experimental data with a nonlinear mathematical model advanced from free, hot cold, fced air flow. The specification of the sterilizers is to achieve ampoule tem- continuous sterilizer was used to examine validity of on the recovery of LPS treated with dry heat in a perature of over 3 C f at least 9 s. The the mathematical models. whole process usually takes less than 15 min, Since dry-heat resistance characteristics of LPS including both heating and cooling operations from various gram-negative microganisms were similar (1), the dry-heat destruction data of LPS from (8) Escherichia coli were used throughout this paper. Ṫhe conventional static dry-heat sterilization oven requires components and materials to be RESULTS AND DISCUSSION loaded batchwise and heated with hot fced air. Sterilization is carried out frequently at 16 to The following equation was used to describe 17 C f a period of 2 to 4 h (11). the dry-heat destruction of LPS (1): All dry-heat sterilization cycles being used log Y = A + B. 1cx (1) today are designed to destroy bacterial spes to achieve sterility. Their ability to depyrogenate where Y = percentage of LPS remaining; A = components and materials should be evaluated constant at a given temperature; B = constant in light of the dry-heat destruction kinetics data at a given temperature; C = constant at a given of lipopolysaccharides (LPS) that were repted temperature; and x = heating time in minutes. previously (1). The equation, log Y = A + Recognizing that at x =, 1% of the LPS B.1C, we used to linearize the dry-heat destruction curves of LPS, however, included three + B loc it is implied that remains, in terms of equation 1, log 1 = A parameters, A, B, and C, all varying with temperature. The purpose of this paper is to simplify A = 2-B (1.5) the equation and to describe practical applica- Substituting equation 1.5 into equation 1 and 715

716 TSUJI AND LEWIS reparameterizing yields: log Y= 2 + B(1cx-1) log (log Y -2+1 = Cx (2) (2.5) The least-square estimates of parameters B and C at various temperatures are listed in Table 1. It should be noted that B is positively crelated with temperature (r =.99) and is not affected by changes in x Y. Therefe, let and substituting in equation 2 log Y' = Cx (4) Equation 4 is identical in its fm to that used by almost all researchers f expression of the thermal inactivation kinetics of bacterial spes (1, 2, 9). The reciprocal of the slope of equation 4, C, can be expressed as D3; i.e., D3 = 1/I Cl. Equation 4 can now be rewritten as x = -D3(log Ya' - log Yb') (5) TABLE 1. List ofparameters f process calculation f the equation, log Y = 2 + B(1O(x - 1) Ti, (OC) B C DP (1/C)" 17 3.447 -.449 223 19 3.777 -.15 95.2 21 4.819 -.311 32.2 23 5.533 -.827 11.9 25 6.65 -.21 4.5 27" 6.825 -.549 1.8 3" 7.874-2.348.43 35" 9.622-26.43.4 a z = b 47.6C. Extrapolated from linear regression models: B = (.349)TB- 2.6134 and log C = (-.21)TB + 5.937. APPL. ENVIRON. MICROBIOL. log Yb' = log Ya' - (x/d3) (6) where Y,,,' = a value proptional to the initial amount of LPS, and Yb' = a value proptional to the amount of LPS remaining after x minutes of heating at a given temperature. Thus, the amount of LPS remaining after a given heatprocessing time may be calculated. Conversely, the heating time required at a process temperature to achieve a desired level of destruction can also be calculated. The decimal reduction time curve relates log D3 to temperature (T); thus, the absolute value of the reciprocal of the slope of this line is defined as z3. Therefe, the differences in the rate of LPS destruction between any two temperatures ( TB and T,) the differences in lethality (L) can be expressed as: (7) T, -TB (D-TB DT) = 1 Zi (7.1) Therefe, the integration of the heat penetration curve with time using equation 7.1 would give the equivalent heating time (F) at the reference temperature (TB). Process calculation. A heat penetration curve of a vial in a static dry-heat sterilizer (Fig. 1) is used as a model to compare the LDec values calculated from the three mathematical models symbolized by their parameters D1, D2, and D3. As has been stated previously (1), D' and DV are reciprocals of the absolute values of the slopes of the initial and second first-der rate curves, respectively. The D3 is the reciprocal of the slope of equation 2, i.e., 1/l Cl. The heating curve shows a lag period at near 1 C; this is caused by evapation of water from vials. The heating cycle used was 3.5 h of sterilization at an oven set temperature of 2 C. The TB value of 19 C, chosen f calculation of the F value, is the temperature at near that reached by the heat penetration curve. Since the heat penetration curve is highly irregular in shape, no attempt was made to linearize it. The parameters used f the conventional thermal process calculations, zl(d') and Z2(D2), are listed in the preceding paper (1), and those of z3(d3) are shown in Table 1. FT,,, the number of minutes required to destroy a given amount of LPS at a given reference temperature (TB), assuming instantaneous come-up and cooling, is defined as the area under the lethality curve where the lethality at temperature Ti is Li: (T' - TB) L-= 1 z (8) I log (D'T,,, DT) =." s (Ti TB)12 I 2 3 4 a FIG. 1. Heat penetration curve of vial during sterilization in a static dry-heat oven.

VOL. 36, 1978 The area FT,, using the trapezoidal approximation, is: FT = + L2 + L3 +... N (8.5) +LN +N At 2 where At = heating time interval in minutes at which recding of temperature (Ti) was made (minutes); Ti = temperature on a heat penetration curve (degrees Celsius); TB = reference temperature, at near the maximum reached by a heat penetration curve (degrees Celsius); and z = 1/slope of the decimal reduction time curve. As may be expected, the Figo values calculated are nearly identical regardless of the mathematical model used (Table 2). This is due to nearly identical zl, z2, and Z3 values. However, the number of logarithmic cycles (LDec) of LPS that may be destroyed by dry heat as calculated by the three mathematical models are quite different. Use of D' gave the highest LDec value (14.3), whereas use of Di resulted in the lowest LDec value (2.9). The LDec value (3.7) calculated from D3 is between those of D' and D2 but closer to that of D2. This indicates that selection of a wrong calculation method could lead to over- underprocessing. Evaluation ofmathematical model. To determine which of the mathematical models should be selected f evaluation of dry-heat process cycles, the following experiment was conducted. A.1-ml ption of an aqueous solution containing approximately 5 ng of LPS was pipetted into a glass vial. After vials were dried under a stream of dry nitrogen, they were treated in a continuous dry-heat sterilizer by using two different process cycles, I and II. The heat penetration curves of cycles I and II are shown in Fig. DRY-HEAT DESTRUCTION OF LPS 717 2. The vials thus treated were assayed by the Limulus amebocyte lysate method (1, 12) to determine the destruction of LPS. The results indicated that LPS still remained in vials treated by heating cycle I; however, heating cycle II reduced the LPS content below the detection limit (.4 ng) of the Limulus amebocyte lysate method. Therefe, heating cycle I realized less than a 3-log-cycle reduction (LDec value), whereas heating cycle II achieved me than a 3-log-cycle destruction. The LDec values calculated by integrating the heat penetration-lethality curves of cycles I and II, using three mathematical models, are shown in Table 2. The LDec values calculated from D' were 3.1 and 5.1, whereas those of D2 were.4 and.6 f heating cycles I and II. Only D3 of the process calculation closely estimated the experimental LDec values. The LDec values, 2.7 and 3.6 f cycles I and II, respectively, closely agreed with the data obtained experimentally. The use of D' overestimated and that of Di underestimated the actual amount of destruction of LPS. The D3 advanced in this rept 22-16- _ 14-12- 11.. Time Mimutes) FIG. 2. Heat penetration curve of vial in a continuous dry-heat sterilizer. TABLE 2. Dry-heat sterilization process calculation Calculation F Dry-heat sterilizer Fig. no. mode LDec' F,,,i Static oven 1 D' 19 177 14.3 ldi 19 172 2.9 LP3 19 177 3.7 Continuous sterilizer, cycle I 2 D' 21 11.4 3.1 D2 21 11.8.4 LD3 21 11.5 2.7 Continuous sterilizer, cycle II 2 D' 21 18.7 5.1 D2 21 18.2.6 D3 21 18.6 3.6 HTST sterilizer 3 DL' 35 2.39 677 D2 35 2.47 36.2 D 3 35 2.4 7.9 alog cycle destruction of LPS from E. coli. T,i

718 TSUJI AND LEWIS resulted in LDec values which agreed well with the experimental data. Thus, the D3 mathematical model may now be used to evaluate the efficiency of dry-heat sterilization cycles in use and to elucidate proper process cycles to achieve a desired level of LPS destruction. The observations made above were based on very limited data. Extensive studies are being planned to confirm the findings. D3, used to calculate the LDec value f heating cycle I, is demonstrated in the following: the parameters t = 1, TB = 21, and z = 47.6 were inserted in equation 8.5 to obtain the F21 value. Ti was read from the heat penetration curve (cf. Fig. 2): F21 = 11.5 min. A Texas Instruments programmable calculat, TI58 (Texas Instruments Inc., Dallas, Tex.), was used as a convenient tool to calculate F values. The LDec may be derived as follows: LDec = 2 - log Y; substituting equation 2 f log Y, LDec = 2 - [2 + B(1cx- 1)]. Therefe, LDec = -B(1cx- 1) (9) Thus, the LDec f heating cycle I is obtained by equating x to F21 as follows: since B = 4.819 and C = -.331 at 21 C (cf. Table 1) LDec = 14.819 (1(-.311) X 11.5-1) = 2.7 Significance of dry-heat kinetic data on process evaluation. To describe the significance of the dry-heat destruction kinetic data of LPS on process evaluation, an ampoule heating curve in an HTST sterilizer was used (Fig. 3). As was observed previously, the F values were nearly identical, regardless of the calculation models used (Table 2). However, the LDec values were again quite different. An LDec value as high as 677 was estimated by using the D' model, whereas that of the D3 model was 7.9. Examination of the dry-heat destruction curve of 21 C (Fig. 4), f example, clearly indicated that the curves tail significantly and that further increases in heating time do not significantly decrease the y value increase in LDec value. This phenomenon is clearly depicted by the D3 mode. The model (equation 2) that relates log percent LPS reduction to heating time at a fixed temperature has the property of decreasing at a decreasing rate. Thus, the log percent LPS will approach a fixed value asymptote with increasing time. The asymptotic value, in terms of number of logarithmic cycles as given by parameter B, is reached after an infinite time. The time required f an N log cycle reduction, t1, is given by: log (1 _ ) tn= c (1) where B and C are model parameters and N < B. As N -- B when tn --. The t9o, time in minutes required to achieve 9% of the maximum LDec, is given by: t9o= log 1 - B ) Cl APPL. ENVIRON. MICROBIOL. C Thus, t9o is the D3 value. The concept of the maximum LDec is not merely an artifact of the empirical model. Several researchers have also repted nonlinear 1 1 -.E.1 L~.1.1.1 T"u (maw) FIG. lizer. 3. Ampoule heating curve in an HTST steri- 8 16 24 32 4 48 TIME (MINUTES) 56 64 72 8 FIG. 4. Dry-heat destruction curve of LPS from E. coli at 21 C.

VOL. 36, 1978 concave thermal destruction curves of bacterial spes when plotted on semilog paper (3-7). The concept of the maximum LDec is quite an imptant observation, since it is contrary to the conventional concept of the thermal destruction kinetics of microbial spes which follow the first-der rate. The maximum LDec and t9 ( I3) values at various process temperatures are presented in Table 3. The dry-heat process at 3 C f 9 s (1.5 min), a guideline commonly used f HTST sterilization of ampoules and vials (8), would achieve 99.97% of the maximum LDec value (7.9) at 3 C. The calculation was made as follows: maximum LDec (percent) = (1cx- 1) x 1 = (lo()(-235) - 1) x 1 = 99.97% Table 4 is presented as a guideline to elucidate proper processing cycles f achieving a desired level of LPS destruction (LDec). It appears that dry-heat processes have real limitations, particularly at the lower temperatures. The LDec value of 4 may not be attainable at process temperatures below 19 C. The notion that increasing exposure time will compensate f lower process temperatures clearly is not defensible. The statements made above are based on an assumption that the decimal reduction time curve, constructed at 17 to 25 C, may be ex- TABLE 3. Maximum amount of destruction oflps (LDec) expected at process temperatures (T) TR (OC) Maximum LDec t53(d3)a 17 3.45 223 19 3.78 95.2 21 4.82 32.2 23 5.53 11.9 25 6.7 4.5 27b 6.83 1.8 3b 7.87.43 35b 9.62.4 a Time in minutes required to achieve 9% of the maximum log number of destruction of LPS from E. coli. z = 47.6 C. b Estimated. DRY-HEAT DESTRUCTION OF LPS 719 TABLE 4. Process time (minutes) required to achieve a desired level of destruction of LPS (LDec) at various temperatures (TB) LDec TB (OC) 2 3 4 5 6 17 84. 198 19 31.2 65.4 Xo 21 7.5 13.6 24.7 23 2.3 4.1 6.7 12.1 25.86 1.5 2.3 3.8 9.8 27.27.46.7 1.4 1.7 3.54.89.13.19.27 35.4.6.9.12.16 tended up to 3 35 C. This assumption must obviously be confirmed by experimental data. LITERATURE CITED 1. Ball, C. O., and F. C. W. Olson. 1957. Sterilization in food technology, they, practice, and calculations. McGraw-Hill Book Co., Inc., New Yk. 2. Block, S. S. 1977. Disinfection, sterilization, and preservation. Lea and Febiger, Philadelphia. 3. Bond, W. W., M. S. Favero, N. J. Petersen, and J. H. Marshall. 197. Dry-heat inactivation kinetics of naturally occurring spe populations. Appl. Microbiol. 2:573-578. 4. Fox, K., and L. J. Pflug. 1968. Effect of temperature and gas velocity on the dry-heat destruction rate of bacteria spes. Appl. Microbiol. 16:343-348. 5. Frank, H. A., and L. L. Campbell. 1957. The nonlogarithmic rate of thermal destruction of spes of Bacillus coagulans. Appl. Microbiol. 5:243-248. 6. Molin, G., and K. Ostlund. 1975. Dry heat inactivation of Bacillus subtilis spes by means of infra-red heating. Antonie van Leeuwenhoek J. Microbiol. Serol. 41:329-335. 7. Oag, R. K. 194. The resistance of bacterial spes to dry heat. J. Pathol. Bacteriol. 51:137-141. 8. Strunck Bosch Gruppe. 1975. Trocknungs und Sterilisiertunnel fur Ampullen, Vials, und Flaschchen. TSQ- ZO1. H. Strunck Co., Cologne, Germany. 9. Townsend, C. T., L. L. Somers, F. C. Lamb, and N. A. Olson. 1956. A labaty manual f the canning industry. National Canners Association, Washington, D.C. 1. Tsuji, K., and S. J. Harrison. 1978. Dry-heat destruction of lipopolysaccharide: dry-heat destruction kinetics. Appl. Environ. Microbiol. 36:71-714. 11. United States Pharmacopeia XIX. 1975. United States Pharmacopeia Convention, Inc., Rockville, Md. 12. Wachtel, R. E., and K. Tsuji. 1977. Comparison of limulus amebocyte lysates and crelation with the United States Pharmacopeial pyrogen test. Appl. Envrion. Microbiol. 33:1265-1269.