CAN. 3. PHYSIOL. PHARMACOL.
k70L. 55. 1977
Simulation of oviductal ovum transport Can. J. Physiol. Pharmacol. Downloaded from www.nrcresearchpress.com by WA STATE UNIV LIBRARIES on 11/24/14 For personal use only.
J. PQRTNOW,~ 8.J. HOBGSON,AND A. T A L Q ~ Center for Research and Training in Reproducra'ce Biology, Depurrrnenrs qf Obstetrics and C?lnecology and Pharmacology, The Universiqy of Texas Health Science Center ar Sarz Ar~tottic,,Sun Antornis, T X , U.S.A. 78284 PORTNOW, J., H O ~ S O N B., J., and TALO,A. 1977. Simulation of oviductal ovum transport. Can. J. Physiol. Pharmacol. 55, 972-974. The present note describes a Monte Carlo simulation of ovum transport in the rabbit oviduct. Ova execute a random walk through a one-dimensional oviduct and the jump probabilities at each point are obtained from in vitra electrical recordings of smooth muscle activity. Simulated transport are compared with experimental findings at 18 and 66-68 h after human chorionic gonadotropin in~ection.
Introduction Transport of ova from the ovary to uterus through the oviduct takes 66-72 h in the rabbit. Ampullary transport is rapid (10 min); ova remain at the ampullary-isthmic junction for several hours and then slowly enter and traverse the isthmus (Pauerstein et al. 2974). The mechanisms which control this transport are still poorly understood. The local, erratic character of ovum trainsport has been reported by several authors (Harper 1961; Boling and Blandau 2971 ; Verdugo et al. 1974). Recently, Portnow et (11. (1977) presented a theoretical model of ovum transpori through the rabbit oviduct as a random walk (probability of transport being described by a d i h s i o n equation), with a reflecting barrier at the fimbriated end and an absorbing barrier at the uterine end. The present note is meant t o test the applicability of this model, and simulate the actual ovum movements with a Monte Carlo computer program (see Morn 1946) that takes individual junap probabilities frsna recordings of time sequences of spontaneous electrical activity of the smooth muscle of the oviductal wall. Hodgson et al. (1977) demonstrated a direct correlation between movement of artificial ova in the oviduct in vitro and direction and distance of propagation of spike bursts of the circular muscle. ABBREVIA~ON: HCG, human chorionic gonadotropin. PPresent address : University of Texas Medical Branch at Galveston, Medical School, Galveston, TX, U.S.A. 77550. *Present address: Zoophysiological Laboratory, Institute Biology, University of Turku, 20500 Turku, 50, Finland. 3 M d e of spread and conducting pathways for spikes are not known but could occur through the inner longitudinal muscle (in the isthmus) or in a helical manner or transverse to the main axis of the circular muscle.
The present model sees the contraction of the circular muscle of the oviduct as the sole propdsive force on the ova and assumes perfect correlation between propagation of electrical activity and ovum movement. The random motion of ova is simply a reflection of the labile nature of the firing of pacemakers or labile electrical coupling between adjacent regions in the circular muscle, and the probabilities for a jump in the ovarian or uterine direction are really probabilities that the circular muscle contraction prspagates and propels the ova in the proper directioin. Methods An ovum is represented as a point particle and moved along the oviduct in discrete steps. At each point x there are probabilities P,, and P,, that the particle will move in the uterine or ovarian direction, respectively. P,,, = 1 - P,, - P,, is the probability that the particle does not move. At each point a four-digit random n~lmber R < 1 is chosen; if R 5 P,, the particle is moved ahead P,, 2 R > P,, it is moved back one one step; if P,,, P,, it remains at the same point. The step; if R > P,, particle cannot leave the tube at the starting point and when it reaches the end point (beyond which no electrical activity was recorded and which comprises the absorbing barrier), the program is stopped and the transport is complete. The end points for 18- and 68-h oviducts were 70 and 85(;{,, respectively, of the length from the fimbriated end, for both real and simulated transport. B'rrobabilities P,,, P,,, and P ,, were derived from recordings of electrical activity of the circular muscle in vitro which used arrays of seven or eight suction electrodes placed 1-2 nnm apart; the array was moved sequentially to cover the majority of the length of the oviduct (Talo and Hodgson 1074, and unpublished results). Briefly, activity was analyzed, after careful visual observations of contractions and measurenlents of time lag of the leading edge of spike bursts, to yield frequency, origin and direction of propagation, and the number of electrodes in each direction to which activity spread. For on the three electrodes (ei, el, ck) within an array ovarian side), the total number of bursts in c1 is given by Ztt, = ni,, 4- n,-+k nlrlp,where rt,,, and n,,, are the number of bursts which have the time sequence for
+ +
(62,
+
Can. J. Physiol. Pharmacol. Downloaded from www.nrcresearchpress.com by WA STATE UNIV LIBRARIES on 11/24/14 For personal use only.
COMMUNICATIONS
1 5 + - ~ - - - - , - 7 - - - - ~ 0 10 2 0 3 0 4 0
0
Y
TIME LmSecondalIr
)
6 8 8 8 0 9 0
loPl
FIG. 1. Location of an individual particle in a simulated oviduct, expressed as percentage total length from fimbriated end (ordinate) with time (abscissa, seconds X lo2). propagation to the adjacent electrode (and which may originate at el or propagate from el, or el, respectively), and qnrs = nl-+j*k f nt+j+k -t ni+j+k. Thus, P,, = ~t~+~,& Pzn n ~=, n l - + k / ~ nand l , P,,, = nj,,/2nj. To increase the sample size (to several hundred bursts for each segment) and because of relative inaccuracies in percentage location between oviducts and because data were not obtained for electrodes at the end of each array or electrodes which did not record, data for each 5% of total length were combined for each oviduct and then combined for oviducts (> 10) from different animals killed after the same interval following the ovulation-inducing injection of 100 IU HCG. In the program, each 55% region was divided into five points with the same period and probability data. The mean values of P,, and P,, for all segments were 0.1732 f 0.021 and 0.2010 f 0.025 (n = 6), respectively, at 18 h and 0.2570 0.020 and 0,2759 + 0.012 (n = 9) at 68 h. These means for P,, and P,, were not significantly different for 18 or 68 h, but 68-h values were significantly greater than the respective 18-h values. Mean frequencies were 137 i 12.6 and 391 f 20.2 bursts/h at 18 and 68 h, respectively. The simulation only considers single jumps and ignores the variable distance of propagation. The particle moves in step sizes equal to lC,'6of the tube length. This corresponds to 1.2-mm jumps in a 12cm tube, and was chosen because the suction electrodes (400pm tip diameter) used to record electrical activity were placed approximately this distance apart along the o ~ i d u c t . ~
+
*We have verified, using the model and by varying the length of the diffusion distance, that a random walk
Five sets of 50 simulations were performed for each data group (18 and 68 h after HCCi) and sinlulations were stopped at 18 000 s.
Results and Discussion Transport experiments were simulated with probability and frequency data taken from oviducts 18 and 68 h after HCG injection. To eliminate, as far as possible, the effect of cilia, simulations were started with the particle already 40'36 of the way down the tube. Since real ampullary transport is rapid in comparison with total transport time, this initial condition serves only to eliminate that part of the transport dominated by ciliary beat. The time courses of typical transport simulations are shown in Fig. 1. In Table 1, the results are compared with previously reported experimental determinations of ovum locations at the time of removal of oviducts from New Zealand White rabbits killed 18 and 66 h after HCG injection. In the simulation, ova placed 407; of the way down the oviduct will not (i.e., Pzo = P,, = 0.5) with such step sizes can be accurately modelled by the diffusion equation: P(,,= 4e-"rr2t1412/rr, where P a , is the probability that the particle has not reached the end point of a diffusion distance I , D is the diffusion coefficient, and t is time.
974
CAN. J. P W S I O L . PHARhfACOL. VOL. 55, 1977
Can. J. Physiol. Pharmacol. Downloaded from www.nrcresearchpress.com by WA STATE UNIV LIBRARIES on 11/24/14 For personal use only.
TABLE1. Ovum location after simulated and experimental transport
Oviduct, h after HCG
Na
Total no. ova
18simulated 1 68simulated 66c
5 4 5 10
250 15 250 48
Locatioil, n/c:, mean, SD
Mean probability of reaching end pointh
47.8 0.45 49.9 1.6 81.1 1.7 82.2d 4.1
0.02+0.006 0.00 0.80k0.02 0.62k0.16
"Number of oviducts studied. bFor simulated and experimental oviducts. mean percentage /100 of ova which reached 70% ( I 8 h) o r 85 % (66 h) of tubal length. For 66-h group, ova which were missing were considered to have reached the end point, a s uterine recovery of ova is poor. 6Data derived from Pauerstein et al. (1974) and Hodgson and Pauerstein (1976). dLocation of oviductal ova w7a379.9% (SD 5.5).
progress towards the uterus but will cluster in the region 4@-5070 of the tubal length, i.e., at the ampullary-isthnlic junction. Ova placed at the same point in an oviduct 68 h after HCC will be transported to the uterine end in a few hours. This agrees with findings that donor or artificial ova put into a 68-h oviduct catch up with normal ova in about 4 h when ova are placed into oviducts in vivo (Tstsumi et crl. 1975; Croxatto, H. B. : personal communication, December 1976) or in vitro (I-Iodgson et al. 1977). In the model, ova in 68-h oviducts cluster in the proxinlal isthmus, at the same location as that for normal ovulated ova beginning transport 12-14 h after H C C injection, whether calculated in the same manner as in the model (uterine and missing ova considered to be at 85y0of the tubal length and assuming some other mechanisna permits uterine entry) or calculated for tubal ova alone. The average mean time to reach the end point was 10 681 k 277 s (n = 5). The very close agreement between mean position, in both groups, for the simulated and actual transport suggests that frequency and (or) bias cxerts a tight control on ovum transport. For the oviduct, time is measured from the moment of MCC injection and mean ovum position is set for each time. Naturally, for each control to operate, there must be a trigger mechanism setting the oviductal clock and letting the know when to start measuring time. The peak in progestin secretion after HCG iniection (Hilliard p t 01. 1968) is intriguing in this regard. This note is meant to demonstrate that a based On quantiof tative data for muscular activity accurately J
\
agrees with obscrved ovum transport. Preliminary results using data from progesterone-treated animals show accelerated transport in experimental and simulated transport. DifTercnces in jump frequency and bias which determine whether the particle is transported or not and a detailed analysis using idcal data must be the subject of a systematic study. Acknowledgments The authors are indebted to L. Scitchik for his invaluable help in the computer programming and thank Dr. H. B. Croxatto for communicating his results before publication. This work was supported by NIH-HB-09339-02. BOLING,J. L., and BLANDAU, R. 1. 1971. Egg transit through the ampullae of the oviducts of rabbits under various experimental conditions. Riol. Keprod. 4, 174-184. HARPLR,M. J. K. 1961. The mechanisms involved in the movements of newly ovulated eggs through the ampulla of the rabbit fallopian tube. J. Keprod. Fertil. 2, 522-524. HILLIARD, J., S P I ~ SH. , G., and SAWYER, C. N. 1968. Cholesterol storage and progestin secretion during pregnancy and pseudopregnancy in the rabbit. Endocrinology, 82, 157-165. H o n ~ s o B. ~ ,J., and PAUERST~IN, C. J. 1976. Comparison of oviductal transport of fertilized and unfertilized ova after HCC or coitus induced ovulation in the rabbit. Biol. Reprod. 14, 377-381. MODGSON, B. J., TALB,A., and PAUERSTEPN, C. J. 1977. Oviductal ovum surrogate movement: interrelation with muscular activity. Biol. Reprod. In press. KORN, G. A. 1966. Random-process simulation and measurements. McGraw-Hill, New York. PAUERSTEIN, C. J., ANDERSON, V., CHATKOFF, M. C., and HODGSON, B. 1. 1974. Effect of estrogen and progesterone on the time course of ovum transport in the rabbit. Am. J. Obstet. Gynecol. 120, 299-308. PORTNOW, J., TALO,A., and MODGSON, B. J. 1977. A random walk model of ovum transport. Bull. Math. Biol. Tn press. B. 1. 1976. Effect of time after TALO,A., and HOBGSON, ovulation and estrogen and progesterone on electrical activity of the rabbit oviduct. (Abstract) Pharmacologist, 18, 181. TSTSUMI,Y., OGURI,N., and HAFEZ,E. S. E. 1975. Rapid transport of alien eggs transplanted 66 hours post coiturn in the oviduct of the rabbit. J. Reprod. Med. 14, 62-63. VmDuGo. P., BLANDAU, R. I., TAM, P. Y., and HALBERT,S. A. 1976, Stochastic elements in the development sf deterministic models of egg transport. in Ovum transport and fertility regulation, World Health Organization Symposium. Edited hy M. J. K. Harper, C. J. Pauerstein, C. E. Adams, E. M. Continho, H. B. Croxatto, and D. M. Paton. Scriptor, Copenhagen.
k70L. 55. 1977
Simulation of oviductal ovum transport Can. J. Physiol. Pharmacol. Downloaded from www.nrcresearchpress.com by WA STATE UNIV LIBRARIES on 11/24/14 For personal use only.
J. PQRTNOW,~ 8.J. HOBGSON,AND A. T A L Q ~ Center for Research and Training in Reproducra'ce Biology, Depurrrnenrs qf Obstetrics and C?lnecology and Pharmacology, The Universiqy of Texas Health Science Center ar Sarz Ar~tottic,,Sun Antornis, T X , U.S.A. 78284 PORTNOW, J., H O ~ S O N B., J., and TALO,A. 1977. Simulation of oviductal ovum transport. Can. J. Physiol. Pharmacol. 55, 972-974. The present note describes a Monte Carlo simulation of ovum transport in the rabbit oviduct. Ova execute a random walk through a one-dimensional oviduct and the jump probabilities at each point are obtained from in vitra electrical recordings of smooth muscle activity. Simulated transport are compared with experimental findings at 18 and 66-68 h after human chorionic gonadotropin in~ection.
Introduction Transport of ova from the ovary to uterus through the oviduct takes 66-72 h in the rabbit. Ampullary transport is rapid (10 min); ova remain at the ampullary-isthmic junction for several hours and then slowly enter and traverse the isthmus (Pauerstein et al. 2974). The mechanisms which control this transport are still poorly understood. The local, erratic character of ovum trainsport has been reported by several authors (Harper 1961; Boling and Blandau 2971 ; Verdugo et al. 1974). Recently, Portnow et (11. (1977) presented a theoretical model of ovum transpori through the rabbit oviduct as a random walk (probability of transport being described by a d i h s i o n equation), with a reflecting barrier at the fimbriated end and an absorbing barrier at the uterine end. The present note is meant t o test the applicability of this model, and simulate the actual ovum movements with a Monte Carlo computer program (see Morn 1946) that takes individual junap probabilities frsna recordings of time sequences of spontaneous electrical activity of the smooth muscle of the oviductal wall. Hodgson et al. (1977) demonstrated a direct correlation between movement of artificial ova in the oviduct in vitro and direction and distance of propagation of spike bursts of the circular muscle. ABBREVIA~ON: HCG, human chorionic gonadotropin. PPresent address : University of Texas Medical Branch at Galveston, Medical School, Galveston, TX, U.S.A. 77550. *Present address: Zoophysiological Laboratory, Institute Biology, University of Turku, 20500 Turku, 50, Finland. 3 M d e of spread and conducting pathways for spikes are not known but could occur through the inner longitudinal muscle (in the isthmus) or in a helical manner or transverse to the main axis of the circular muscle.
The present model sees the contraction of the circular muscle of the oviduct as the sole propdsive force on the ova and assumes perfect correlation between propagation of electrical activity and ovum movement. The random motion of ova is simply a reflection of the labile nature of the firing of pacemakers or labile electrical coupling between adjacent regions in the circular muscle, and the probabilities for a jump in the ovarian or uterine direction are really probabilities that the circular muscle contraction prspagates and propels the ova in the proper directioin. Methods An ovum is represented as a point particle and moved along the oviduct in discrete steps. At each point x there are probabilities P,, and P,, that the particle will move in the uterine or ovarian direction, respectively. P,,, = 1 - P,, - P,, is the probability that the particle does not move. At each point a four-digit random n~lmber R < 1 is chosen; if R 5 P,, the particle is moved ahead P,, 2 R > P,, it is moved back one one step; if P,,, P,, it remains at the same point. The step; if R > P,, particle cannot leave the tube at the starting point and when it reaches the end point (beyond which no electrical activity was recorded and which comprises the absorbing barrier), the program is stopped and the transport is complete. The end points for 18- and 68-h oviducts were 70 and 85(;{,, respectively, of the length from the fimbriated end, for both real and simulated transport. B'rrobabilities P,,, P,,, and P ,, were derived from recordings of electrical activity of the circular muscle in vitro which used arrays of seven or eight suction electrodes placed 1-2 nnm apart; the array was moved sequentially to cover the majority of the length of the oviduct (Talo and Hodgson 1074, and unpublished results). Briefly, activity was analyzed, after careful visual observations of contractions and measurenlents of time lag of the leading edge of spike bursts, to yield frequency, origin and direction of propagation, and the number of electrodes in each direction to which activity spread. For on the three electrodes (ei, el, ck) within an array ovarian side), the total number of bursts in c1 is given by Ztt, = ni,, 4- n,-+k nlrlp,where rt,,, and n,,, are the number of bursts which have the time sequence for
+ +
(62,
+
Can. J. Physiol. Pharmacol. Downloaded from www.nrcresearchpress.com by WA STATE UNIV LIBRARIES on 11/24/14 For personal use only.
COMMUNICATIONS
1 5 + - ~ - - - - , - 7 - - - - ~ 0 10 2 0 3 0 4 0
0
Y
TIME LmSecondalIr
)
6 8 8 8 0 9 0
loPl
FIG. 1. Location of an individual particle in a simulated oviduct, expressed as percentage total length from fimbriated end (ordinate) with time (abscissa, seconds X lo2). propagation to the adjacent electrode (and which may originate at el or propagate from el, or el, respectively), and qnrs = nl-+j*k f nt+j+k -t ni+j+k. Thus, P,, = ~t~+~,& Pzn n ~=, n l - + k / ~ nand l , P,,, = nj,,/2nj. To increase the sample size (to several hundred bursts for each segment) and because of relative inaccuracies in percentage location between oviducts and because data were not obtained for electrodes at the end of each array or electrodes which did not record, data for each 5% of total length were combined for each oviduct and then combined for oviducts (> 10) from different animals killed after the same interval following the ovulation-inducing injection of 100 IU HCG. In the program, each 55% region was divided into five points with the same period and probability data. The mean values of P,, and P,, for all segments were 0.1732 f 0.021 and 0.2010 f 0.025 (n = 6), respectively, at 18 h and 0.2570 0.020 and 0,2759 + 0.012 (n = 9) at 68 h. These means for P,, and P,, were not significantly different for 18 or 68 h, but 68-h values were significantly greater than the respective 18-h values. Mean frequencies were 137 i 12.6 and 391 f 20.2 bursts/h at 18 and 68 h, respectively. The simulation only considers single jumps and ignores the variable distance of propagation. The particle moves in step sizes equal to lC,'6of the tube length. This corresponds to 1.2-mm jumps in a 12cm tube, and was chosen because the suction electrodes (400pm tip diameter) used to record electrical activity were placed approximately this distance apart along the o ~ i d u c t . ~
+
*We have verified, using the model and by varying the length of the diffusion distance, that a random walk
Five sets of 50 simulations were performed for each data group (18 and 68 h after HCCi) and sinlulations were stopped at 18 000 s.
Results and Discussion Transport experiments were simulated with probability and frequency data taken from oviducts 18 and 68 h after HCG injection. To eliminate, as far as possible, the effect of cilia, simulations were started with the particle already 40'36 of the way down the tube. Since real ampullary transport is rapid in comparison with total transport time, this initial condition serves only to eliminate that part of the transport dominated by ciliary beat. The time courses of typical transport simulations are shown in Fig. 1. In Table 1, the results are compared with previously reported experimental determinations of ovum locations at the time of removal of oviducts from New Zealand White rabbits killed 18 and 66 h after HCG injection. In the simulation, ova placed 407; of the way down the oviduct will not (i.e., Pzo = P,, = 0.5) with such step sizes can be accurately modelled by the diffusion equation: P(,,= 4e-"rr2t1412/rr, where P a , is the probability that the particle has not reached the end point of a diffusion distance I , D is the diffusion coefficient, and t is time.
974
CAN. J. P W S I O L . PHARhfACOL. VOL. 55, 1977
Can. J. Physiol. Pharmacol. Downloaded from www.nrcresearchpress.com by WA STATE UNIV LIBRARIES on 11/24/14 For personal use only.
TABLE1. Ovum location after simulated and experimental transport
Oviduct, h after HCG
Na
Total no. ova
18simulated 1 68simulated 66c
5 4 5 10
250 15 250 48
Locatioil, n/c:, mean, SD
Mean probability of reaching end pointh
47.8 0.45 49.9 1.6 81.1 1.7 82.2d 4.1
0.02+0.006 0.00 0.80k0.02 0.62k0.16
"Number of oviducts studied. bFor simulated and experimental oviducts. mean percentage /100 of ova which reached 70% ( I 8 h) o r 85 % (66 h) of tubal length. For 66-h group, ova which were missing were considered to have reached the end point, a s uterine recovery of ova is poor. 6Data derived from Pauerstein et al. (1974) and Hodgson and Pauerstein (1976). dLocation of oviductal ova w7a379.9% (SD 5.5).
progress towards the uterus but will cluster in the region 4@-5070 of the tubal length, i.e., at the ampullary-isthnlic junction. Ova placed at the same point in an oviduct 68 h after HCC will be transported to the uterine end in a few hours. This agrees with findings that donor or artificial ova put into a 68-h oviduct catch up with normal ova in about 4 h when ova are placed into oviducts in vivo (Tstsumi et crl. 1975; Croxatto, H. B. : personal communication, December 1976) or in vitro (I-Iodgson et al. 1977). In the model, ova in 68-h oviducts cluster in the proxinlal isthmus, at the same location as that for normal ovulated ova beginning transport 12-14 h after H C C injection, whether calculated in the same manner as in the model (uterine and missing ova considered to be at 85y0of the tubal length and assuming some other mechanisna permits uterine entry) or calculated for tubal ova alone. The average mean time to reach the end point was 10 681 k 277 s (n = 5). The very close agreement between mean position, in both groups, for the simulated and actual transport suggests that frequency and (or) bias cxerts a tight control on ovum transport. For the oviduct, time is measured from the moment of MCC injection and mean ovum position is set for each time. Naturally, for each control to operate, there must be a trigger mechanism setting the oviductal clock and letting the know when to start measuring time. The peak in progestin secretion after HCG iniection (Hilliard p t 01. 1968) is intriguing in this regard. This note is meant to demonstrate that a based On quantiof tative data for muscular activity accurately J
\
agrees with obscrved ovum transport. Preliminary results using data from progesterone-treated animals show accelerated transport in experimental and simulated transport. DifTercnces in jump frequency and bias which determine whether the particle is transported or not and a detailed analysis using idcal data must be the subject of a systematic study. Acknowledgments The authors are indebted to L. Scitchik for his invaluable help in the computer programming and thank Dr. H. B. Croxatto for communicating his results before publication. This work was supported by NIH-HB-09339-02. BOLING,J. L., and BLANDAU, R. 1. 1971. Egg transit through the ampullae of the oviducts of rabbits under various experimental conditions. Riol. Keprod. 4, 174-184. HARPLR,M. J. K. 1961. The mechanisms involved in the movements of newly ovulated eggs through the ampulla of the rabbit fallopian tube. J. Keprod. Fertil. 2, 522-524. HILLIARD, J., S P I ~ SH. , G., and SAWYER, C. N. 1968. Cholesterol storage and progestin secretion during pregnancy and pseudopregnancy in the rabbit. Endocrinology, 82, 157-165. H o n ~ s o B. ~ ,J., and PAUERST~IN, C. J. 1976. Comparison of oviductal transport of fertilized and unfertilized ova after HCC or coitus induced ovulation in the rabbit. Biol. Reprod. 14, 377-381. MODGSON, B. J., TALB,A., and PAUERSTEPN, C. J. 1977. Oviductal ovum surrogate movement: interrelation with muscular activity. Biol. Reprod. In press. KORN, G. A. 1966. Random-process simulation and measurements. McGraw-Hill, New York. PAUERSTEIN, C. J., ANDERSON, V., CHATKOFF, M. C., and HODGSON, B. 1. 1974. Effect of estrogen and progesterone on the time course of ovum transport in the rabbit. Am. J. Obstet. Gynecol. 120, 299-308. PORTNOW, J., TALO,A., and MODGSON, B. J. 1977. A random walk model of ovum transport. Bull. Math. Biol. Tn press. B. 1. 1976. Effect of time after TALO,A., and HOBGSON, ovulation and estrogen and progesterone on electrical activity of the rabbit oviduct. (Abstract) Pharmacologist, 18, 181. TSTSUMI,Y., OGURI,N., and HAFEZ,E. S. E. 1975. Rapid transport of alien eggs transplanted 66 hours post coiturn in the oviduct of the rabbit. J. Reprod. Med. 14, 62-63. VmDuGo. P., BLANDAU, R. I., TAM, P. Y., and HALBERT,S. A. 1976, Stochastic elements in the development sf deterministic models of egg transport. in Ovum transport and fertility regulation, World Health Organization Symposium. Edited hy M. J. K. Harper, C. J. Pauerstein, C. E. Adams, E. M. Continho, H. B. Croxatto, and D. M. Paton. Scriptor, Copenhagen.
