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/ . Embryol. exp. Morph. Vol. 25, l,pp. 85-96, 1971
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The origin and movement
of the limb-bud epithelium and mesenchyme in
the chick embryo as determined by
radioautographic mapping
By GLENN C. ROSENQUIST 1
From the Department of Pediatrics, The Johns Hopkins Hospital
SUMMARY
The origin of the limb-bud cells was determined by tracing the movements of [3H]thymidinelabelled grafts excised from late medium-streak to 5-somite stage chick embryos and transplanted to the epiblast, streak, and endoderm-mesoderm of similarly staged recipient
embryos.
Although exact definition of the prelimb areas was not possible because of the small
number of grafts placed at each developmental stage, the study showed in general that at the
late medium-streak stage the future limb-bud epithelium is in the epiblast (dorsal) layer near
the lateral margin of the area pellucida. It moves medially toward the embryonic axis, just
lateral to the premesoderm cells which will be invaginated at the primitive streak. With
regression of the streak, the limb-bud epithelium moves relatively anteriorly into a position
dorsal to the limb-bud mesoderm, beginning at least as early as the early head-fold stage.
At the definitive-streak stage, the future limb-bud mesoderm is in the epiblast layer about
halfway from the streak to the lateral margin of the area pellucida, at a level about halfway
between the anterior and posterior ends of the streak. From this position the prelimb mesoderm migrates medially to the streak, and is invaginated into the mesoderm layer at a position
about halfway between the anterior and posterior ends of the streak; after the head-process
stage, it migrates anteriorly and laterally into the somatic layer of the lateral plate, ventral to
the limb-bud epithelium. Mesoderm which will form the anterior limb-bud migrates anterior
to mesoderm which will form the posterior limb-bud; mesoderm which will form the ventral
portion of each limb-bud migrates posterolateral to mesoderm which will form the dorsal
portion of each limb-bud.
INTRODUCTION
The limb-buds of the chick embryo begin to form at about the 30-somite stage,
when the somatic mesoderm along the right and left flanks begins to accumulate
into mounds of mesenchyme, covered by a layer of epidermal ectoderm.
Although previous investigators (Wolff, 1936; Rudnick, 1945; Chaube,
1959) have identified areas of limb-bud-forming tissue in the right and left
flanks of embryos prior to the 30-somite stage, the position of this tissue prior
to the head-fold stage has not been investigated.
1
Author's address: Department of Pediatrics, The Johns Hopkins Hospital, Baltimore,
Maryland 21205, U.S.A.
86
G. C. ROSENQUIST
Using radioautographic analysis the present investigation traces the movement
of [3H]thymidine-labelled transplants from their original positions in the epiblast, streak and endoderm-mesoderm layer of recipient embryos into the limbbuds of these embryos. Although the small number of grafts placed prevents
exact definition of the prelimb areas, these regions are more precisely defined
than they were previously, and the mesoderm and ectoderm layers are treated
separately.
MATERIALS AND METHODS
The methods of preparation of recipient and [3H]thymidine-labelled donor
embryos and of transplantation and radioautographic analysis of the grafts
were identical to those described in previous publications (Rosenquist, 1966,
19706) and the description will not be repeated here.
The late medium-streak to head-process stages of both donor and host embryos
have been described previously (Rosenquist, 1970a) and are shown diagrammatically in Fig. 1A-C. Early head-fold (EHF) stage embryos had an elongated
head process and a depression at the site of the future head fold, which had not as
yet formed a pocket (Fig. 1D). Host embryos fixed prior to the 7-somite stage
were normal when examined with the naked eye or microscopically. In those
host embryos which survived to the 26-somite to early limb-bud stage the heart
was beating, but extra-embryonic circulation had ceased and the development of
the embryos was retarded compared to that of similar embryos incubated in ovo.
The number of pairs of somites could not always be determined accurately
(Fig. 2B, E).
In the older host embryos which had not as yet developed limb-buds, the
anterior and posterior limb regions, and their dorsal and ventral portions, were
designated in cross-sections on the basis of their distance from the anterior
intestinal portal, primitive streak, midline axis and nephrotome in comparison
with embryos which had already developed limb-buds. This stage is referred to
as the 26-30-somite stage in the Table and text, and is equivalent to stage 1
(Hamburger, 1938) and stage 15 (Hamburger & Hamilton, 1951).
Host embryos which had developed limb-buds (stages 2-3 of Hamburger,
1938; stages 16-17 of Hamburger & Hamilton, 1951) were said to be at the early
limb-bud (ELB) stage. In these embryos the portion of the ectoderm and somatic
mesoderm lateral to the crest of the ectodermal cone is referred to in the text
and Table as the future ventral portion of the limb, while the portion of the
ectoderm and somatic mesoderm medial to the ectodermal cone is called the
future dorsal portion of the limb.
Although a part of each of the labelled transplants lay in the limb-budforming region of its host embryo, the number of embryos investigated was
relatively small, and each transplant contained cells other than those destined
for the limb-buds (as indicated in Table 1). Therefore the positions of the transplants at each stage in Fig. 1 suggest the location of the limb-bud cells at that
stage, but do not define it precisely.
Origin of limb-bud
87
The mapping of the limb-bud regions is based upon the following assumptions:
(1) that since previous studies have established the general position of the premesoderm and pre-ectoderm cells in the epiblast layer of the chick blastoderm
without mapping every part of that layer at each stage (Rosenquist, 1966), a
small number of transplants carefully placed can demonstrate the position of
more specific portions of the mesoderm and ectoderm, such as the limb-buds.
(2) That similar graft positions in different embryos of the same stage are homologous even if the embryos were incubated for different lengths of time, and that
the migration pathways followed by more than one accurately placed graft can be
combined to follow movements of a group of cells through several overlapping
stages of development. (3) That maps of presumptive organ-forming regions of
the embryo are valid even if structures in the recipient embryos other than the
organ to be mapped contain labelled cells.
Throughout the text and figures, an asterisk (*) after the embryo number
indicates that the position shown is that of the graft after its migration in the
host embryo.
RESULTS
Limb-bud epithelium
At the late medium-streak stage the cells which would form the epithelium of
the limb-buds were in the epiblast layer at the lateral edge of the area pellucida,
lateral to the primitive streak; in some cases they may have been on or outside
the boundary between the area pellucida and the area opaca (embryos 1-5,
Table 1, Fig. 1A).
At the early head-fold stage, the cells which would form the epithelium of the
anterior limb-bud were in the epiblast layer near the anterior half of the streak,
about halfway between the streak and the lateral margin of the area pellucida
(embryos 6, 7, Table 1, Fig. ID).
By the 4-7-somite stage, the transplant in embryo 6* had migrated anteriorly
and laterally to a position between the anterior end of the streak and the somite
region (Table 1, Fig. 1E). If embryo 6 had been allowed to develop to the limbbud stage, labelled cells would have migrated into the anterior limb-bud, as did
those in embryo 7* (Fig. ID, G). Therefore, the transplants in embryos l*-4*,
which had reached positions similar to that of the graft in embryo 6* (Fig. 1E),
also were considered to be destined for the anterior limb-bud. The transplant in
embryo 5* and the posterior end of the transplant in embryo 3* were posterior
to the transplants in embryos l*-4* and 6* at this stage; although there is no
evidence from the present study that they would have contributed to the posterior
limb-bud, they lay in the presumptive posterior limb-bud region as it was defined
by Rudnick (1945) and Chaube (1959) (Fig. 3C), and were therefore considered
to be destined for the epithelium of the posterior limb-bud.
At the early limb-bud stage (equivalent to stages 2-3 of Hamburger, 1938 and
16-17 of Hamburger & Hamilton, 1951), labelled cells from the transplant in
88
G. C. ROSENQUIST
embryo 7* had formed portions of the epithelium of the right anterior limb-bud,
extending along the dorsal side of the ectodermal cone; other labelled cells
from this transplant contributed to the epithelial layer of the embryo between
the anterior limb-bud and the neural crest, but not to the ectoderm between the
anterior and posterior limb-buds, nor to the posterior limb-bud (Table 1,
Figs. 1G, 2).
Table 1. Position of labelled cells in recipient embryos carrying
tritiated thymidine-labelled grafts*
Embryo
no.
Incubated f
(h)
Stage
fixed
Position of labelled cells
1
LMS
2
3
LMS
LMS
22
23
5S
7S
Ec: ALBJ
Ec: ALBJ
22
5S
Ec: ALBJ
4
5
6
7
LMS
LMS
EHF
EHF
DS
HP
HP
EHF
EHF
EHF
EHF
EHF
EHF
EHF
EHF
EHF
EHF
4S
4S
5S
15
19
7
66
5
4
10
48
108
66
108
68
66
68
68
48
92
56
66
60
6S
Ec: ALBJ
Ec: PLBJ
Ec: ALBJ
Ec: ALB; Px M
St M: PLBJ
LP M: ALBJ, PLBJ; YS En
LP M: ALBJ, PLBJ; YS En
LPM: ALBJ (dv); YSEn
LPM: ALBJ(v); YSEn
LPM: ALBJ (d); YSEn
LP M: ALBJ (dv), PLBJ (dv); YS En
LP M: ALB (v), PLB (v); YS En
LP M: ALBJ (d), PLBJ (d); YS En
LP M: ALBJ (d), PLBJ (d); YS En
LP M: ALB (dv), PLB (dv); YS En
LP M: ALBJ (d), PLBJ (d); YS En
LP M: ALB (v), PLB (v); YS En
LPM: ALBJ (dv); YSEn
LPM: ALB (v); YSEn
Px, LPM: PLB (d); YSM
8
/
Stage
grafted
9
110
11
12
13
14
I115
16
-17
Us19
20
21
22
23
6S
7S
ELB
EHF
EHF
4S
26-30S
26-30S
26-30S
26-30S
ELB
26-30S
26-30S
ELB
26-30S
ELB
26-30S
ELB
ELB
* Key to abbreviations: ALB, anterior limb-bud; d, dorsal; DS, definitive-streak stage;
Ec, ectoderm; EHF, early head-fold stage; ELB, early limb-bud stage; En, endoderm;
HP, head-process stage; LMS, late medium-streak stage; LP, lateral plate; M, mesoderm;
Px, paraxial; PLB, posterior limb-bud; S, somite; St, streak; v, ventral; YS, yolk sac.
t Hours of incubation after placement of the graft.
J Presumptive limb-bud region.
Limb-bud mesoderm
At the definitive streak stage, the cells which would form the mesoderm of the
limb-buds were in the epiblast layer on each side of the primitive streak, at a
level about halfway between the anterior and posterior ends of the streak, and
about halfway from the streak to the lateral margin of the area pellucida. The
transplant in embryo 8 (Table 1, Fig. IB) was within the area destined to be
Origin of limb-bud
89
invaginated at the streak, which was identified in a previous mapping study
(Rosenquist, 1966).
By the head-process stage the mesoderm which would form portions of the
limb-buds had been invaginated at the primitive streak and had migrated into
the lateral plate mesoderm on each side of the streak, at a level about 40-50 %
of the distance from the anterior to the posterior end of the streak (embryos 9,
10, Table 1, Fig. 1C).
At the early head-fold stage, a portion of the mesoderm which would form
D
(ehf)
A
(Ims)
\ a
E (4-7s)
F (26-30s)
12*. 21"
11*, 14*, 16*-18*
Fig. 1. Drawings (ventral views) illustrating the position of thepresumptivelimb-bud
material in the epiblast or mesoderm layer. The positions of [3H]thymidine-labelled
grafts (shaded areas) which contributed to the limb-bud epithelium are shown on the
left side of each figure. The positions of labelled grafts (shaded areas) which contributed to the limb-bud mesoderm are shown on the right side of each figure. Abbreviations: Ims, late medium-streak stage; ds, definitive-streak stage; hp, head-process
stage; ehf, early head-fold stage; s, somite; elb, early limb-bud stage.
As in the text, an asterisk (*) after the embryo number indicates that the position
shown is that of the graft after its migration in the host embryo. Each graft is
therefore shown in two positions—immediately after it was placed, and after
incubation.
90
G. C. ROSENQUIST
ec
Origin of limb-bud
91
the anterior limb-bud (embryos 9*, 11-13, Table 1, Fig. ID) had migrated
anteriorly and laterally from the streak into the strip of somatic mesoderm
ventral to the ectoderm which would form the anterior limb-bud (Rudnick,
1945 and embryos 6 and 7, Fig. ID). Additional mesoderm which would form
portions of the anterior limb-bud was located closer to the streak (embryos
14-20, Table 1; Fig. 1D). Mesoderm which would form the posterior limb-bud
was located in the streak or in the nearby mesoderm (embryos 14-20). Mesoderm
which would form the ventral portion of each limb was positioned more
posteriorly in the streak and more posterolaterally in the lateral plate mesoderm
(embryos 12, 19, 20, Table 1, Fig. ID) than was mesoderm which would form
the dorsal portions of the limbs (embryos 13, 16-18, Table 1, Fig. ID). The
transplants in embryos 11,14 and 15 were placed in an intermediate position and
contributed to both dorsal and ventral portions of the somatic layer of mesoderm or the limbs (Table 1, Fig. ID).
At the 4-7-somite stage, the limb-bud mesoderm had migrated further into
more lateral and anterior portions of the lateral plate. The transplants in embryos
10*, 21 and 22 indicated the position of the mesoderm which would form the
anterior limb-bud, which was in the portion of the embryo identified as destined
for the anterior limb-bud by Rudnick (1945), Chaube (1959), and by the
ectodermal grafts in the present study (embryos l*-4*, 6*, 7*, Table 1, Fig. 1D,
E, G). The anterior end of this zone was about at the level of the last somite
which had formed; the posterior end of this zone was anterior to the anterior
Fig. 2. (A) [3H]thymidine-labelled transplant (arrow) was placed in the epiblast layer
of an early head-fold stage recipient embryo (embryo 7).
(B) After 66 additional h of incubation, the recipient embryo had a well-developed
heart. Cellsfromthe transplant formed the dorsal epithelium of theanterior limb-bud.
The plane of the cross-section in (C) is shown by the dotted line at the lower right.
s — sinoatrium; v = ventricle.
(C) Cross-section (x200) through embryo 7 at the plane indicated in (B), illustrating how the radioautographed cells from the transplant (black grains over
nuclei, arrows) formed the epithelium of the trunk of the embryo, extending into
the medial (dorsal) portion of the anterior limb-bud, d — dorsal; ec = ectodermal
cone; v = ventral.
(D) A [3H]thymidine-labelled transplant (arrow) was placed in the endodermmesoderm layer and primitive streak of an early head-fold stage recipient embryo
(embryo 20).
(E) After 92 additional h of incubation, the recipient embryo had a well-developed
heart (Ji) and both anterior (alb) and posterior limb-buds (plb), but was otherwise
poorly developed compared to embryos incubated in ovo. Cells from the transplant
contributed to the mesenchyme of both anterior and posterior limb-buds. The plane
of the cross-section in (F) is indicated by the dotted line through the posterior limbbud.
(F) Cross-section (x200) through embryo 20 at the level shown in (E). The radioautographed cells from the transplant (black grains over nuclei, arrows) contributed to the posterior limb-bud mesoderm, which at this level had formed from the
somatic layer of the lateral plate, d = dorsal; ec = ectodermal cone; v = ventral.
92
G. C. ROSENQUIST
end of the streak. The transplant which later formed the mesoderm of the
posterior limb-bud was more posteriorly positioned; it was adjacent to the
primitive streak, and extended anteriorly and laterally into the lateral plate
mesoderm (embryo 23, Table 1, Fig. IE, G). This position corresponded with
the areas previously identified as destined for the posterior limb-bud by Rudnick
(1945), Chaube (1959), and an ectodermal graft of the present investigation
(embryo 5*, Table 1, Fig. IE). The transplant in embryo 22 contributed to the
ventral portion of the anterior limb-bud mesoderm and was positioned slightly
lateral to the transplant in embryo 21, which would have contributed to both
dorsal and ventral portions of the limb-bud mesoderm. It was in a migration
pathway lateral to the pathway which is believed would be followed by the
transplant which contributed to the dorsal portion of the posterior limb-bud
mesoderm (embryo 23).
At the 26-30-somite stage (equivalent to stage 1 of Hamburger, 1938, and 15 of
Hamburger & Hamilton, 1951), the cells which would form the mesoderm of the
anterior limb-bud were located in the lateral portion of the somatic layer of the
lateral plate, posterior to the anterior intestinal portal (embryos 12*, 21*,
Table 1, Fig. IF). Cells which would form the mesoderm of the posterior limbbud were even more posteriorly located in the lateral part of the somatic part of
the mesoderm (embryos 11*, 14*, 16*—18*, Table 1, Fig. IF).
At the early limb-bud stage, the transplants in embryos 13*, 15*, 19*, 20*
and 22* all had formed portions of the anterior limb-bud mesoderm (Table 1,
Fig. 1G). Of these only the transplants in embryos 22* and 13* did not also
form portions of the posterior limb-bud mesoderm; they were among the more
anteriorly positioned transplants at the early head-fold and 4-7-somite stages,
respectively (Fig. ID, E). The transplant in embryo 23* formed the dorsal
portion of the posterior limb-bud mesoderm; it was the most posteriorly
positioned transplant at the 4-7-somite stage (Fig. 1E).
DISCUSSION
Previous attempts to learn the origin and movements of the cells which form
the limbs have utilized several different experimental techniques. Wolff (1936)
produced localized injury withX-irradiation to embryos asyoungas9-13-somites,
and proposed that the anterior limb-bud regions were at the level of the anterior
end of the rhomboid sinus (i.e. posterior to the last somite), while the posterior
limb-bud regions were close to the midline and posterior to the anterior end of
the streak. Rudnick (1945) divided chick blastoderms into full-thickness pieces
of various sizes, and transplanted them into the right coelomic space of host
embryos incubated 2\ days; after 8-10 additional days of incubation in this
environment, the fragments differentiated into morphologically recognizable
limbs. Using this method, Rudnick demonstrated that the anterior limb-buds
would differentiate from a strip of tissue which extended laterally and posteriorly
Origin of limb-bud
93
from the anterior end of the streak at the head-fold stage (Fig. 3 A), and from a
strip of tissue which extended laterally from the anterior end of the streak
toward the lateral margin of the area pellucida at the 6-7-somite stage (Fig. 3C).
Rudnick did not find posterior limb-bud material at the head-fold stage; however, in 6-7-somite stage embryos, she did find such material slightly posterior to
the prospective anterior limb-bud material, lateral to the anterior end of the
streak (Fig. 3C). Rudnick and Wolff both noted a gradual anterior movement of
both anterior and posterior limb-bud regions with additional development, but
the presumptive anterior limb-bud remained anterior to the presumptive
A
0>f)
Fig. 3. Diagrams illustrating the position of the limb-bud material as determined by
previous investigators. Left side of each figure: Rudnick, 1945, using coelomic grafting techniques. Right side: Chaube, 1959, using chalk particles in ovo. Hatched
area = anterior limb-bud material; shaded area = posterior limb-bud material.
/;/= head-fold stage; s = somite.
posterior limb-bud in all their preparations. In no instance did limbs differentiate
from material which originated at a level anterior to the last somite which had
developed.
One disadvantage of the studies with grafted blastoderm fragments in the
embryonic coelom was that the mesoderm and ectoderm layers contained in the
fragments could no longer move independently of each other as they might have
done in the uncut blastoderm. The in ovo studies of Chaube (1959) overcame
this difficulty. With chalk particles on glass needles introduced from the dorsal
surface, Chaube marked adjacent points in the ectoderm and mesoderm layers,
beginning at the 2-somite stage. The movement of the chalk particles during the
subsequent development of the embryos showed that although both layers
94
G. C. ROSENQUIST
expanded in an anteroposterior direction and moved anteriorly in relation to the
streak, the points in each layer which were marked with chalk remained adjacent
to each other. Chaube thus agreed with Rudnick that the prospective limb
mesoderm had completed its gastrulation movements and had reached its
definitive position in relation to the ectoderm by the 2-somite stage. Chaube also
noted stable right-to-left relationships: laterally placed marks assumed ventral
positions in the limb-buds while medially placed marks assumed dorsal positions
in the limb-buds.
Both Rudnick and Chaube attempted to study the limb regions of younger
embryos. Although Rudnick (1945) transplanted portions of embryos as young
as the primitive-streak stage into coelomic cultures, limbs did not form from
fragments excised before the early head-fold stage. The present study indicates
that at the early stages studied by Rudnick, the prelimb ectoderm is in a
stable position in the epiblast (ectoderm); however, the prelimb mesoderm
which has been invaginated at this stage has not as yet reached a position directly
ventral to the prelimb ectoderm, so that the stable relationship between the
two which Rudnick found at all later stages had not as yet developed.
Chaube marked a total of thirty-five head-fold stage embryos; a large number
died soon after they were marked and the remainder 'gave such bizarre results'
that they could not be satisfactorily interpreted. From the present study it is
clear that at the head-fold stage some of the prelimb mesoderm cells may still be
in the epiblast layer, others are in the process of invaginating at the streak, and
still others are migrating anteriorly and laterally from the streak toward the
prelimb ectoderm regions. Chalk marks placed in such an environment would
indeed give bizarre results since only some of the prelimb ectoderm and mesoderm cells have reached a stable position in relation to each other.
The present study indicates that the migration of the prelimb mesoderm is as
orderly and highly organized as that noted for mesoderm destined for the splanchnic layer (Rosenquist, 1970a). After its imagination at the streak, mesoderm
destined for the dorsal portion of each limb is anterior to mesoderm destined
for the ventral portion of each limb. This suggests (but does not prove) that
equally organized relationships exist in the epiblast prior to invagination at the
streak. Premesoderm destined for the dorsal portion of each limb may be
anteromedial to premesoderm destined for the ventral portion of each limb.
Since the ectoderm which will form the limbs is probably similarly arranged, we
may consider the limb regions of the epiblast as consisting of two parallel
bands: the more anteromedial band contains the ectoderm and mesoderm cells
which will form the dorsal body wall, including the dorsal portion of each limb,
while the more posterolateral band contains the ectoderm and mesoderm cells
which will form the ventral body wall, including the ventral portion of each
limb. The premesoderm is nearer to the streak than is the pre-ectoderm; it
migrates to a position below the ectoderm, and then the ectoderm and mesoderm
migrate together in their respective bands. Such a concept may also apply to the
Origin of limb-bud
95
portions of the epiblast destined to form ectoderm and mesoderm of more
proximal and distal portions of the embryo. In future research it should be
possible to place smaller transplants into the epiblast layer at these early stages,
and incubate the host embryos to later stages, so that further details of these
movements may be learned.
RESUME
Uorigine et les mouvements de Vepithelium et du mesenchyme dans le bourgeon
de membre du Poulet demontres par le marquage radioautographique
L'origine des cellules du bourgeon de membre a ete mise en evidence en suivant les mouvements de greffes marquees par la [3H]thymidine, excisees d'embryons de Poulet aux stades
depuis la ligne primitive moyenne et avanceejusqu'a celui de 5 somites et transplants dans
l'epiblaste, la ligne primitive et l'endo-mesoderme d'embryons notes d'age correspondant.
Malgre qu'une definition exacte des aires presomptives des membres n'ait pas ete possible
vu le nombre limite de greffes executees a chacun des stades, l'etude a pu demontrer de facon
generate qu'au stade de la ligne primitive moyenne et avancee l'epithelium du futur bourgeon
de membre se place dans la couche epiblastique (dorsale) proche de la marge laterale de
1'area pellucida. II se meut en dedans en direction de l'axe embryonnaire, pour se placer tout
juste en dehors des cellules pre-mesodermiques qui vont s'invaginer dans la ligne primitive.
Au cours de la regression de la ligne primitive, l'epithelium du membre se deplace relativement vers l'avant, atteignant une position dorsale vis-a-vis du mesoderme de ce membre, et
ceci au moins depuis le stade du premier repli cephalique.
Au stade de la ligne primitive a son terme, le mesoderme presomptif du bourgeon de membre
se trouve dans la couche epiblastique a peu pres a mi-chemin entre la ligne primitive
et la marge laterale de l'area pellucida, et a mi-distance entre les extremites anterieure
et posterieure de la ligne primitive. A partir de cette position le mesoderme presomptif
du membre migre vers le dedans et s'invagine dans la ligne primitive a mi-distance
de ses deux extremites (anterieure et posterieure); apres le stade du prolongement cephalique,
il migre vers l'avant et le dehors dans la couche parietopleurale de la lame laterale,
ventralement par rapport a l'epithelium correspondant. Le mesoderme qui formera le
membre anterieur migre en avant de celui qui formera le membre posterieur; le mesoderme
qui formera la partie ventrale de chaque membre migre en arriere et en dehors de celui qui
formera la partie dorsale.
This investigation was supported by USPHS research grants HE 10191 and K3 HE 20074
from the National Heart Institute. The author wishes to thank James D. Ebert for his
continued interest in this research, Soame D. Christianson for help in the preparation of the
manuscript, and Dorothea Rudnick for a critical reading of the manuscript.
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(Manuscript received 26 June 1970)