A METHOD FOR CALCULATING THE AREA

Transcription

1 Lab. Anim. (1968) 2, ]21 A METHOD FOR CALCULATING THE AREA OF BREEDING AND GROWING ACCOMMODATION REQUIRED FOR A GIVEN OUTPUT OF SMALL LABORATORY ANIMALS by MICHAEL FESTING and JOHN BLEBY Medical Research Council, Laboratory Animals Centre, Woodmansterne Road, Carshalton, Surrey SUMMARY A method is given for the calculation of the area of animal accommodation needed to produce a given output of small laboratory animals. This method depends on determining the number of cages needed according to productivity, the age of animals at time of use, the proportion of animals not suitable for use, and the stocking density of the growing stock for the output needed. The area needed to hold this number of cages can then be calculated according to the shelf length taken by the cages, working space required, numbers of tiers of cages, and the proportion of animals that will be wasted due to fluctuations in supply and demand. An example is given and compared with actual results, and the effects of errors in the estimation of some of the variables are discussed. An early step in the planning of new breeding accommodation for laboratory animals is the calculation of the area of floor space that will be needed. This calculation depends on the species and type of animal to be produced, the age at which they will be used, the productivity, the type of caging, and the effects of variations in demand and supply. There appears to be no published method for making these calculations, and little information is available on the relationship between the variables mentioned above and the final area that is required. This paper outlines a method for calculating the area of animal accommodation required, and illustrates the calculations by means of an example.

2 122 MlCHAEL FESTING AND JOHN BLEBY The method used to calculate the area of accommodation required depends on determining, first, the number of cages required (which depends on the number, age and type of animal to be produced, the productivity, the size of the cage, and the numbers of growing animals per cage), and second, the area of accommodation required to house these cages. The latter assumes that the cages are placed in racks or on shelves, and it is therefore possible to work out the length of 'shelf' space needed. The area required can then be calculated by accounting for the number of tiers of cages and the area of floor space needed to service one linear unit of 'wall space', though the use of free-standing units is not excluded. These calculations must be done separately for each species, with the final results combined to give a total estimate of the area required. Number of cages For the purposes of this paper it is assumed that cages used to hold breeding stock, and cages used to hold young growing stock (stock which has been weaned but is not yet old enough to be issued), are the same size, but provision is made to allow for any number of animals per cage in the case of growing stock. No assumptions are made about the number of breeding stock housed per cage, but productivity is defined as the output per cage per week, which will largely depend on the number of breeding animals per cage, as well as the strain and species of animal. Under these conditions, it can be deduced tbat the number of cages needed for a given output, OW, per week is given by formula 1: N = OW{ _1 _ + W} P(1-K) D where: N OW = P K W D number of cages needed; average number of animals to be used per week (output); productivity (Heine, 1965)-the number of weaned animals produced per breeding cage per week; proportion of animals not suitable for use (e.g. surplus females, if males are mostly used for research); maximum length of the growing period in weeks; number of growing future experimental animals maintained per brcedingsize cage (this figure can be adjusted if in fact a different sort of cage is used for growing only). National Research Council (J ) gives recommendations for caging density. Calculation of area Having calculated the number of cages required to produce the desired output, this number can be used to calculate the area of animal room needed (formula 2):

3 ANIMAL SPACE REQUIREMENTS RQN A= -- T(l-F) 123 where: A R Q T F N area of animal room needed (ft 2 or m 2); number of units of floor space (ft 2 or m 2) needed to service a linear unit (ft or m) of wall space; width of a single cage (ft or m). Note: it is assumed that the cages are placed on shelves or racking with the longest horizontal dimension adjacent to the next cage, and the narrowest dimension facing the working area. Note also, cage dimensions and R are closely related; number of tiers (shelves) of cages for the given species; average proportion of animals that are not used due to fluctuations in supply and demand; number of cages needed (from formula I). (N.B. Measurement must be either all metric or all in feet). Most of these terms are self-explanatory, except possibly for F, the average proportion of animals that cannot be used due to fluctuations in supply and demand. Tn practice, it is very difficult to match supply and demand exactly, and fluctuations in either can lead to periods of shortage (which could have serious consequences for some experimenters) or over-production, necessitating the disposal of the unwanted animals. Factors influencing the value of F are discussed in a later section. Formulae 1 and 2 may be combined (formula 3): R Q OW {I W} A = TO-F) P(l-K) + D where the variables are as previously defined. Choosing values for the variables Formula 3 allows the calculation of the area of accommodation required to produce the number and type of animal of each species that are needed, provided that it is possible to choose suitable values for each of the variables. The value of many of the parameters will be determined by the type of animal to be produced, the equipment available, and the type of demand to be catered for. Figures for productivity can be obtained from previous records, and an informed guess made about future trends. Where previous experience is not applicable, Table I may be consulted for some suggested values of the variables though this table should only be used as a guide.

4 124 MICHAEL FESTING AND JOHN BLEBY Variable Table 1. Suggested values for some of the variables used in calculating space requirements for breeding and growing laboratory animals. R Calculated from Walker & Poppleton (1967) for rats and mice Value at LAC Specific Pathogen Free unit for rats and mice Rabbits, cats, guinea-pigs F Demand irregular, short' shelf life' Typical departmental production unit All animals used P Comment Mice poor inbred line, pairs good inbred/poor non-inbred, pairs good non-inbred pairs good non-inbred trios good non-inbred polygamous Rats inbred line, pairs non-inbred pairs polygamous systems (different-sized cages) Cats 8-10 kittens/breeder/year, single cat per cage Hamsters inbred: 5 litters x 4 young non-inbred: 6 litters x 8 young, single pair/cage Rabbits average 5 matings at 2.74 offspring per matingt single doe/cage Guinea-pigs young weaned per sow per yeart *Estimated from Lipscombe, Bleby & Porter (1966). tnapier (1963). *F. Hoyland (]967, unpublished data). The number so the figures are given on a per sow basis rather than per cage. Suggested value 3.7 ft2/linear ft 1.11 m 2Jlinear m 4.7 ft2jlinear ft 1.44 m 2Jlinear m ft 2Jlinear ft m 2/linear m /cage/week " " " " " per sow per week of females per cage is more variable with guinea-pigs than with other species, Specimen calculation The Laboratory Animals Centre maintains a number of inbred strains of mice as a source of breeding nuclei for other laboratories that wish to produce

5 ANIMAL SPACE REQUIREMENTS 125 their own experimental animals. The production/demand relationships of two of these strains (CBA and BALB/c) have been used to illustrate the use of formula 3 and to check the estimated results for a six month period (early in 1968) against the actual results. Table 2 presents the required information on the two strains. Information is given of the number of breeding females, average sales per week, average number cuiled and average productivity. The information was split up into three periods, corresponding roughly with the first and second half of 1967, and the first half of Table 2. Breeding data on mice used in the specimen calculation. Pro- Period Av. no. Av. sales AI'. no. ductivity Strain (6 months) No. weeks breeding week culledfwk (Yf '?fwk)* '? '? CBA {estimated actual BALBfc {estimated actual *Bred as monogamous pairs, so that results per cage and per female are identical. The 1967 data was then used to estimate how much space would be required to produce these two strains of mice in Variables were estimated to be as follows: W=9 mice were weaned at 3 weeks of age, and culled at 12 weeks if not required; D=4 since total output per week was relatively low, only a certain amount of grouping could occur; in practice, only an average of 4 mice were housed per cage; K=O equal numbers were required of each sex, and all animals were suitable for use; R=4.7 rooms were designed to give this ratio of floor space to wall space; Q=O.5 plastic cages were used, and they were about 6 in (15 cm) wide;

6 126 MICHAEL FESTJNG AND JOHN BLEBY T=6 six tiers of shelves; OW=20(CBA) and 19 (BALB/c); in this case, demand was estimated simply as the average demand over the previous year. It is possible that seasonal effects are important, but there was not sufficient information to estimate these; p= 1.27 (CBA) and 1.03 (BALB/c); these figures were both above the productivity figures given by Festing (1968) for these strains, but Festing's figures give the productivity that would be expected in the absence of cuiling; in practice, culling sterile pairs and sl<:>wbreeders considerably increases the apparent productivity; F=0.2 the value of F calculated from the data in Table 2 was 40/80=0.50 for CBA and 19/56=0.34 for BALB/c. However, at the end of 1967 it had become obvious that the wastage was too great, and it was decided that a level of wastage of 20 per cent (F=0.2) would be more acceptable, so this value was assumed in the calculations. Substituting these values into formula 3 gives the following: Space required (CBA) 4.7 x 0.5 x 20 {I 9 } = 29.7 ft 2 (2.759m 2 ) 6 (1-0.2) xO.5x 19 {I 9} Space required (BALB/c) = = 29.3 ft 2 (2.722m 2) 6 (1-0.2) In practice, each of these strains occupied approximately one-fifth of the space in an animal room of 168 ft 2 (15.6 m 2), or about 34 ft 2 (3.1 m 2). Thus there is reasonably good agreement between the estimated space requirements for the projected demand and the actual space allocated. Inspection of Table 2 shows that in both cases the estimated demand was in reasonable agreement with actual demand. Also, the value of F (the proportion of animals not used due to fluctuations in supply and demand) was successfully reduced from 50 to 15 per cent in the case of CBA, and from 34 to 13 per cent in the case of BALB/c. This compares favourably with the 'acceptable' level of 20 per cent used in the calculations. Effects of errors in the estimation of the variables Estimates of some of the variables will be subject to considerable uncertainty, and it is worth considering what effect an incorrect estimate will have on the results of the calculations.

7 ANIMAL SPACE REQUIREMENTS 127 The variables that are most difficult to estimate are the demand (OW), the productivity (P) and the proportion of the animals that are not used due to fluctuations in supply and demand (F). From formula 3 it can be seen that the area of animal room required is directly proportional to the total demand. Generally, if demand doubles, then the area of animal room needed to meet this demand will also double, though with a higher general level of demand it may be possible to reduce the wastage (F). This saving will usually only be marginal. With an entirely new animal facility it may be extremely difficult to estimate future demand, though when a large investment is involved it may be worthwhile to use market research methods. In this case, it may even be possible to assign a confidence interval to the estimate of demand. Where market research is not practicable or economic, a more subjective estimate will have to be used, but again it may be possible to postulate a range of possible demand. Where the new animal house is planned to take account of a regular expansion of demand, data will usually be available on past demand, and regression methods may be employed to estimate future demand, together with a confidence interval. Extrapolation of this type is subject to considerable error, and all possible supplementary information should be used. Having obtained an estimate of future demand and, say, a standard error of this estimate, it is then relatively easy to calculate the area of accommodation needed to have a 90 (say) and a 95 per cent probability that there will be sufficient space to meet demand. The cost of extra space can then be balanced against the cost of failing to meet demand, and the probability that this will occur. Suppose, for example, that demand is estimated to be 2000 ± 200 animals per week, and the rest of the parameters are such that this would take 3000 ft 2 (278.7 m 2) of floor space, there would be approximately a 10 per cent chance that demand would exceed 2256 animals (assuming demand is normally distributed), needing a floor space of ft 2 (314.4 m 2), and a 5 per cent chance that demand would exceed animals needing a floor space of ft 2 (324.4 ill 2). Assuming that animal house costs 151 ft 2 ( 161/m 2 ) it would cost an extra 15 x 108 = to reduce the chance of being unable to meet demand from 10 to 5 per cent. The decision then has to be taken as to whether the reduced risk is worth this outlay. In contrast, errors in the estimate of productivity have a less dramatic influence on the total space requirements, though the actual influence depends very much on the values of some of the other parameters. The reason for this is that for any given level of demand, the amount of space required for growing stock is constant. If the productivity is half what was estimated, then double the number of breeding cages will be required, but the number of growing cages will stay constant. Suppose, for example, that productivity

8 128 MICHAEL FESTING AND JOHN BLEBY in the BALB/c mice had been only 0.52 instead of 1.03 in the example given, then the floor space requirement would have risen from 29.3 to 38.0 ft 2 (from to m 2). Thus, in this particular case, a reduction of 50 per cent in productivity would mean that about 30 per cent more space was required to achieve the same output. In general, minor errors of estimation of productivity are not serious if the absolute level of productivity is high, or if the growing period is long. However, where there is any doubt about the level of productivity an attempt should be made to carry out the same general procedure as recommended for demand, that is to obtain estimates of the standard error associated with the productivity estimate, and to use this to calculate the cost of various levels of safety margin. The proportion of animals that are not used due to fluctuations in supply and demand is the third parameter whose estimation is subject to a certain amount of error. The average wastage depends mainly on three factors: fluctuation in demand, fluctuation in production, and the shelf life of the animals. Unfortunately, the relationships between these factors are complicated, and the best method of estimating this parameter is to rely on previous experience. In the example given the value of F achieved in the first half of 1968 was per cent. In this case, demand fluctuated violently, ranging from 0 to 148 mice in a four-week period. Production varied from 53 to 139 mice in a four-week period, and the shelf life of the mice was relatively long since they were available for use from about four weeks to about twelve weeks of age. If the shelf life of the mice had been shorter, the large fluctuations in demand would have resulted in much greater levels of wastage. Some steps can be taken to reduce wastage, and again formula 3 may be used to weigh up the relative costs of reducing this' wastage, and of planning for it. For example, demand can be evened out by allowing a waiting list to develop for the animals, supplying the animals as they become available. Methods of solving this type of 'queueing' problem are given by Houlden (1962). Another method which has been used is to choose a strain of animal with a relatively long shelf life. Thus, if rats are used by weight, a slow-growing strain will have a relatively long shelf life. On the other hand, the savings thus made in wastage must be balanced against the increased growing period needed to reach the minimum usable weight. This type of comparison can be made very easily by substituting various values of growing period and wastage in formula 3. Unplanned fluctuations in production will generally increase wastage, so attempts should be made to have a regular policy for the culling and replacement of breeding stock designed to reduce periods of surplus and shortage. The other variables should all be relatively easy to estimate, though if any of them are subject to errors, the floor area required under the worst and best sets of conditions can easily be worked out.

9 ANIMAL SPACE REQUIREMENTS 129 Service areas The formulae presented here give the area of animal room required for the various types of animals needed. Information on other aspects of the design and function of laboratory animal houses are given by Hare & O'Donoghue (1968), but care should be taken to ensure that adequate room area is allowed for services and storage. REFERENCES Festing, M. (1968). Some aspects of reproductive performance in inbred mice. Lab. Anim. 2,89. Hare, R. & O'Donoghue, P. N. (eds) (1968). The design and function of laboratory animal hollses. Lab. Anim. Symp. 1. Heine, W. (1965). Problems of large scale production. Fd Cosmet. Toxicol. 3, 223. Houlden, B. T. (ed.) (1962). Operational research. London: English Universities Press. Lipscombe, c., Bleby, J. & Porter, G. (1966). The effect of three methods of mating on reproduction in mice. J. Inst. Anim. Techs 17, I. Napier, R. A. N. (1963). Rabbits. In Animals for research (ed. W. Lane-Petter). London & New York: Academic Press. National Research Council Standards. Published in Washington by U.S.A. National Academy of Sciences, National Research Council, and Institute of Laboratory Animal Resources. Standards for the breeding, care and management of Syrian hamsters (1960). Standards for the breeding, care and management of laboratory mice (1962). Standards for the breeding, care and management of laboratory rats (1962). Standards for the breeding, care and management of laboratory cats (1964). Standards for the breeding, care and management of guinea pigs (19M). Walker, A. J. T. & Poppleton, W. R. A. (1967). The establishment of a specific-pathogenfree (SPF) rat and mouse breeding unit. Lab. Anim. 1, l.

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