Updated: 8/1/00
Contents
Food poisoning caused by Bacillus cereus may occur when foods are prepared and held without adequate refrigeration for several h before serving. B. cereus is an aerobic sporeforming bacterium that is commonly found in soil, on vegetables, and in many raw and processed foods. Consumption of foods that contain >106B. cereus/g may result in food poisoning. Foods incriminated in past outbreaks include cooked meat and vegetables, boiled or fried rice, vanilla sauce, custards, soups, and raw vegetable sprouts. Two types of illness have been attributed to the consumption of foods contaminated with B. cereus. The first and better known is characterized by abdominal pain and diarrhea; it has an incubation period of 4-16 h and symptoms that last for 12-24 h. The second, which is characterized by an acute attack of nausea and vomiting, occurs within 1-5 h after consumption of contaminated food; diarrhea is not a common feature in this type of illness (Rhodehamel and Harmon, 1998).
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B. cereus is a common food contaminant. Effective control measures depend on destruction by a heat process and temperature control to prevent spore germination and multiplication of vegetative cells in cooked, ready-to-eat foods. Measures to reduce or eliminate the threat of food poisoning by B. cereus include: 1) Avoid preparing food too far in advance of planned service, 2) Avoid holding cooked foods at room temperature, 3) Use quick chill methods to cool foods below 7.2 ºC (45ºF) within 4 h of preparation; store in shallow pans/small quantities with the food less than 4 inches (10.2 cm) deep; if food is especially thick (e.g., refried beans), store no more than 3 inches [7.6 cm] deep). Hold/store hot foods above 60ºC (140ºF) until served, and 5) Reheat foods rapidly to 74ºC (165ºF) or above (Kramer and Gilbert, 1989; Reed, 1994).
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FDA to assess situations on a case by case basis.
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Table 10-1. Limiting conditions for B. cereus growth.
Parameter |
Values |
References |
Min. aw |
0.92 |
FDA, 1998 |
Min. pH |
4.3 |
Reed, 1994 |
Max. pH |
9.3 |
Fluer and Ezepchuk, 1970 |
Max.%NaCl |
18 |
Pradhan et al., 1985 |
Min. temp. |
4oC (39.2oF) |
FDA, 1998 |
Max. temp. |
5oC (131oF) |
FDA, 1998 |
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Table 10-2. B. cereus spore heat resistance.
Temperature |
D-Values |
Medium |
References |
|
(oC) |
(oF) |
(min) |
||
90 |
194 |
21-137 |
Water |
Gilbert et al., 1974 |
95 |
203 |
5-36 |
Water |
Gilbert et al., 1974 |
100 |
212 |
6.7-8.3 |
Water |
Gilbert et al., 1974 |
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Food Sampling and Preparation of Sample Homogenate (Andrews and June, 1998)
The adequacy and condition of the sample or specimen received for examination are of primary importance. If samples are improperly collected and mishandled or are not representative of the sampled lot, the laboratory results will be meaningless. Because interpretations about a large consignment of food are based on a relatively small sample of the lot, established sampling procedures must be applied uniformly. A representative sample is essential when pathogens or toxins are sparsely distributed within the food or when disposal of a food shipment depends on the demonstrated bacterial content in relation to a legal standard.
The number of units that comprise a representative sample from a designated lot of a food product must be statistically significant. The composition and nature of each lot affects the homogeneity and uniformity of the total sample mass. The proper statistical sampling procedure, according to whether the food is solid, semisolid, viscous, or liquid, must be determined by the collector at the time of sampling by using the Investigations Operation Manual (FDA, 1993). Sampling and sample plans are discussed in detail in ICMSF (1986).
Whenever possible, submit samples to the laboratory in the original unopened containers. If products are in bulk or in containers too large for submission to the laboratory, transfer representative portions to sterile containers under aseptic conditions. There can be no compromise in the use of sterile sampling equipment and the use of aseptic technique. Sterilize one-piece stainless steel spoons, forceps, spatulas, and scissors in an autoclave or dry-heat oven. Use of a propane torch or dipping the instrument in alcohol and igniting is dangerous and may be inadequate for sterilizing equipment.
Use containers that are clean, dry, leak-proof, wide-mouthed, sterile, and of a size suitable for samples of the product. Containers such as plastic jars or metal cans that are leak-proof may be hermetically sealed. Whenever possible, avoid glass containers, which may break and contaminate the food product. For dry materials, use sterile metal boxes, cans, bags, or packets with suitable closures. Sterile plastic bags (for dry, unfrozen materials only) or plastic bottles are useful containers for line samples. Take care not to overfill bags or permit puncture by wire closure. Identify each sample unit (defined later) with a properly marked strip of masking tape. Do not use a felt pen on plastic because the ink might penetrate the container. Whenever possible, obtain at least 100 g for each sample unit. Submit open and closed controls of sterile containers with the sample.
Deliver samples to the laboratory promptly with the original storage conditions maintained as nearly as possible. When collecting liquid samples, take an additional sample as a temperature control. Check the temperature of the control sample at the time of collection and on receipt at the laboratory. Make a record for all samples of the times and dates of collection and of arrival at the laboratory. Dry or canned foods that are not perishable and are collected at ambient temperatures need not be refrigerated. Transport frozen or refrigerated products in approved insulated containers of rigid construction so that they will arrive at the laboratory unchanged. Collect frozen samples in pre-chilled containers.
Place containers in a freezer long enough to chill them thoroughly. Keep frozen samples solidly frozen at all times. Cool refrigerated samples, except shellfish and shell stock, in ice at 0-4ºC and transport them in a sample chest with suitable refrigerant capable of maintaining the sample at 0-4ºC until arrival at the laboratory. Do not freeze refrigerated products. Unless otherwise specified, refrigerated samples should not be analyzed more than 36 h after collection. Special conditions apply to the collection and storage of shucked, unfrozen shellfish and shell stock (APHA, 1985). Pack samples of shucked shellfish immediately in crushed ice (no temperature specified) until analyzed; keep shell stock above freezing but below 10ºC. Examine refrigerated shellfish and shell stock within 6 h of collection but in no case more than 24 h after collection. Further details on sample handling and shipment may be found in the Investigations Operation Manual (FDA, 1993) and the Laboratory Procedures Manual (FDA, 1989). The Investigations Operation Manual (FDA, 1993) contains sampling plans for various microorganisms. Some of those commonly used are presented here.
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Examination of Foods for B. cereus
If the quantity of food to be examined is large, take representative samples of 50 g each from different parts of the suspect food because contamination may be unevenly distributed.
Transport and examine samples promptly without freezing, if possible. If samples must be shipped to the laboratory, pack them in insulated shipping containers with enough gel-type refrigerant to maintain them at 6ºC or below. Upon receipt in the laboratory, store the samples at 4ºC and analyze as soon as possible. If analysis cannot be started within 4 d after collection, freeze samples rapidly and store at -20ºC until examined. Thaw at room temperature and proceed with analysis as usual. Dehydrated foods may be stored at room temperature and shipped without refrigeration.
Enumeration and Confirmation of B. cereus in Foods
Using aseptic technique, weigh 50 g of sample into sterile blender jar.
Add 450 ml Butterfield's phosphate-buffered dilution water (1:10 dilution) and blend for 2
min at high speed (18,000-21,000 rpm). Using the 1:10 dilution, make serial dilutions of
sample for enumeration of B. cereus as described in D or E, below.
Prepare serial dilutions from 10-2 to 10-6 by transferring 10 ml homogenized sample (1:10 dilution) to 90 ml dilution blank, mixing well with vigorous shaking, and continuing until 10-6 dilution is reached. Inoculate duplicate MYP agar plates with each dilution of sample (including 1:10) by spreading 0.1 ml evenly onto surface of each plate with sterile glass spreading rod. Incubate plates 24 h at 30ºC and observe for colonies surrounded by precipitate zone, which indicates that lecithinase is produced. B. cereus colonies are usually a pink color which becomes more intense after additional incubation.
If reactions are not clear, incubate plates for additional 24 h before counting colonies. Select plates that contain an estimated 15-150 eosin pink, lecithinase-producing colonies. Mark bottom of plates into zones with black felt pen to facilitate counting and count colonies that are typical of B. cereus. This is the presumptive plate count of B. cereus. Pick 5 or more presumptive positive colonies from the MYP agar plates and transfer to nutrient agar slants for confirmation as B. cereus. Confirm isolates as B. cereus as described in F and G, below. Calculate number of B. cereus cells/g of sample, based on percentage of colonies tested that are confirmed as B. cereus. For example, if average count obtained with 10-4 dilution of sample was 65 and 4 of 5 colonies tested were confirmed as B. cereus, the number of B. cereus cells/g of food is 65 x 4/5 x 10,000 x 10 = 5,200,000. (NOTE: Dilution factor is tenfold higher than sample dilution because only 0.1 ml was tested.)
The MPN technique is recommended for enumerating B. cereus in foods that are expected to contain fewer than 10 B. cereus organisms/g. It may also be preferred for examining certain dehydrated starchy foods for which the plate count technique is inappropriate.
Inoculate 3-tube MPN series in trypticase soy-polymyxin broth, using 1 ml inoculum of 10-1, 10-2, and 10-3 dilutions of sample with 3 tubes at each dilution. (Additional dilutions should also be tested if B. cereus population is expected to exceed 103/g.) Incubate tubes 48 ± 2 h at 30ºC and observe for dense growth, which is typical of B. cereus. Streak cultures from positive tubes onto separate MYP agar plates and incubate plates 24-48 h at 30ºC. Pick one or more eosin pink, lecithinase-positive colonies from each MYP agar plate and transfer to nutrient agar slants for confirmation as B. cereus. Confirm isolates as B. cereus as described in F and G, below, and calculate MPN of B. cereus cells/g of sample based on the number of tubes at each dilution in which the presence of B. cereus was confirmed.
Pick 5 or more eosin pink, lecithinase-positive colonies from MYP agar plates and transfer to nutrient agar slants. Incubate slants 24 h at 30ºC. Prepare Gram-stained smears from slants and examine microscopically. B. cereus will appear as large Gram-positive bacilli in short-to-long chains; spores are ellipsoidal, central to subterminal, and do not swell the sporangium. Transfer 3 mm loopful of culture from each slant to 13 x 100 mm tube containing 0.5 ml of sterile phosphate-buffered dilution water and suspend culture in diluent with Vortex mixer. Use suspended cultures to inoculate the following confirmatory media:
These basic characteristics are shared with other members of the B. cereus group, including the rhizoid strains B. mycoides, the crystalliferous insect pathogen B. thuringiensis, and the mammalian pathogen B. anthracis. However, these species can usually be differentiated from B. cereus by determining specific characteristics typical of each species or variety. The tests described in G, below, are useful for this purpose and can easily be performed in most laboratories. Strains that produce atypical results from these tests require additional analysis before they can be classified as B. cereus.
Table 10-3. Differential characteristics of large-celled Group I Bacillus species.
Feature |
B. cereus |
B. thuringiensis |
B. cereus var. mycoides |
B. anthracis |
B. megaterium |
Gram reaction |
+a |
+ |
+ |
+ |
+ |
Catalase |
+ |
+ |
+ |
+ |
+ |
Motility |
+/-b |
+/- |
-c |
- |
+/- |
Reduction of nitrate |
+ |
+/- |
+ |
+ |
-d |
Tyrosine decomposed |
+ |
+ |
+/- |
-d |
+/- |
Lysozyme-resistant |
+ |
+ |
+ |
+ |
- |
Egg yolk reduction |
+ |
+ |
+ |
+ |
- |
Anaerobic utilization of glucose |
+ |
+ |
+ |
+ |
- |
VP reaction |
+ |
+ |
+ |
+ |
- |
Acid produced from mannitol |
- |
- |
- |
- |
+ |
Hemolysis (sheep RBC) |
+ |
+ |
+ |
-d |
- |
Known pathogenicityc | Produces enterotoxins | Endotoxin crystals pathogenic to insects | Rhizoidal growth | Pathogenic to animals and humans |
a
+, 90-100% of strains are positiveThe following tests are useful for differentiating typical strains of B. cereus from other members of the B. cereus group, including B. mycoides, B. thuringiensis, and B. anthracis.
Wait 1-2 min and repeat this step. Let stand 30 s, pour off stain, and rinse slide thoroughly with clean tap water. Dry slide without blotting and examine under oil immersion for presence of free spores and darkly stained tetragonal (diamond-shaped) toxin crystals. Crystals are usually somewhat smaller than spores. Toxin crystals are usually abundant in a 3-4 d old culture of B. thuringiensis but cannot be detected by the staining technique until lysis of the sporangium has occurred. Therefore, unless free spores can be seen, cultures should be held at room temperature for a few more d and re-examined for toxin crystals. B. thuringiensis usually produces protein toxin crystals that can be detected by the staining technique either as free crystals or parasporal inclusion bodies within the exosporium. B. cereus and other members of the B. cereus group do not produce protein toxin crystals.
The method described is intended primarily for use in the routine examination of foods. As noted in F, above, and in Table 10-3, the confirmatory tests recommended may in some instances be inadequate for distinguishing B. cereus from culturally similar organisms that could occasionally be encountered in foods. These organisms include 1) the insect pathogen B. thuringiensis, which produces protein toxin crystals; 2) B. mycoides, which characteristically produces rhizoid colonies on agar media; and 3) B. anthracis, which exhibits marked animal pathogenicity and is nonmotile. With the exception of B. thuringiensis, which is currently being used for insect control on food and forage crops, these organisms are seldom encountered in the routine examination of foods. The tests described in G, above, are usually adequate for distinguishing the typical strains of B. cereus from other members of the B. cereus group. However, results with atypical strains of B. cereus are quite variable, and further testing may be necessary to identify the isolates. Although a few diarrheal toxin detection kits are commercially available, none are recommended, pending further evaluation. At present, no practical tests for detecting the emetic toxin are available. Until reliable tests are available, cultural tests such as those described in this method must be relied upon for confirming isolates from foods as B. cereus.
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Bacillus cereus is an aerobic sporeformer that is commonly found in soil, on vegetables, and in many raw and processed foods. Consumption of foods that contain large numbers of B. cereus (106or more/g) may result in food poisoning, especially when foods are prepared and held for several h without adequate refrigeration before serving. Cooked meat and vegetables, boiled or fried rice, vanilla sauce, custards, soups, and raw vegetable sprouts have been incriminated in past outbreaks (Bennett and Harmon, 1988). Two types of illness are attributed to the consumption of foods contaminated with B. cereus. The first and better known is characterized by abdominal pain and diarrhea; it has an incubation period of 4-16 h and symptoms that last for 12-24 h (Lancette and Harmon, 1980; McFarland, 1907). The second, which is characterized by an acute attack of nausea and vomiting that occurs within 1-5 h after a meal; diarrhea is not a common feature in this type of illness.
Although certain physiological and cultural characteristics are necessary for identifying B. cereus (Lancette and Harmond, 1980), its enterotoxigenicity indicates whether a suspect strain may be a public health hazard. Evidence shows that diarrheal toxin is a distinct serological entity; in vitro methods that use specific antibodies have been developed to detect the toxin in culture fluids. The evidence for the emetic toxin, however, is still incomplete. This chapter presents a method for the routine culturing of suspect Bacillus spp., using a semisolid agar medium and a serological procedure (the microslide gel double diffusion test) to identify the enterotoxin.
Immediately lay silicone-coated template on melted agar and edges of bordering tapes. Place one edge of template on one of the tapes and bring opposite edge to rest gently on the other tape. Place slide in prepared petri dish (see 3-g, below) soon after agar solidifies and label slide with number, date, or other information.
For examining food products, use procedures described for detecting B. cereus. Test isolates for enterotoxigenicity as described in 5, below.
Production of enterotoxin. Of the methods described for the production of enterotoxin, cultivation of B. cereus in BHIG (0.1% glucose, pH 7.4) is simple and requires no special apparatus other than a shaker. Add loopful of growth from nutrient agar slants to 3-5 ml sterile distilled water or saline. Inoculate BHIG with 0.5 ml of this aqueous suspension, which should contain about 300 million organisms/ml. Turbidity of suspension should be equivalent to No. 1 on McFarland nephelometer scale. Deliver suspension with sterile 1.0 ml pipet. Shake flasks at 3 ± 2ºC at 84-125 cycles/ml for 12 h. Good surface growth is obtained after 12 h of incubation. Transfer contents of flasks to 50 ml centrifuge tube. Remove organisms by high speed centrifugation (10 min at 32,800 x g). Examine supernatant for presence of enterotoxin by filling depots in slide gel diffusion assembly, as directed in 5, below.
To prepare record sheet, draw hole pattern of template on record sheet, indicate contents of each well, and give each pattern on record sheet a number to correspond with number on slide.
Fill wells to convexity with reagents, using Pasteur pipet (prepared by drawing out glass tubing of about 7 mm od) or disposable 30 or 40 µl pipet. Remove bubbles from all wells by probing with fine glass rod. Make rods by pulling glass tubing very fine, as in making capillary pipets, breaking it into about 2-1/2 inch (6.4 cm) lengths, and melting ends in flame. It is best to fill wells and remove bubbles against a dark background. Insert rods into all wells to remove trapped air bubbles that may not be visible. Let slides remain at room temperature in covered petri dishes containing moist sponge strips for 48-72 h before examination or for 24 h at 37ºC.
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Background
The most probable number (MPN) is particularly useful for low concentrations of organisms (<100/g), especially in milk and water, and for those foods whose particulate matter may interfere with accurate colony counts. The following background observations are adapted and extended from the article on MPN by James T. Peeler and Foster D. McClure in the Bacteriological Analytical Manual (BAM), 7th edition.
Only viable organisms are enumerated by the MPN determination. If, in the microbiologist's experience, the bacteria in the prepared sample in question can be found attached in chains that are not separated by the preparation and dilution, the MPN should be judged as an estimate of growth units (GUs) or colony-forming units (CFUs) instead of individual bacteria. For simplicity, however, this appendix will speak of these GUs or CFUs as individual bacteria.
The following assumptions are necessary to support the MPN method. The sample is prepared in such a way that the bacteria are distributed randomly within it. The bacteria are separate, not clustered together, and they do not repel each other. The growth medium and conditions of incubation have been chosen so that every inoculum that contains even one viable organism will produce detectable growth.
The essence of the MPN method is the dilution of a sample to such a degree that inocula will sometimes but not always contain viable organisms. The "outcome", i.e., the numbers of inocula producing growth at each dilution, will imply an estimate of the original, undiluted concentration of bacteria in the sample. In order to obtain estimates over a broad range of possible concentrations, microbiologists use serial dilutions, incubating several tubes (or plates, etc.) at each dilution.
The first accurate estimation of the number of viable bacteria by the MPN method was published by McCrady (1915). Halvorson and Ziegler (1933), Eisenhart and Wilson (1943), and Cochran (1950) published articles on the statistical foundations of the MPN. Woodward (1957) recommended that MPN tables should omit those combinations of positive tubes (high for low concentrations and low for high concentrations) that are so improbable that they raise concerns about laboratory error or contamination. De Man (1983) published a confidence interval method that was modified to make the tables for this appendix.
Confidence intervals
The 95% confidence intervals in the tables have the following meaning.
Before the tubes are inoculated, the chance is at least 95% that the confidence interval associated with the eventual result will enclose the actual concentration.
It is possible to construct many different sets of intervals that satisfy this criterion. This manual uses a modification of the method of de Man (1983). De Man calculated his confidence limits iteratively from the smallest concentrations upward. Because this manual estimates concentrations of pathogens, the intervals have been shifted slightly upward by iterating from the largest concentrations downward.
Improbable outcomes
When excluding improbable outcomes, de Man's (1983) preferred degree of improbability was adopted. The included combinations of positive tubes are those that would be among the 99.985% most likely to result if their own MPNs were the actual bacterial concentrations. Therefore the entire set of results on any 10 different samples will be found in these tables at least 99% of the time.
Precision, bias, and extreme results
The MPNs and confidence limits have been expressed to 2 significant digits. For example, the entry "400" has been rounded from a number between 395 and 405.
Numerous articles have noted a bias toward over-estimation of microbial concentrations by the MPN. Garthright (1993) has shown, however, that there is no appreciable bias when the concentrations are expressed as logarithms, the customary units used for regressions and for combining results. Therefore, these MPNs have not been adjusted for bias.
Prior to this revision, the 8th edition tables showed the MPN for the (0,0,0) outcomes as less than the MPN of the (1,0,0) outcome. This made good numerical sense, but made for unacceptable complexity in trying to write acceptance standards for raw materials in terms of the BAM. This revision returns to the prior practice of recording the MPN for the (0,0,0) outcomes as less than the MPN for the (0,0,1) outcome, so that standards can once again be written in a simple manner in terms of all-negative outcomes.
Since no particular density is indicated for an outcome of (0.0.0), a density must be assigned arbitrarily (and stated explicitly in the report) in order to calculate statistics. For the logarithm of the density, log[0.5*MPN(1,0,0)] is a reasonable choice. For statistics using the (non-logarithmic) density itself, calculate once with a density of 0.0 and once with a density of 0.5*MPN(1,0,0). Either report both statistics or report one statistic accompanied by a comment on the difference between that statistic and the other one.
Selecting three dilutions for table reference
An MPN can be computed for any numbers of tubes at any numbers of dilutions. MPN values based on 3 decimal dilutions, however, are very close approximations to those based on 4 or more dilutions. When more than three dilutions are used in a decimal series of dilutions, refer to the 3 dilution table according to the following two cases, illustrated by Table 10-6 (with 5 tubes at each dilution).
Case 1. One or more dilutions show all tubes positive. Select the highest dilution that gives positive results in all tubes (even if a lower dilution gives negative results) and the next two higher dilutions (examples a and b); if positive results occur in higher unselected dilutions, shift each selection to the next higher dilution (example c). If there are still positive results in higher unselected dilutions, add those higher-dilution positive results to the results for the highest selected dilution (example d). If there were not enough higher dilutions tested to select three dilutions, then select the next lower dilutions (example e).
Case 2. No dilutions show all tubes positive. Select the 3 lowest dilutions (example f). If there are positive results in higher unselected dilutions, add those higher-dilution positive results to the results for the highest selected dilution (example g).
Other compendia of methods require that no excluded lower dilutions may have any negative tubes. This manual differs when the highest dilution that makes all tubes positive follows a lower dilution that has one or more negative tubes. Example b above would be read according to other compendia as (4, 5, 1, 0, 0) with MPN 4.8/g. The BAM reading, 33/g, is 7 times larger. The BAM selection method is based on FDA experience that for some organisms in some food matrices such outcomes as (2, 5, 1, 0, 0) and (0, 3, 1, 0, 0) occur too often to be random occurrences. In these cases, it appears that some factor (a competing organism or adverse set of compounds) is present at the lowest dilutions in such concentrations that it can reduce the detection of the target microbes.
Table 10-4. Table of examples.
Example |
1.0 g |
0.1 g |
0.01 g |
0.001 g |
0.0001 g |
Combination of positives |
MPN/g |
a |
5 |
5 |
1 |
0 |
0 |
5-1-0 |
33 |
b |
4 |
5 |
1 |
0 |
0 |
5-1-0 |
33 |
c |
5 |
4 |
4 |
1 |
0 |
4-4-1 |
40 |
d |
5 |
4 |
4 |
0 |
1 |
4-4-1 |
40 |
e |
5 |
5 |
5 |
5 |
2 |
5-5-2 |
5400 |
f |
0 |
0 |
1 |
0 |
0 |
0-0-1 |
0.20 |
g |
4 |
4 |
1 |
1 |
0 |
4-4-2 |
4.7 |
Until further research clarifies this situation, analysts should continue to exclude dilutions lower than the highest dilution with all tubes positive. The findings should, however, report the extent to which such lower, partially negative dilutions have been excluded. Analysts working with materials with known limited complexity in research settings will want to use their professional judgement to read outcomes such as (4, 5, 1, 0, 0) as (4, 5, 1, 0, 0). They may also read outcomes such as (3, 5, 1, 0, 0) as too improbable to record, because they are not included in the tables.
Conversion of units
Tables 10-5 to 10-7 apply directly to inocula 0.1, 0.01, and 0.001 g. When different inocula are selected for table reference, multiply the MPN/g and confidence limits by whatever number is required to make the inocula match the table inocula. For example, if the inocula were 0.01, 0.001, and 0.0001 for 3 tubes each, multiplying by 10 would make these inocula match the table inocula. If the positive results from this 3 tube series were (3, 1, 0), one would multiply the Table 1 MPN/g estimate, 43/g, by 10 to arrive at 430/g.
Approximations for an unusual series of dilutions
The MPNs for a series of dilutions not addressed by any tables (e.g., resulting from accidental loss of some tubes) may be computed by iteration or may be estimated as follows. First, select the lowest dilution that doesn't have all positive results. Second, select the highest dilution with at least one positive result. Finally, select all the dilutions between them. Use only the selected dilutions in the following formula of Thomas (1942):
where ( )1/2 means square root, P is the number of positive results, T is the total g in the selected dilutions, and N is the g of sample in the selected negative tubes.
The following examples will illustrate the application of Thomass formula. We assume that the dilutions are 1.0, 0.1, 0.01, 0.001, and 0.0001 g.
Example (1). Dilution results are (5/5, 10/10, 4/10, 2/10, 0/5). We use only (--,--, 4/10, 2/10,--); so T= 10*0.01 + 10*0.001 = 0.11. There are 6 negative tubes at 0.01 and 8 negative tubes at 0.001, so N = 6*0.01 + 8*0.001 = 0.068. There are 6 positive tubes, so
Example (2). Dilution results are (5/5, 10/10, 10/10, 0/10, 0/5). We use only(--,--, 10/10, 0/10,--), so by Thomass formula,
These two approximated MPNs compare well with the MPNs for (10, 4, 2) and (10,10,0) (i.e., 70/g and 240/g, respectively).
Example (2) above is a special case for which an exact solution for the two selected dilutions can be calculated directly, as follows. When all the results at the highest dilutions are negative, all the results at the remaining dilutions are positive, and when V is an individual inoculum at the highest dilution with all positive tubes, then
where T and N are defined as for Thomas's formula. For the second example above, the third dilution is the highest with positive portions, so V = 0.01. The MPN for the third and fourth dilution would be exactly
Approximate confidence limits can be calculated for the MPN by using the method of Cochran as follows. Let "a" denote the dilution ratio (e.g., a = 10 for the tables in this appendix). If there are n tubes per dilution, the standard error of log (MPN) is
where c = 0.58 for dilution ratios of 10 or more and c = 0.55 for dilution ratios less than 10. If the dilutions used for the MPN determination are not all the same, Peeler et al. (1992) recommend using for n the harmonic mean number of tubes in the k dilutions:
Special requirements and tables included
Requests for special computations and different designs will be honored as resources permit. Designs may be requested with more or less than 3 dilutions, uneven numbers of tubes, different confidence levels, etc. (Telephone or write the Division of Mathematics, FDA/CFSAN, 200 C St., SW, Washington, DC 20204.) The most-published designs, three 10-fold dilutions with 3, 5, or 10 tubes at each dilution, are presented here.
Table 10-5. For 3 tubes each at 0.1, 0.01, and 0.001 g inocula, the MPNs/g and 95% confidence intervals.
Positive tubes |
MPN/g |
Confidence limit |
Positive tubes |
MPN/g |
Confidence limit |
||||||
0.10 |
0.01 |
0.001 |
Low |
High |
0.10 |
0.01 |
0.001 |
Low |
High |
||
0 |
0 |
0 |
<3.0 |
-- |
9.5 |
2 |
2 |
0 |
21 |
4.5 |
42 |
0 |
0 |
1 |
3.0 |
0.15 |
9.6 |
2 |
2 |
1 |
28 |
8.7 |
94 |
0 |
1 |
0 |
3.0 |
0.15 |
11 |
2 |
2 |
2 |
35 |
8.7 |
94 |
0 |
1 |
1 |
6.1 |
1.2 |
18 |
2 |
3 |
0 |
29 |
8.7 |
94 |
0 |
2 |
0 |
6.2 |
1.2 |
18 |
2 |
3 |
1 |
36 |
8.7 |
94 |
0 |
3 |
0 |
9.4 |
3.6 |
38 |
3 |
0 |
0 |
23 |
4.6 |
94 |
1 |
0 |
0 |
3.6 |
0.17 |
18 |
3 |
0 |
1 |
38 |
8.7 |
110 |
1 |
0 |
1 |
7.2 |
1.3 |
18 |
3 |
0 |
2 |
64 |
17 |
180 |
1 |
0 |
2 |
11 |
3.6 |
38 |
3 |
1 |
0 |
43 |
9 |
180 |
1 |
1 |
0 |
7.4 |
1.3 |
20 |
3 |
1 |
1 |
75 |
17 |
200 |
1 |
1 |
1 |
11 |
3.6 |
38 |
3 |
1 |
2 |
120 |
37 |
420 |
1 |
2 |
0 |
11 |
3.6 |
42 |
3 |
1 |
3 |
160 |
40 |
420 |
1 |
2 |
1 |
15 |
4.5 |
42 |
3 |
2 |
0 |
93 |
18 |
420 |
1 |
3 |
0 |
16 |
4.5 |
42 |
3 |
2 |
1 |
150 |
37 |
420 |
2 |
0 |
0 |
9.2 |
1.4 |
38 |
3 |
2 |
2 |
210 |
40 |
430 |
2 |
0 |
1 |
14 |
3.6 |
42 |
3 |
2 |
3 |
290 |
90 |
1,000 |
2 |
0 |
2 |
20 |
4.5 |
42 |
3 |
3 |
0 |
240 |
42 |
1,000 |
2 |
1 |
0 |
15 |
3.7 |
42 |
3 |
3 |
1 |
460 |
90 |
2,000 |
2 |
1 |
1 |
20 |
4.5 |
42 |
3 |
3 |
2 |
1100 |
180 |
4,100 |
2 |
1 |
2 |
27 |
8.7 |
94 |
3 |
3 |
3 |
>1100 |
420 |
-- |
Table 10-6. For 5 tubes each at 0.1, 0.01, and 0.001 g inocula, the MPNs and 95% confidence intervals.
Positive tubes |
MPN/g |
Confidence limit |
Positive tubes |
MPN/g |
Confidence limit |
||||||
0.10 |
0.01 |
0.001 |
Low |
High |
0.10 |
0.01 |
0.001 |
Low |
High |
||
0 |
0 |
0 |
<1.8 |
-- |
6.8 |
3 |
3 |
2 |
24 |
9.8 |
70 |
0 |
0 |
1 |
1.8 |
0.09 |
6.8 |
3 |
4 |
0 |
21 |
6.8 |
40 |
0 |
1 |
0 |
1.8 |
0.09 |
6.9 |
3 |
4 |
1 |
24 |
9.8 |
70 |
0 |
1 |
1 |
3.69 |
0.7 |
10 |
3 |
5 |
0 |
25 |
9.8 |
70 |
0 |
2 |
0 |
3.7 |
0.7 |
10 |
4 |
0 |
0 |
13 |
4.1 |
35 |
0 |
2 |
1 |
5.5 |
1.8 |
15 |
4 |
0 |
1 |
17 |
5.9 |
36 |
0 |
3 |
0 |
5.6 |
1.8 |
15 |
4 |
0 |
2 |
21 |
6.8 |
40 |
1 |
0 |
0 |
2.0 |
0.1 |
10 |
4 |
0 |
3 |
25 |
9.8 |
70 |
1 |
0 |
1 |
4.0 |
0.7 |
10 |
4 |
1 |
0 |
17 |
6.0 |
40 |
1 |
0 |
2 |
6.0 |
1.8 |
15 |
4 |
1 |
1 |
21 |
6.8 |
42 |
1 |
1 |
0 |
4.0 |
0.7 |
12 |
4 |
1 |
2 |
26 |
9.8 |
70 |
1 |
1 |
1 |
6.1 |
1.8 |
15 |
4 |
1 |
3 |
31 |
10 |
70 |
1 |
1 |
2 |
8.1 |
3.4 |
22 |
4 |
2 |
0 |
22 |
6.8 |
50 |
1 |
2 |
0 |
6.1 |
1.8 |
15 |
4 |
2 |
1 |
26 |
9.8 |
70 |
1 |
2 |
1 |
8.2 |
3.4 |
22 |
4 |
2 |
2 |
32 |
10 |
70 |
1 |
3 |
0 |
8.3 |
3.4 |
22 |
4 |
2 |
3 |
38 |
14 |
100 |
1 |
3 |
1 |
10 |
3.5 |
22 |
4 |
3 |
0 |
27 |
9.9 |
70 |
1 |
4 |
0 |
11 |
3.5 |
22 |
4 |
3 |
1 |
33 |
10 |
70 |
2 |
0 |
0 |
4.5 |
0.79 |
15 |
4 |
3 |
2 |
39 |
14 |
100 |
2 |
0 |
1 |
6.8 |
1.8 |
15 |
4 |
4 |
0 |
34 |
14 |
100 |
2 |
0 |
2 |
9.1 |
3.4 |
22 |
4 |
4 |
1 |
40 |
14 |
100 |
2 |
1 |
0 |
6.8 |
1.8 |
17 |
4 |
4 |
2 |
47 |
15 |
120 |
2 |
1 |
1 |
9.2 |
3.4 |
22 |
4 |
5 |
0 |
41 |
14 |
100 |
2 |
1 |
2 |
12 |
4.1 |
26 |
4 |
5 |
1 |
48 |
15 |
120 |
2 |
2 |
0 |
9.3 |
3.4 |
22 |
5 |
0 |
0 |
23 |
6.8 |
70 |
2 |
2 |
1 |
12 |
4.1 |
26 |
5 |
0 |
1 |
31 |
10 |
70 |
2 |
2 |
2 |
14 |
5.9 |
36 |
5 |
0 |
2 |
43 |
14 |
100 |
2 |
3 |
0 |
12 |
4.1 |
26 |
5 |
0 |
3 |
58 |
22 |
150 |
2 |
3 |
1 |
14 |
5.9 |
36 |
5 |
1 |
0 |
33 |
10 |
100 |
2 |
4 |
0 |
15 |
5.9 |
36 |
5 |
1 |
1 |
46 |
14 |
120 |
3 |
0 |
0 |
7.8 |
2.1 |
22 |
5 |
1 |
2 |
63 |
22 |
150 |
3 |
0 |
1 |
11 |
3.5 |
23 |
5 |
1 |
3 |
84 |
34 |
220 |
3 |
0 |
2 |
13 |
5.6 |
35 |
5 |
2 |
0 |
49 |
15 |
150 |
3 |
1 |
0 |
11 |
3.5 |
26 |
5 |
2 |
1 |
70 |
22 |
170 |
3 |
1 |
1 |
14 |
5.6 |
36 |
5 |
2 |
2 |
94 |
34 |
230 |
3 |
1 |
2 |
17 |
6.0 |
36 |
5 |
2 |
3 |
120 |
36 |
250 |
3 |
2 |
0 |
14 |
5.7 |
36 |
5 |
2 |
4 |
150 |
58 |
400 |
3 |
2 |
1 |
17 |
6.8 |
40 |
5 |
3 |
0 |
79 |
22 |
220 |
3 |
2 |
2 |
20 |
6.8 |
40 |
5 |
3 |
1 |
110 |
34 |
250 |
3 |
3 |
0 |
17 |
6.8 |
40 |
5 |
3 |
2 |
140 |
52 |
400 |
3 |
3 |
1 |
21 |
6.8 |
40 |
5 |
3 |
3 |
180 |
70 |
400 |
5 |
3 |
4 |
210 |
70 |
400 |
5 |
5 |
0 |
240 |
70 |
710 |
5 |
4 |
0 |
130 |
36 |
400 |
5 |
5 |
1 |
350 |
100 |
1100 |
5 |
4 |
1 |
170 |
58 |
400 |
5 |
5 |
2 |
540 |
150 |
1700 |
5 |
4 |
2 |
220 |
70 |
440 |
5 |
5 |
3 |
920 |
220 |
2600 |
5 |
4 |
3 |
280 |
100 |
710 |
5 |
5 |
4 |
1600 |
400 |
4600 |
5 |
4 |
4 |
350 |
100 |
710 |
5 |
5 |
5 |
>1600 |
700 |
-- |
5 |
4 |
5 |
430 |
150 |
1100 |
Table 10-7. For 10 tubes at each of 0.1, 0.01, and 0.001 g inocula, the MPNs and 95% confidence intervals.
Positive tubes |
MPN/g |
Confidence limit |
Positive tubes |
MPN/g |
Confidence limit |
||||||
0.10 |
0.01 |
0.001 |
Low |
High |
0.10 |
0.01 |
0.001 |
Low |
High |
||
0 |
0 |
0 |
<0.90 |
-- |
3.1 |
4 |
0 |
2 |
6.8 |
3.0 |
14 |
0 |
0 |
1 |
.9 |
.040 |
3.1 |
4 |
1 |
0 |
5.6 |
2.2 |
12 |
0 |
0 |
2 |
1.8 |
.33 |
5.1 |
4 |
1 |
1 |
6.8 |
3.0 |
14 |
0 |
1 |
0 |
.90 |
.04 |
3.6 |
4 |
1 |
22 |
8.0 |
3.6 |
17 |
0 |
1 |
1 |
1.8 |
.33 |
5.1 |
4 |
2 |
0 |
6.8 |
3.0 |
15 |
0 |
2 |
0 |
1.8 |
.33 |
5.1 |
4 |
2 |
1 |
8.0 |
3.6 |
17 |
0 |
2 |
1 |
2.7 |
.80 |
7.2 |
4 |
2 |
2 |
9.2 |
3.7 |
17 |
0 |
3 |
0 |
2.7 |
.80 |
7.2 |
4 |
3 |
0 |
8.1 |
3.6 |
17 |
1 |
0 |
0 |
.94 |
.05 |
5.1 |
4 |
3 |
1 |
9.3 |
4.5 |
18 |
1 |
0 |
1 |
1.9 |
.33 |
5.1 |
4 |
3 |
2 |
10 |
5.0 |
20 |
1 |
0 |
2 |
2.8 |
.80 |
7.2 |
4 |
4 |
0 |
9.3 |
4.5 |
18 |
1 |
1 |
0 |
1.9 |
.33 |
5.7 |
4 |
4 |
1 |
11 |
5.0 |
20 |
1 |
1 |
1 |
2.9 |
.80 |
7.2 |
4 |
5 |
0 |
11 |
5.0 |
20 |
1 |
1 |
2 |
3.8 |
1.4 |
9.0 |
4 |
5 |
1 |
12 |
5.6 |
22 |
1 |
2 |
0 |
2.9 |
.80 |
7.2 |
4 |
6 |
0 |
12 |
5.6 |
22 |
1 |
2 |
1 |
3.8 |
1.4 |
9.0 |
5 |
0 |
0 |
6.0 |
2.5 |
14 |
1 |
3 |
0 |
3.8 |
1.4 |
9.0 |
5 |
0 |
1 |
7.2 |
3.1 |
15 |
1 |
3 |
1 |
4.8 |
2.1 |
11 |
5 |
0 |
2 |
8.5 |
3.6 |
17 |
1 |
4 |
0 |
4.8 |
2.1 |
11 |
5 |
0 |
3 |
9.8 |
4.5 |
18 |
2 |
0 |
0 |
2.0 |
.37 |
7.2 |
5 |
1 |
0 |
7.3 |
3.1 |
15 |
2 |
0 |
1 |
3.0 |
.81 |
7.3 |
5 |
1 |
1 |
8.5 |
3.6 |
17 |
2 |
0 |
2 |
4.0 |
1.4 |
9.0 |
5 |
1 |
2 |
9.8 |
4.5 |
18 |
2 |
1 |
0 |
3.0 |
.82 |
7.8 |
5 |
1 |
3 |
11 |
5.0 |
21 |
2 |
1 |
1 |
4.0 |
1.4 |
9.0 |
5 |
2 |
0 |
8.6 |
3.6 |
17 |
2 |
1 |
2 |
5.0 |
2.1 |
11 |
5 |
2 |
1 |
9.9 |
4.5 |
18 |
2 |
2 |
0 |
4.0 |
1.4 |
9.1 |
5 |
2 |
2 |
11 |
5.0 |
21 |
2 |
2 |
1 |
5.0 |
2.1 |
11 |
5 |
3 |
0 |
10 |
4.5 |
18 |
2 |
2 |
2 |
6.1 |
3.0 |
14 |
5 |
3 |
1 |
11 |
5.0 |
21 |
2 |
3 |
0 |
5.1 |
2.1 |
11 |
5 |
3 |
2 |
13 |
5.6 |
23 |
2 |
3 |
1 |
6.1 |
3.0 |
14 |
5 |
4 |
0 |
11 |
5.0 |
21 |
2 |
4 |
0 |
6.1 |
3.0 |
14 |
5 |
4 |
1 |
13 |
5.6 |
23 |
2 |
4 |
1 |
7.2 |
3.1 |
15 |
5 |
4 |
2 |
14 |
7.0 |
26 |
2 |
5 |
0 |
7.2 |
3.1 |
15 |
5 |
5 |
0 |
13 |
6.3 |
25 |
3 |
0 |
0 |
3.2 |
.90 |
9.0 |
5 |
5 |
1 |
14 |
7.0 |
26 |
3 |
0 |
1 |
4.2 |
1.4 |
9.1 |
5 |
6 |
0 |
14 |
7.0 |
26 |
3 |
0 |
2 |
5.3 |
2.1 |
11 |
6 |
0 |
0 |
7.8 |
3.1 |
17 |
3 |
1 |
0 |
4.2 |
1.4 |
10 |
6 |
0 |
1 |
9.2 |
3.6 |
17 |
3 |
1 |
1 |
5.3 |
2.1 |
11 |
6 |
0 |
2 |
11 |
5.0 |
20 |
3 |
1 |
2 |
6.4 |
3.0 |
14 |
6 |
0 |
3 |
12 |
5.6 |
22 |
3 |
2 |
0 |
5.3 |
2.1 |
12 |
6 |
1 |
0 |
9.2 |
3.7 |
18 |
3 |
2 |
1 |
6.4 |
3.0 |
14 |
6 |
1 |
1 |
11 |
5.0 |
21 |
3 |
2 |
2 |
7.5 |
3.1 |
15 |
6 |
1 |
2 |
12 |
5.6 |
22 |
3 |
3 |
0 |
6.5 |
3.0 |
14 |
6 |
1 |
3 |
14 |
7.0 |
26 |
3 |
3 |
1 |
7.6 |
3.1 |
15 |
6 |
2 |
0 |
11 |
5.0 |
21 |
3 |
3 |
2 |
8.7 |
3.6 |
17 |
6 |
2 |
1 |
12 |
5.6 |
22 |
3 |
4 |
0 |
8.7 |
3.6 |
17 |
6 |
2 |
2 |
14 |
7.0 |
26 |
3 |
4 |
1 |
8.7 |
3.6 |
17 |
6 |
2 |
3 |
15 |
7.4 |
30 |
3 |
5 |
0 |
8.8 |
3.6 |
17 |
6 |
3 |
0 |
12 |
5.6 |
23 |
4 |
0 |
0 |
4.5 |
1.6 |
11 |
6 |
3 |
1 |
14 |
7.0 |
26 |
4 |
0 |
1 |
5.6 |
2.2 |
12 |
6 |
3 |
2 |
15 |
7.4 |
30 |
Table 10-7 (cont.). For 10 tubes at each of 0.1, 0.01, and 0.001 g inocula, the MPNs and 95% confidence intervals.
Positive tubes |
MPN/g |
Confidence limit |
Positive tubes |
MPN/g |
Confidence limit |
||||||
0.10 |
0.01 |
0.001 |
Low |
High |
0.10 |
0.01 |
0.001 |
Low |
High |
||
6 |
4 |
0 |
14 |
7.0 |
26 |
8 |
3 |
1 |
21 |
10 |
39 |
6 |
4 |
1 |
15 |
7.4 |
30 |
8 |
3 |
2 |
24 |
11 |
44 |
6 |
4 |
2 |
17 |
9.0 |
34 |
8 |
3 |
3 |
26 |
12 |
50 |
6 |
5 |
0 |
16 |
7.4 |
30 |
8 |
4 |
0 |
22 |
10 |
39 |
6 |
5 |
1 |
17 |
9.0 |
34 |
8 |
4 |
1 |
24 |
11 |
44 |
6 |
5 |
2 |
19 |
9.0 |
34 |
8 |
4 |
2 |
26 |
12 |
50 |
6 |
6 |
0 |
17 |
9.0 |
34 |
8 |
4 |
3 |
29 |
14 |
58 |
6 |
6 |
1 |
19 |
9.0 |
34 |
8 |
5 |
0 |
24 |
11 |
44 |
6 |
7 |
0 |
19 |
9.0 |
34 |
8 |
5 |
1 |
27 |
12 |
50 |
7 |
0 |
0 |
10 |
4.5 |
20 |
8 |
5 |
2 |
29 |
14 |
58 |
7 |
0 |
1 |
12 |
5.0 |
21 |
8 |
5 |
3 |
32 |
15 |
62 |
7 |
0 |
2 |
13 |
6.3 |
25 |
8 |
6 |
0 |
27 |
12 |
50 |
7 |
0 |
3 |
15 |
7.2 |
28 |
8 |
6 |
1 |
30 |
14 |
58 |
7 |
1 |
0 |
12 |
5.0 |
22 |
8 |
6 |
2 |
33 |
15 |
62 |
7 |
1 |
1 |
13 |
6.3 |
25 |
8 |
7 |
0 |
30 |
14 |
58 |
7 |
1 |
2 |
15 |
7.2 |
28 |
8 |
7 |
1 |
33 |
17 |
73 |
7 |
1 |
3 |
17 |
7.7 |
31 |
8 |
7 |
2 |
36 |
17 |
74 |
7 |
2 |
0 |
13 |
6.4 |
26 |
8 |
8 |
0 |
34 |
17 |
73 |
7 |
2 |
1 |
15 |
7.2 |
28 |
8 |
8 |
1 |
37 |
17 |
74 |
7 |
2 |
2 |
17 |
7.7 |
31 |
9 |
0 |
0 |
17 |
7.5 |
31 |
7 |
2 |
3 |
19 |
9.0 |
34 |
9 |
0 |
1 |
19 |
9.0 |
34 |
7 |
3 |
0 |
15 |
7.2 |
30 |
9 |
0 |
2 |
22 |
10 |
39 |
7 |
3 |
1 |
17 |
9.0 |
34 |
9 |
0 |
3 |
24 |
11 |
44 |
7 |
3 |
2 |
19 |
9.0 |
34 |
9 |
1 |
0 |
19 |
9.0 |
39 |
7 |
3 |
3 |
21 |
10 |
39 |
9 |
1 |
1 |
22 |
10 |
40 |
7 |
4 |
0 |
17 |
9.0 |
34 |
9 |
1 |
2 |
25 |
11 |
44 |
7 |
4 |
1 |
19 |
9.0 |
34 |
9 |
1 |
3 |
28 |
14 |
58 |
7 |
4 |
2 |
21 |
10 |
39 |
9 |
1 |
4 |
31 |
14 |
58 |
7 |
4 |
3 |
23 |
11 |
44 |
9 |
2 |
0 |
22 |
10 |
44 |
7 |
5 |
0 |
19 |
9.0 |
34 |
9 |
2 |
1 |
25 |
11 |
46 |
7 |
5 |
1 |
21 |
10 |
39 |
9 |
2 |
2 |
28 |
14 |
58 |
7 |
5 |
2 |
23 |
11 |
44 |
9 |
2 |
3 |
32 |
14 |
58 |
7 |
6 |
0 |
21 |
10 |
39 |
9 |
2 |
4 |
35 |
17 |
73 |
7 |
6 |
1 |
23 |
11 |
44 |
9 |
3 |
0 |
25 |
12 |
50 |
7 |
6 |
2 |
25 |
12 |
46 |
9 |
3 |
1 |
29 |
14 |
58 |
7 |
7 |
0 |
23 |
11 |
44 |
9 |
3 |
2 |
32 |
15 |
62 |
7 |
7 |
1 |
26 |
12 |
50 |
9 |
3 |
3 |
36 |
17 |
74 |
8 |
0 |
0 |
13 |
5.6 |
25 |
9 |
3 |
4 |
40 |
20 |
91 |
8 |
0 |
1 |
15 |
7.0 |
26 |
9 |
4 |
0 |
29 |
14 |
58 |
8 |
0 |
2 |
17 |
7.5 |
30 |
9 |
4 |
1 |
33 |
15 |
62 |
8 |
0 |
3 |
19 |
9.0 |
34 |
9 |
4 |
2 |
37 |
17 |
74 |
8 |
1 |
0 |
15 |
7.1 |
28 |
9 |
4 |
3 |
41 |
20 |
91 |
8 |
1 |
1 |
17 |
7.7 |
31 |
9 |
4 |
4 |
45 |
20 |
91 |
8 |
1 |
2 |
19 |
9.0 |
34 |
9 |
5 |
0 |
33 |
17 |
73 |
8 |
1 |
3 |
21 |
10 |
39 |
9 |
5 |
1 |
37 |
17 |
74 |
8 |
2 |
0 |
17 |
7.7 |
34 |
9 |
5 |
2 |
42 |
20 |
91 |
8 |
2 |
1 |
19 |
9.0 |
34 |
9 |
5 |
3 |
46 |
20 |
91 |
8 |
2 |
2 |
21 |
10 |
39 |
9 |
5 |
4 |
51 |
25 |
120 |
8 |
2 |
3 |
23 |
11 |
44 |
9 |
6 |
0 |
38 |
17 |
74 |
8 |
3 |
0 |
19 |
9.0 |
34 |
9 |
6 |
1 |
43 |
20 |
91 |
Table 10-7 (cont.). For 10 tubes at each of 0.1, 0.01, and 0.001 g inocula, the MPNs and 95% confidence intervals.
Positive tubes |
MPN/g |
Confidence limit |
Positive tubes |
MPN/g |
Confidence limit |
||||||
0.10 |
0.01 |
0.001 |
Low |
High |
0.10 |
0.01 |
0.001 |
Low |
High |
||
9 |
6 |
2 |
47 |
21 |
100 |
10 |
6 |
0 |
79 |
34 |
180 |
9 |
6 |
3 |
53 |
25 |
120 |
10 |
6 |
1 |
94 |
39 |
180 |
9 |
7 |
0 |
44 |
20 |
91 |
10 |
6 |
2 |
110 |
50 |
210 |
9 |
7 |
1 |
49 |
21 |
100 |
10 |
6 |
3 |
120 |
57 |
220 |
9 |
7 |
2 |
54 |
25 |
120 |
10 |
6 |
4 |
140 |
70 |
280 |
9 |
7 |
3 |
60 |
26 |
120 |
10 |
6 |
5 |
160 |
74 |
280 |
9 |
8 |
0 |
50 |
25 |
120 |
10 |
6 |
6 |
180 |
91 |
350 |
9 |
8 |
1 |
55 |
25 |
120 |
10 |
7 |
0 |
100 |
44 |
210 |
9 |
8 |
2 |
61 |
26 |
120 |
10 |
7 |
1 |
120 |
50 |
220 |
9 |
8 |
3 |
68 |
30 |
140 |
10 |
7 |
2 |
140 |
61 |
280 |
9 |
9 |
0 |
57 |
25 |
120 |
10 |
7 |
3 |
150 |
73 |
280 |
9 |
9 |
1 |
63 |
30 |
140 |
10 |
7 |
4 |
170 |
91 |
350 |
9 |
9 |
2 |
70 |
30 |
140 |
10 |
7 |
5 |
190 |
91 |
350 |
10 |
0 |
0 |
23 |
11 |
44 |
10 |
7 |
6 |
220 |
100 |
380 |
10 |
0 |
1 |
27 |
12 |
50 |
10 |
7 |
7 |
240 |
110 |
480 |
10 |
0 |
2 |
31 |
14 |
58 |
10 |
8 |
0 |
130 |
60 |
250 |
10 |
0 |
3 |
37 |
17 |
73 |
10 |
8 |
1 |
150 |
70 |
280 |
10 |
1 |
0 |
27 |
12 |
57 |
10 |
8 |
2 |
170 |
80 |
350 |
10 |
1 |
1 |
32 |
14 |
61 |
10 |
8 |
3 |
200 |
90 |
350 |
10 |
1 |
2 |
38 |
17 |
74 |
10 |
8 |
4 |
220 |
100 |
380 |
10 |
1 |
3 |
44 |
20 |
91 |
10 |
8 |
5 |
250 |
120 |
480 |
10 |
1 |
4 |
52 |
25 |
120 |
10 |
8 |
6 |
280 |
120 |
480 |
10 |
2 |
0 |
33 |
15 |
73 |
10 |
8 |
7 |
310 |
150 |
620 |
10 |
2 |
1 |
39 |
17 |
79 |
10 |
8 |
8 |
350 |
150 |
620 |
10 |
2 |
2 |
46 |
20 |
91 |
10 |
9 |
0 |
170 |
74 |
310 |
10 |
2 |
3 |
54 |
25 |
120 |
10 |
9 |
1 |
200 |
91 |
380 |
10 |
2 |
4 |
63 |
30 |
140 |
10 |
9 |
2 |
230 |
100 |
480 |
10 |
3 |
0 |
40 |
17 |
91 |
10 |
9 |
3 |
260 |
120 |
480 |
10 |
3 |
1 |
47 |
20 |
100 |
10 |
9 |
4 |
300 |
140 |
620 |
10 |
3 |
2 |
56 |
25 |
120 |
10 |
9 |
5 |
350 |
150 |
630 |
10 |
3 |
3 |
66 |
30 |
140 |
10 |
9 |
6 |
400 |
180 |
820 |
10 |
3 |
4 |
77 |
34 |
150 |
10 |
9 |
7 |
460 |
210 |
970 |
10 |
3 |
5 |
89 |
39 |
180 |
10 |
9 |
8 |
530 |
210 |
970 |
10 |
4 |
0 |
49 |
21 |
120 |
10 |
9 |
9 |
610 |
280 |
1300 |
10 |
4 |
1 |
59 |
25 |
120 |
10 |
10 |
0 |
240 |
110 |
480 |
10 |
4 |
2 |
70 |
30 |
150 |
10 |
10 |
1 |
290 |
120 |
620 |
10 |
4 |
3 |
82 |
38 |
180 |
10 |
10 |
2 |
350 |
150 |
820 |
10 |
4 |
4 |
94 |
44 |
180 |
10 |
10 |
3 |
430 |
180 |
970 |
10 |
4 |
5 |
110 |
50 |
210 |
10 |
10 |
4 |
540 |
210 |
1300 |
10 |
5 |
0 |
62 |
26 |
140 |
10 |
10 |
5 |
700 |
280 |
1500 |
10 |
5 |
1 |
74 |
30 |
150 |
10 |
10 |
6 |
920 |
350 |
1900 |
10 |
5 |
2 |
87 |
38 |
180 |
10 |
10 |
7 |
1200 |
480 |
2400 |
10 |
5 |
3 |
100 |
44 |
180 |
10 |
10 |
8 |
1600 |
620 |
3400 |
10 |
5 |
4 |
110 |
50 |
210 |
10 |
10 |
9 |
2300 |
810 |
5300 |
10 |
5 |
5 |
130 |
57 |
220 |
10 |
10 |
10 |
>2300 |
1300 |
-- |
10 |
5 |
6 |
140 |
70 |
280 |
Contents
Contents
Table 10-8. Commercial test products for B. cereus.
Test Kit | Analytical Technique | Approx. Total Test Time1 | Supplier |
BCET-RPLA TD950 [Used to identify B. cereus diarrheal enterotoxin] |
Reversed passive latex agglutination | 24 h (food) 48 h (bacterial culture) |
Oxoid, Inc. Contact: Jim Bell 217 Colonnade Rd. Nepean, Ontario K2E 7K3 Canada Phone: 613/226-1318 E-mail: jbell@oxoid.ca |
TECRA Bacillus diarrheal Enterotoxin
VIA [Used to detect GDE toxin and Bacillus spp. capable of producing enterotoxin] |
ELISA | 4-24 h | InternationalBioProducts Contact: Mike Yeager 14780 NE 95th St. Redmond, WA 98052 Phone: 425/861-4918 E-mail: myeager@intlbioproducts.com Web: intlbioproducts.com |
Andrews, W.H., and June, G.A. 1998. Food sampling and preparation of sample homogenate, Ch. 1. In Food and Drug Administration Bacteriological Analytical Manual, 8th ed. (revision A), (CD-ROM version). R.L. Merker (Ed.). AOAC International, Gaithersburg, MD.
AOAC. 1995a. Bacillus cereus in foods: Enumeration and confirmation microbiological methods. Sec. 17.8.01, Method 980.31. In Official Methods of Analysis of AOAC International, 16th ed., P.A. Cunniff (Ed.), 52-54.AOAC International, Gaithersburg, MD.
AOAC. 1995b. Differentiation of members of Bacillus cereus group: Microbiological method. Sec. 17.8.02, Method 983.26. In Official Methods of Analysis of AOAC International, 16th ed., P.A. Cunniff (Ed.), 54-55.AOAC International, Gaithersburg, MD.
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