A statistical study of the sensitivity of the haematocrit centrifuge technique in the detection of trypanosomes in blood

319 TRANSACTIONSOF THE ROYAL SOCIETYOF TROPICALMEDICINEAND HYGIENE. Vol. 68. No. 4. 1974.

A STATISTICAL STUDY OF THE SENSITIVITY OF THE HAEMATOCRIT CENTRIFUGE TECHNIQUE IN THE DETECTION OF TRYPANOSOMES IN BLOOD* P. T. K. WOO Department of Veterinary Microbiology and Immunology, University of Guelph, Guelph, Ontario, Canada D. J. ROGERS Hope Department of Zoology (Entomology), University Museum, University of Oxford, Oxford, England The haematocrit centrifuge technique (Woo, 1969) has been found to be rapid and reliable for the diagnosis of human trypanosomiasis (Woo, 1970). Consequently, it has now been adopted by the hospital attached to the East African Trypanosomiasis Research Organization for routine use (O~YA~qGO and M~WABI, 1970). This technique has also been shown to be useful for the survey of human trypanosomiasis and filariasis (Woo, 1971). Using the haematocrit centrifuge technique (H.C.T.), we were able to detect and study low virulent strains of Trypanosoma congolense from reservoir hosts in East Africa (Woo and KAUFFMAN, 1971). Some of these strains would not have been detected if the technique was not used. More recent studies (RoKMANA, 1972; WALKER, 1972) have confirmed the usefulness of the technique in detecting animal trypanosomiasis. The H.C.T. is particularly useful for detection of species or strains of trypanosomes which are not infective to laboratory rodents (Woo, 1970). RUKMANA(1972) also demonstrated that the technique was better than animal inoculation even with strains that are infective to rodents. The purpose of the present study is (i) to measure the efficiency of the technique; (ii) to predict the number of tubes that would have to be examined in order to detect any predetermined proportion of infected individuals to any given parasitaemia, and (iii) to find out if there is any relationship between the probability that a trypanosome will be missed and trypanosome density.

Materials and methods All trypanosomes used in this study were obtained from the East African Trypanosomiasis Research Organization, Tororo, Uganda. Most strains (except S.S. 975, S.S. 978) were stored in liquid nitrogen before use. The strains of T. rhodesiense (S.S. 975 and S.S. 978) were obtained directly from the blood of 2 patients at the E.A.T.R.O. hospital. A brief history of each of the strains is given in Table I. TABLE I. Brief history of each of the strains used. Species

Strain number

Strain originally isolated from

T. brucei

EATRO 1093 blood of naturally infected Hippotragus niger, Tanzania

T. brucei

EATRO 1416 old laboratory strain (monomorphic)

T. brucei

EATRO 1386

Number of mouse or rat subpassages 3 Numerous (> 20)

salivary gland of Glossina fuscipes, Uganda

8

T. rhodesiense SS 975

patient at EATRO hospital by blood inoculation, Uganda

1

7". rhodesiense SS 978

patient at EATRO hospital by blood inoculation, Uganda

1

T. evansii

EATRO 1188 blood of naturally infected camel, Kenya

2

T. evansii

EATRO 1342 blood of naturally infected camel, Kenya

11

T. congolense EATRO 1415 salivary gland of Glossina pallidipes, Uganda

2

*This work was supported by the International Development Research Centre (Canada), the Food and Agriculture Organisation and the Wellcome Trust, London, to whom we offer sincere thanks. We are indebted to the Director, East African Trypanosomiasis Research Organisation, Uganda, for providing facilities for the work.

320

DETECTION OF TRYPANOSOMES IN BLOOD

White Swiss mice were inoculated intraperitoneaUy with trypanosomes (either from the blood of patients or from the thawed-out materials from the E.A.T.R.O. Trypanosome Bank). Tail blood from each mouse was examined daily after the third day. When large numbers of trypanosomes were seen, the mouse was bled from the ventricle using a 1 ml. disposable syringe which had been previously rinsed with heparmized saline. The infected blood was added to about 5 ml. of freshly collected heparinized rat blood (diluent). The suspension was mixed thoroughly and divided into 5 different samples (except strains E.A.T.R.O. 1093, and 1416). The number of trypanosomes in each of the 5 samples was estimated from counts made in a haemocytometer (Neubauer ruling) and this was expressed as number of trypanosomes per ml. of blood (Table I I). Each of the set of data for strains EATRO 1903 and EATRO 1416 (Table I I) was collected on different occasions. While the number of trypanosomes in each sample was being estimated, each of the samples was diluted serially tenfold in freshly collected heparinized rat blood. This was done by carrying over 0-2 ml. (in 0.20 ml. pipettes) after mixing, to 1.8 ml. of freshly collected rat blood. Dilution was by two-fold after i : 100,000. After dilution, 3 capillary tubes* were filled with blood from each dilution. The column of blood in each tube was 55 mm. long. The tubes were sealed at one end with plasticine and centrifuged at 12,000 r.p.m, for 4 minutes in an "International Microcapillary Centrifuge" (Model MB). After centrifugation, the tubes were placed in a capillary tube holder and examined for trypanosomes under a microscope using a × 10 objective (Woo 1969). The volume of fluid in the 55 mm. column was estimated by gravimetric means. 30 capillary tubes were individually weighed before and after they were filled with distilled water (55 ram.). In the analysis of the results it is assumed that trypanosomes are distributed at random throughout the sample of tubes examined, and that there is a specific probability that any particular trypanosome will be missed by the examiner. This probability (q) is, in the first instance, made independent of the density of trypanosomes in the sample. At each trypanosome density, a proportion of haematocrit tubes examined will be scored as negative. This proportion is the sum of i) the proportion of tubes which do not contain trypanosomes, and ii) the proportion of the tubes containing 1 or 2 or 3 etc. trypanosomes, all of which are missed by the examiner. Each of these proportions can be predicted from formulae for random distributions. There are two "models" for the random distribution of (x) trypanosomes among (N) haematocrit tubes: these are the binomial and Poisson formulae. The binomial formula is applicable over all ranges of (x) and (N), since it is based on the probability of any one tube receiving any one trypanosome (i.e. l/N) or not receiving the trypanosome (i.e. (l-l/N)). The Poisson is an approximation to the binomial; and applies only when both (x) and (N) are large (SN~-VECORand COCmULN 1967). The purpose of the present study was to estimate (q), the probability of missing any one trypanosome, for a variety of trypanosome species and strains. In the discussion it will be shown that (q) estimated from the Poisson distribution is always lower than that estimated from the binomial distribution. This is especially true when (q) is small and means that the Poisson will always tend to over-estimate the efficiency of the H.C.T. In the following analysis, the binomial distribution is described while the discussion shows how the Poisson can be used in an approximate graphical presentation of the results. The binomial model I f (x) trypanosomes are distributed at random in the (N) haematocrit tubes, the successive terms in the expansion of ((1-- l/N) q- l/N) x .. I give the proportions of the tubes with 0, 1, 2, 3 and more trypanosomes (STOY 1932). The general term in this expansion, en = xCa (1 -- l/N) x'n (l/N) n, (n -----0, 1, 2, 3, etc.), . .2 gives the proportion (P,) of the tubes containing (n) trypanosomes. I f (q) is the probability that a single trypanosome will be missed, then (q") is the probability that all the trypanosomes in the tube containing (n) trypanosomes will be missed by the examiner, i.e. that the tube will be scored as negative. Therefore the proportion of the tubes containing (n) trypanosomes and scored as negative (i.e. (P~).ve) is (Pn).ve= XCn (1 -- l/N)x'n(l/N)n(q) n ..3

*"Red-Tips", Heparinized Capillary Tubes. Fisher Scientific Co., Pittsburgh, Pennsylvania, U.S.A.

P. T. K. WOO AND D. J. ROGERS

321

- - *C~ (1 -- I/N)x-n(q/N)n . .4 This is the general term in the expansion o f ( (1 -- l/N) + (q/N))* . .5 which therefore gives the proportion of all tubes scored as negative. Assuming that (x) and (N) are known, (q) can be calculated. Thus if P_v¢ = ( (1 - - l/N) + (q/N))x . .6 where (P_vc) is the proportion of all tubes scored as negative, then q ---- N ((P_vc) 1Ix -- (1 -- l/N) ) . .7

Results T h e average volume o f sample fluid in a 55 ram. column o f capillary tube was found to be 0-0547 ml. (s.d. 0-005: sample size -----30 tubes). This is the value used in aU subsequent calculations. All centrifuged tubes were positive at the lower dilutions (1/10 -- 1/10,000) while trypanosomes were not seen in some of the tubes at the higher dilutions (1/100,000 - - 1/400,000). T h e results are summarized in Table II. T h e number of trypanosomes in each of the positive tubes (at the highest dilution) varied from 1-4 per tube. TABLE II. Summary of results showing the number of positive tubes for each of the samples at high dilutions. Trypanosome

Strain

Number of trypanosomes per ml.

Dilution 1/10-1/10,000

1/100,000

1/200,000

1/400,000

E A T R O 1093

4-4 x 106 5'1 × 106

3/3* 3/3

3/3 3/3

3/3 2/3

N.D. N.D.

E A T R O 1416

3"0 x 106 5"6 × 106

3/3 3/3

3/3 3/3

2/3 3/3

N.D. N.D.

E A T R O 1386

6.4 5.7 6.9 6'6 6.4

x x × x ×

106 106 108 106 106

3/3 3/3 3/3 3/3 3/3

3/3 3/3 3/3 3/3 3/3

2/3 1/3 3/3 3/3 2/3

N.D. N.D. N.D. N.D. N.D.

SS 975

4"7 4.3 4.3 4-0 4"6

x × × x x

106 106 106 106 106

3/3 3/3 3/3 3/3 3/3

2/3 3/3 2/3 3/3 2/3

2/3 2/3 1/3 1/3 2/3

N.D. 2/3 N.D. N.D. 2/3

SS 978

5.1 4.8 4.8 4-6 5.4

× x x x x

106 106 106 106 106

3/3 3/3 3/3 3/3 3/3

3/3 3/3 3/3 3/3 3/3

2/3 3/3 2/3 1/3 2/3

0/3 1/3 2/3 0/3 2/3

E A T R O 1188

2"6 2.4 2"4 1"8 2"4

x x × x x

106 106 106 106 106

3/3 3/3 3/3 3/3 3/3

3/3 2/3 1/3 2/3 2/3

1/3 1/3 1/3 0/3 0/3

N.D. N.D. N.D. N.D. N.D.

E A T R O 1342

3"8 4.2 3"6 4-4 3"6

x x x x x

106 10° 106 106 106

3/3 3/3 3/3 3/3 3/3

3/3 2/3 3/3 3/3 3/3

2/3 3/3 2/3 1/3 3/3

N.D. N.D. N.D. N.D. N.D.

T. congolense E A T R O 1415

6.4 5-8 7.0 5.6 5.6

x x × x ×

10e l0 s 10e 106 l0 s

3/3 3/3 3/3 3/3 3/3

2/3 3/3 2/3 3/3 2/3

1/3 1/3 2/3 1/3 0/3

0/3 1/3 1/3 0/3 0/3

T. brucei

T. rhodesiense

r . e'utll,lsii

*number of positive tubes to number of tubes examined,

t N . D . - - n o t done.

t

322

DETECTION OF TRYPANOSOMES I N BLOOD

Table I I I shows the experimental results used in the estimation of (q). For each trypanosome strain or species, the arithmetic average of the haemocytometer readings in Table I I has been calculated, and the results for each 'dilution' have been combined. Column 4 in the Table lists the average number of trypanosomes per H.C.T. tube on the assumption that the volume of blood sampled is 0.0547 ml. In the calculation of (q) from formula 7, (x) was made equal to the product of this average and the total number of tubes examined in the sample (i.e. N). TABLE I I I . Values derived from Table I I and used in the estimation of (q), the probability of a trypanosome being missed by the H.C.T. Trypanosome

Density per ml.

Dilution

Density per capillary

Positives

Proportion +vc

Proportion -ve

T. brucei

5-46 × 10e

1/200,000

1"493

21/37

0.778

0-222

T. rhodesiense

4"66 × 106

1/100,000 1/200,000 1/400,000

2.549 1"275 0-637

27/30 18/30 9/21

0.900 0" 600 0"429

0.100 0.400 0.571

T. evansii

3" 12 × 10e

1/100,000 1/200,000

1.707 0" 853

24/30 14/30

0"800 0" 467

0"200 0.535

T. congolense

6"08 × 106

1/100,000 1/200,000 1/400,000

3.326 1" 663 0" 831

12/15 5/15 2/15

0.800 0"333 0" 133

0.200 0" 667 0" 867

Table IV lists the estimated values of (q) for the various trypanosomes studied. 7-figure logarithms were used in the calculation of the root of (P.ve), although 4 or 5-figure logarithms would be sufficiently accurate for most purposes. Table IV also lists the values of (1 -- q), which is the probability of seeing any single trypanosomes by the H.C.T., and is thus a measure of the efficiency of the technique. TABLE IV. Results of the estimation of (q) and (1 - q) derived from the application of equation 7 to the experimental results of Table III. Trypanosome

Density per capillary

Sample size (N)

Proportion -re

q

(1 - q)

T. brucei

1.493

27

0.222

0"011

0" 989

T. rhodesiense

2.549 1.275 0"637

30 30 21

0.100 0- 400 0"571

0" 110 0- 290 0-140

0" 890 0.710 0"860

T. evansff

1-707 0.835

30 30

0.200 0.533

0.072 0"272

0.928 0.728

0' 149

0" 851

0"524 0"758 0"829

0-476 0"242 0"171

0.704

0.296

Average values ( T. brucei, T. rhodesiense and T. evansii)

T, congo~nse

3"326 1.663 0"831

15 15 15

0"200 0"667 0"867

Average values (T. congolense only)

The analysis shows that the H.C.T. is extremely successful in detecting trypanosomes, even at very low densities. T h e probability of seeing any one trypanosome varies between 0.17 for T. congolense and 0.99 for T. brucd. Within the group (T. brucei, T. rhodesiense and T. evansii) the average probability is 0.85, which indicates that 85% of all the trypanosomes of this group are seen by the experimenter.

323

P. T. K. WOO AND D. J. ROGERS

Sample size in the detection of trypanosome infections The more tubes examined by the experimeter, the greater is the likelihood that any particular infection will be detected. Assuming that (q) is known for the particular trypanosome (and examiner) involved, it is possible to predict the number of tubes it would be necessary to examine in order to detect any predetermined proportion of infected individuals to any given parasitaemia. I f (P_ve) is the proportion of tubes scored as negative, then ((p.ve)N) is the probability that all tubes in a sample of (N) will be scored as negative. Thus if a population is being sampled for infected individuals, and if a sample of (N) tubes is taken from each individual, the solution of OR

(P_vo) N

~<

0.05

..8

(P_ve)N

~< 0.01

..9

for (N) will determine the number of tubes that must be examined in order to detect 95% or 99% of infected individuals with parasitaemias of greater than any predetermined figure (this figure appearing as (x) in formula 7 for (P.ve)). Figures la (95% detection rate) and lb (99% detection rate) show a series of curves derived from the solution of equations 8 and 9. The sample size, (N) tubes, is shown on the horizontal axis, and the minimum parasitaemias detected on the vertical axis (logarithmic scale) for a range of values of (q), the probability of failing to see any one trypanosome. For example, assuming that q ~ 0.45 and that 5 tubes (each of capacity 0.0547 ml.) are taken from each subject, the technique will detect 95% of all individuals with parasitaemias of 19 (or more) trypanosomes per ml. and 99% of all individuals with parasitaemias of 29 (or more) trypanosomes per ml. o

b.

500

500

400

40O

300

3OO

200

_~00

100

,oo t

CZ

E 0 ~h 0 r¢Z

b ~d

50

50

10

10

L

E c

E E c

Z

1.

. 2.

Number

3. of

.4

5

"6

H.C.I~ t u b e s

87' 9 " " exornined,

10 '~'N

1

:~

Number

3

4. of

.5 . 6.

HC-[

tubes

.7

. 8 .

9

exomined,

10 N

FIG. 1. The relationship between the minimum parasitaemias detected by the H.C.T. and the sample size, N tubes, for various values of q, the probability of failing to see a single trypanosome: la 95% of all infections detected lb 99% of all infections detected

324

D E T E C T I O N OF TRYPANOSOMES I N BLOOD

The range of values of (q) The efficiency of the H.C.T. depends on the value of(q) for the trypanosome being studied. Especially for field use, it is necessary to know the maximum expected (q), since this will determine the number of tubes to be examined. I f in the present instance the trypanosomes (T. brucei, T. rhodesiense and T. evansii) which give similar values for (q), are considered as a single group, then the average expected q = 0.149 with sample variance s ~ = 0.123 (n = 6). In Figure 1 the heavy lines represent the success of the technique for q = 0.15. The sample variance (s 2) is related to the population variances (o) according to the formula X2 ~

(n --

1)

s2

(SNEDECOR and COCHRAN 1967)

.. 10

The upper confidence limit for (~2), which is exceeded in only one out of 20 cases, is found from g 6max.

--

--

(11 - -

1) s ~

.

.ll

~20.95

(5) (0.123) 1.15 Crmax2 = 0"054 and ~max = 0"231 Thus, where trypanosomes of this group are being studied, most of the populations sampled will have an average q = 0.149 and standard deviations less than *max= 0"231. With such a population, 95% of the samples taken will have a value of (q) less than (qm~), where qmax ---~ q + l'65amax = 0"149 + 1"65 (0"231) = 0"531 It therefore seems unlikely that (q) in any sample of these trypanosomes will exceed 0.55: this value gives the broken curves in Figure 1. Thus under normal conditions, it would be expected that any sample of 7". brucei, T. rhodesiense or T. evansii is likely to be characterized by the thick lines in Figure 1 and only rarely will be more extreme than the broken lines.

The relationship between (q) and trypanosome density In the previous sections, it has been assumed that (q) is independent of trypanosome density. This was tested by calculating the correlation coefficient between the values of (q) and the trypanosome densities per tube shown in Table III. For the group (T. brucd, T rhodesiense and T. evansii) the correlation coefficient r = 0.422 (4 degrees of freedom) and for T. congolense,r = 0-994 (i degree of freedom). Although neither correlation is significant at the 5%tevel, there is a suggestion (especially in the T. congolense samples) that (q) decreases with trypanosome density. Whilst we can at present offer no explanation for this, we do not consider it necessary to make allowance for it until a statistically significant relationship is demonstrated. Discussion

The choice of a suitable mathematical model for the analysis of H.C.T. results affects estimations of the parameter (q). In this paper we have chosen the binomial model: the alternative Poisson approximation tends to under-estimate the H.C.T. failure rate in all instances. Thus equation 6 can be re-written P.ve = ( 1 + ( q - - x 1N) ) ..13 Converting this to the Poisson formula by the usual approximation P.ve - : e x(Q-1)/N . . 14 where (Q) is now the Poisson estimate of the probability of failing to see a single trypanosome and all t h e other symbols remain the same. I f both equations are applied to the same experimental results, then N

=

P.ve

~---

e x(Q-1)/N

..15

325

P. T. K. WOO AND D. J. ROGERS

or, taking roots, 1 + (q-

1)

)

e (Q-1)IN

• .16

-- 1 +

+

1

~

y,

+

...1

n

..17

Since (Q - 1) is negative and less than one and since (N) is always positive it follows that the sum of the right hand series excluding the first two terms is positive and therefore that 1 +

(q --

1)

~

1 +

N

(Q

-

1)

N

. .18

from which q > Q ..19 The Poisson thus over-estimates the efficiency of the H.C.T. and should not be used for complete accuracy. Equation 14 can be rewritten - - lne(P_ve) = x (1 -- Q) ..2o N Values of (Q) can be calculated from this equation which also indicates that the relationship between (-- lne (P-v~)) and the average number of trypanosomes per capillary tube (x/N) is linear, with a slope of (1 -- Q). In Table V, Poisson estimates of (Q) are compared with the earlier estimates of (q) using the binomial, and Figure 2 shows how the results appear graphically. Under certain conditions, the differences between (q) and (Q) might be accepted as negligible, and the graphical method preferred for simplicity. In Figure 2 T. brucei, T. rhodesiense and T. evansii have again been considered as a single group, and the regression constrained (for which t = 0.837, 0"5 > p > 0.4) in order for it to pass through the origin (without constraint y = 0-97x -- 0.12). The slope of the regression (0.898) is quite similar to the average value of (1 -- Q) given in Table V (0-871). The non-linear result for T. congolense illustrates the point made previously that (Q) tends to decrease with increasing densities of this trypanosome species. The usefulness of this graphical short-cut is that it can provide an immediate estimate of the success rate of the haematocrit centrifuge technique under various conditions. It is an easy matter to plot -- ln~(P_ve) against the average number of trypanosomes per capillary tube and to draw a straight line through the origin and the experimental points. The slope of the line then indicates the proportion of the trypanosomes of that particular strain that are seen by the experimenter. TABLE V. A comparison of the values of (q) (binomial), and (Q) (Poisson), estimated from the experimental results of Table III. Trypanosome

Density per capillary

Sample size (N)

q

T. brucei T. rhodesiense

1.493 2-549 1"275 0"637 1'707 0-853

27 30 30 24 30 30

0.011 0"110 0"290 0"140 0"072 0"272

T. evansff

3"326 1"663 0"831

15 15 15

(1 - Q)

-0-007 0"097 0"281 0"121 0'057 0"263

1.007 0"903 0-719 0"879 0"943 0'737

0-129

0"871

0.524 0"758 0-829

0'516 0.756 0"828

0.484 0.244 0"172

0" 704

0" 700

0"300

Average values ( T. brucei, T. rhodesiense and T. evansii) 0"149 T. congolense

Q

Average values (T. congolense only)

326

DETECTION

OF

TRYPANOSOMES

IN

BLOOD

o "IT bt"ucei o T rhodcsJgnse x T evansii n -[ c o n g o l e n s e

~> 4.0 E (95%

y : 0.898x limits b y f - O . ~

rf

43

2

FIG. 2. The relationship between the natural logarithm of the proportion of tubes scored as negative by the H.C.T. and the average trypanosome density per capillary tube.

2.0 O ×

oa. o

n

./ /2"2 o

o

_c

i

0

1.0

2.0

Trypanosomes

3.0

4.0

pet" c a p i l l o r y

This quantitative study shows that under laboratory conditions, the technique is extremely sensitive for the detection of T. brucei, T. rhodesiense and T. evansii in blood. However, it is less sensitive for T. congolense. This may be because T. congolense has a specific gravity similar to that of erythrocytes, as was suggested by WAt,KER (1972), and hence would come down more readily with erythrocytes during centrifugation. Also, because T. congolense is smaller and much less active, it is more likely to be missed by the examiner when there are only a few trypanosomes in the tube. However, it is still more sensitive than detection by wet preparation or thick smear or even animal inoculation in some cases (Woo and KAUFFMAN, 1971; RUKMANA, 1972). Work currently in progress in Nigeria also shows that the technique is very sensitive in detecting primary T. vivax infections in cattle (P. LEEFLANG,personal communication). Since T. vivax is not infective to laboratory rodents by blood inoculation, the usefulness of the technique as a diagnostic procedure for detection of T. vivax infections in animals cannot be overemphasized.

Summary The sensitivity of the haematocrit centrifuge technique in detecting trypanosomes was investigated using both old laboratory and freshly isolated strains. Two alternative methods of analysing the results are suggested, based on the binomial and Poisson distributions. The analysis shows that the H.C.T. can detect about 85% of the trypanosomes present in capillary samples of Trypanosoma brucei, T. rhodesiense and T. evansii, and 30% of T. congolense group trypanosomes. The technique is therefore much more sensitive than previous wet preparation or thick smear techniques. Graphs are provided showing the minimum number of tubes that would have to be examined for 95% and 99% detection of low infections (i.e., in the range up to 500 trypanosomes per ml.). Analysis of the results using the Poisson model includes details of a simple method that estimates the efficiency of the H.C.T. from the slope of a graph. The present results do not show any significant relationship between the probability that a trypanosome will be missed by the H.C.T. and trypanosome density. REFERENCES ONYANGO,R. J. & IMBWABI,D. L. (1970). Annual Report, EATRO., 1970, p. 79. RUKSt~A, M. P. (1972). Z. Tropenmed. Parasit., 28, 156. SNEDECOR,G. W. & COCHRAN,W. G. (1967). Statistical Methods. 6th ed. Iowa State University Press, Iowa. STOY, R, H. (1932). Bull. ent. Res., 23, 215. WALKER, P. J. (1972). Trans. R. Soc. trop. Med. Hyg., 66, 348. Woo, P. T. K. (1969). Canad. J. Zool., 47, 921. (1970). Acta trop., 27, 384. (1971). Ibid., 28, 298. - & KAUFFMANN,M. (1971). Ibid., 28, 304.