Download The development of cytogenetically normal, abnormal and mosaic

Human Reproduction Update, Vol.10, No.1 pp. 79±94, 2004
DOI: 10.1093/humupd/dmh005
The development of cytogenetically normal, abnormal and
mosaic embryos: a theoretical model
Frans J.Los1, Diane Van Opstal and Cardi van den Berg
Department of Clinical Genetics, Erasmus Medical Centre, P.O.Box 1738, NL-3000 DR Rotterdam, The Netherlands
1
To whom correspondence should be addressed. E-mail: [email protected]
Assisted reproduction and preimplantation genetic diagnosis (PGD) involve various complicated techniques, each of
them with its own problems. However, the greatest problem with PGD for chromosome abnormalities is not of a
technical nature but is a biological phenomenon: chromosomal mosaicism in the cleavage stage embryo. Here, we
present a hypothetical, quantitative model for the development of chromosomally normal, abnormal and mosaic
embryos. The arising of mosaicism in 2±8-cell embryos was described by a binomial probability model on the
occurrence of mitotic events inducing chromosomal changes in the blastomeres. This model converted the `mean'
rate of mosaicism found in cross-sectional studies (60%) into an equal rate of mosaic embryos at arrival at the 8-cell
stage (59.8%). The disappearance of >90% of the mosaic embryos or the mosaicism itself from surviving embryos
during the morula stage was explained by mitotic arrest of most of the mitotically changed cells under increasing
cell cycle control. In our model, 25.9 and 14.3% of the embryos at the 8-cell stage are normal and abnormal
respectively. The remaining 59.8% of the embryo shows mosaicism: 34.6% of abnormal/normal cells and 25.2% of
abnormal/abnormal cells. The high proportion of abnormal and mosaic embryos together explains the high rate of
abnormal laboratory ®ndings in PGD for chromosomal abnormalities and aneuploidy screening. The poor
representation of a 1- or 2-cell biopsy for the 7- or 6-cell post-biopsy embryo in the case of mosaicism explains the
high rate of false-negative and false-positive results.
Key words: chromosomal mosaicism/embryo/model/preimplantation genetic diagnosis/uniparental disomy
Introduction
The chance of a live birth following conception is estimated
between 22 and 50% in the human (Roberts and Lowe, 1975;
Edmonds et al., 1982; Chard, 1991; Norwitz et al., 2001; Macklon
et al., 2002). The majority of the conceptional losses occurs
unnoticed through non- or failed implantation, and only a minority
through spontaneous abortion of recognized pregnancies
(Edmonds et al., 1982; Wilcox et al., 1988, 1999; Norwitz et al.,
2001). A high rate of chromosomal abnormalities has been found
in preimplantation embryos (Angell et al., 1986; Plachot et al.,
1988; Papadopoulos et al., 1989; Jamieson et al., 1994; MunneÂ
et al., 1997; Bielanska et al., 2002; Clouston et al., 2002) and in
embryonic/fetal or extraembryonic tissues after spontaneous
abortion (Boue and BoueÂ, 1976; Warburton et al., 1978; Hassold
et al., 1980; Byrne et al., 1985; Fritz et al., 2001). A markedly
lower rate has been encountered in induced abortion specimens
and in vital pregnancies at prenatal diagnosis (Kajii et al., 1978;
Los et al., 2001). This indicates that chromosomal abnormalities
are the major cause of embryonic loss.
High frequencies of mosaicism up to 70% have been reported in
preimplantation embryos (Munne et al., 1995, 1997; Voullaire
et al., 2000; Wells and Delhanty, 2000; Bielanska, 2002).
However, the frequency of chromosomal mosaicism in spontaneous abortion specimens is <10% (Warburton et al., 1978;
Hassold, 1982; Fritz et al., 2001). In vital pregnancies, a low but
regular frequency of mosaicism of ~2% is encountered at prenatal
diagnosis in chorionic villi: the smaller part (12%) represents true
or generalized mosaicism and the greater part (88%) con®ned
placental mosaicism (CPM) (mosaicism or homogeneous
abnormality present in the extraembryonic tissues only, the fetus
being normal) (Kalousek and Dill, 1983; Pittalis et al., 1994;
Wolstenholme, 1996; Hahnemann and Vejerslev, 1997a,b). Most
mosaic embryos are lost apparently prior to the period of ®rst
trimester spontaneous abortion.
For a good understanding of the loss of chromosomally normal,
abnormal and mosaic embryos before, during and after implantation, a quantitative model might be helpful. Such knowledge
could be essential in the interpretation of diagnostic results of
preimplantation genetic diagnosis (PGD) of chromosomal
abnormalities and PGD aneuploidy screening (PGD-AS).
PGD-AS is carried out increasingly at present (Gianaroli et al.,
1999; Munne et al., 1999; Kahraman et al., 2000; Vandervorst
et al., 2000; ESHRE PGD Consortium Steering Committee, 2002;
Human Reproduction Update Vol. 10 No. 1 ã European Society of Human Reproduction and Embryology 2004; all rights reserved
79
F.J.Los, D.Van Opstal and C.van den Berg
Voullaire et al., 2002). Qualitative or (semi)quantitative models
for cause and effects of chromosomal abnormalities during (early)
pregnancy are scarce (Leridon, 1973; Plachot et al., 1987, 1988;
Wolstenholme, 1995, 1996; Clouston et al., 2002). The `audit of
trisomy 16 in man' (Wolstenholme, 1995) is an example of a
detailed quantitative model con®ned to one speci®c chromosome
(chromosome 16). Here, we would like to present a general
quantitative model describing the fate of chromosomally normal,
abnormal and mosaic embryos from fertilization to viable
pregnancy at the end of the ®rst trimester of pregnancy comprising
the total of numerical and structural chromosome abnormalities.
For this model, we used cytogenetic data from earlier studies as
well as from the most recent literature on oocytes, sperm, embryos,
spontaneous abortions and viable ®rst trimester pregnancies. The
cytogenetic data on preimplantation embryos were derived over
the years from many IVF programmes and concerned nontransferred embryos of selected patients. The embryos have been
partially investigated (karyotyping a single blastomere or some of
the blastomeres at most) or totally investigated with techniques
allowing for the study of a restricted number of chromosomes
[¯uorescence in-situ hybridization (FISH) of some chromosomes
of all blastomeres]. In some instances, however, embryos were
totally investigated with still experimental techniques but allowing
for the study of all chromosomes including imbalanced structural
abnormalities [whole genome ampli®cation (WGA) and single cell
comparative genomic hybridization (CGH) of all blastomeres].
Various limitations and biases might be present in the translation
of these in vitro data to the presumed in vivo situation.
For the description of the arising of mosaicism, we converted
the `mean' ®gure of mosaicism in 2±8-cell embryos derived from
cross-sectional studies into a `longitudinal' ®gure of mosaicism
after the ®rst three mitotic cell divisions that are without full cell
cycle control. This was done with binomial probability calculations: we assumed that a mitotic event changing the chromosomal
condition of a cell could hit any blastomere at random with a
certain probability. After the third post zygotic cell division at the
8-cell stage, the cumulative `longitudinal' ®gure of arisen mosaic
embryos was assumed to be equal to the mean `cross-sectional'
®gure. For the description of the disappearance of mosaic embryos
and of mosaicism itself from surviving embryos, we developed
another concept that was also applicable to non-mosaic abnormal
embryos. Chromosomal abnormalities of meiotic origin and
mitotically induced chromosomal alterations can make the
affected embryonic cells survive or non-survive cell cycle control,
which becomes fully active during the morula stage. These
concepts on the arising of mosaicism during the cleavage stage and
on the disappearance of mosaic embryos and of mosaicism itself
during the morula stage, enabled us to construct a model for the
rise and fall of mosaicism during embryonic development up to the
blastocyst stage. We extended this to a general, quantitative model
for the development of chromosomally normal, abnormal and
mosaic embryos throughout the ®rst trimester of pregnancy.
morula, free blastocyst, hatched blastocyst, embryo, and early
fetus. Additionally, the change of these numbers by events or
conditions separating the various levels of development such as
fertilization, mitotic arrest, occurrence of mitotic chromosome
errors, occult abortion, ®rst trimester spontaneous abortion, etc.,
are presented.
The various phases of the cell cycle are regulated by a
complicated system: the cell cycle control system (for review, see
Alberts et al., 2002a,b). In the early embryo, cell cycle control is
performed by maternal transcripts present in the ooplasm (Braude
et al., 1988; Lighten et al., 1997; Alberts et al., 2002a,b).
However, some of the checkpoints of the cell cycle control system
are lacking in the ®rst postzygotic cell divisions (Alberts et al.,
2002a,b). Only after the expression of the embryonic genome, cell
cycle control becomes gradually present from the 8-cell stage
onwards during the morula stage (TesarÏik et al., 1986; Braude
et al., 1988; Lighten et al., 1997). Also the mechanism of
programmed cell death (apoptosis) becomes active during the
morula stage (Jurisicova et al., 1996, 2003; Hardy et al., 2001).
The fact that maternal transcripts are responsible for the cell cycle
control in the ®rst embryonic cell divisions implies theoretically
that the effects of control are `maximal' in the ®rst division and
decrease in each following division. For our model, we assumed a
limitation of cell cycle control in the ®rst three postzygotic cell
divisions to such an extent, that mitosis was not blocked for the
majority of cells: 17.5% of the embryos were affected by mitotic
arrest (see Numbers). Furthermore, we assumed an increasing cell
cycle control during the morula stage (8±64-cell stage) and a fully
active one from the free blastocyst stage (> 64-cell stage)
onwards.
The separation of omnipotent blastomeres into the compartments of trophoblast and inner cell mass (ICM) takes place
between the 8- and 16-cell stage (Crane and Cheung, 1988;
Bianchi et al., 1993). In case of chromosomal mosaicism at the 8cell stage, there has been found no indication for a non-random
allocation of chromosomally abnormal cells to the trophoblast
compartment (Mottla et al., 1995; Evsikov and Verlinsky, 1998;
Magli et al., 2000). However, the blastomeres showing the fastest
development are preferentially allocated to the ICM in the
preimplantation mouse embryo (Spindle, 1982). Tetraploid cells
are predominantly distributed to the compartments of trophoblast
and extra-embryonic mesoderm (EEM), but not to that of the
embryo/fetus proper (James and West, 1994; James et al., 1995).
At the free blastocyst stage (probably between the 64- and 128-cell
stage), the ICM separates into the compartments of the epiblast
(the future embryo/fetus proper) and the hypoblast (the future
EEM) (Hinrichsen, 1990). It is not known if there is a non-random
allocation of normal cells present in the ICM to the compartment
of the embryo/fetus proper. For tetraploid cells, a preferential
allocation to the compartment of the EEM rather than to that of the
embryo/fetus proper in the mouse has been found (James et al.,
1995). As far as of importance for our model, we assumed random
distributions.
Background
Numbers
General
In the model, the numbers of cytogenetically normal, abnormal
and mosaic embryos are calculated and described at the level of
zygote, 2-, 4- and 8-cell cleavage stage embryo, 16- and 32-cell
80
The starting point of the model was the number of 100 000
zygotes. We assumed that 100 000 zygotes would ®nally result in
25 000 viable fetuses (25%) at the beginning of the second
trimester of pregnancy, close to the estimate (22%) of Roberts and
Model of embryo development
Lowe (1975). In the in vitro situation, 40±50% of the zygotes
develop into a free blastocyst (Almeida and Bolton, 1996; Jones
et al., 1998; Rijnders and Jansen, 1998; Alikani et al., 2000;
Zollner et al., 2002). We considered this range indicative for the
presumed in vivo situation in our model: this assumption might
imply a source of bias.
The rate of pregnancy loss after recognized implantation
(detected with sensitive assays for hCG in women's urine) is
~31% (Wilcox et al., 1988; Zinaman et al., 1996). The loss rate of
clinically recognized pregnancies through spontaneous abortion is
positively correlated with maternal age; the average ®gure of 15%
for the pregnant population was assumed in our model (Hassold
and Chiu, 1985; Fonteyn and Isada, 1988).
Mitotic arrest of the ®rst cell division was assumed to occur in
12.5% of zygotes (Wimmers and Van der Merwe, 1988;
Benkhalifa et al., 1996; Wittemer et al., 2000). Mitotic arrest in
both the second and third cell division was assumed to affect an
arbitrary number of 2500 embryos (~3%) since cell cycle control
might be less prevalent in these divisions than in the ®rst cell
division (see General).
Cytogenetics
The cytogenetic condition of embryos at the various levels of
development from gamete until the end of the ®rst trimester of
pregnancy is presented in Table I. Insuf®cient data or no data at all
were available at the various cell stages of the morula, free,
hatched and implanting blastocyst, at the levels of recognized
implantation and clinically recognized pregnancy and, ®nally, of
the event of occult abortion.
The cytogenetic data from oocytes were derived from
unfertilized oocytes of women in IVF programmes, a selected
population of oocytes of a selected population of women that
might not be representative for the oocytes of the general
population of pregnant women in the in vivo situation. Plachot
et al. (1988) and Pellestor et al. (2002), however, did not ®nd
signi®cant differences between the various types of female or male
infertility and the frequency of aneuploidy in oocytes. Also, the
process of fertilization seems not to be in¯uenced by the level of
chromosome abnormalities of the oocyte (Plachot et al., 1988;
Almeida and Bolton, 1994; Pellestor et al., 2002). Maternal age
selection could introduce a wrong estimate of cytogenetically
abnormal oocytes, since the frequency of chromosome abnormalities increases in preimplantation embryos and spontaneous
abortion specimens with advancing maternal age due to increased
meiotic non-disjunction (Hassold et al., 1984; Hassold and Chiu,
1985; Bielanska et al., 2002; Munne et al., 2002). Some authors
actually found the expected, increased rate of aneuploidy in
oocytes of women of advanced maternal age (Plachot et al., 1988;
Angell et al., 1997), but others did not ®nd this so clearly
(Pellestor, 1991; Pellestor et al., 2002). In the studies on
chromosome abnormalities in oocytes of Table I, the maternal
ages were, if skewed, skewed towards an advanced rather than to a
younger maternal age. For instance, Pellestor et al. (2002) studied
the oocytes from women aged 33.7 6 4.7 (mean 6 SD) years with
a range from 19 to 46 years. We believed that our assumed
abnormality rate of 26% in oocytes might be fairly representative
for the general female population. The cytogenetic data of sperm
were derived from normal men and were considered to re¯ect the
general male population.
Cleavage stage embryos (arrested and developing embryos)
have initially been studied using karyotyping of cultured
blastomeres. Although allowing for complete investigation of all
chromosomes comprising numerical as well as structural abnormalities, the yield of harvested and analysable metaphases has
always been low. This is the reason why karyotyping is not
suitable for the investigation of mosaicism in embryos. Therefore,
the FISH technique allowing for the investigation of blastomeres
at the interphase level has been widely applied, notwithstanding
the serious limitation that numerical abnormalities of a restricted
number of chromosomes can be investigated (up to nine chromosomes in the studies of Table I). Structural chromosome
rearrangements can only be investigated to some extent, in case
of parental carriership (Scriven et al., 1998). However, FISH is
very suitable for the investigation of mosaicism of the chromosomes of concern (Munne et al., 1994, 1995; Bielanska et al.,
2002). Extrapolation of FISH data on mosaicism of certain
chromosomes to the presumed frequency of mosaicism of all
chromosomes has been proposed by the use of certain multiplication factors, but generally resulted in overestimation of this
frequency (Wells and Delhanty, 2000). The complicated and still
experimental technique of WGA and subsequent single cell CGH
combines most of the possibilities of karyotyping and the
advantages of FISH (Wells and Delhanty, 2000; Voullaire et al.,
2000, 2002). Although experimental and carried out on a small
sample of selected embryos, the WGA + CGH analyses on 3±8cell embryos conducted by Wells and Delhanty (2000) and
Voullaire et al. (2000) showed comparable and similar results to
an extent that could not be explained by coincidence. Their values
for the frequency of mosaicism in preimplantation embryos of
67% must be a fairly good estimate of the frequency of
chromosomal mosaicism in the population of human embryos.
Mosaicism comprised mosaicism of abnormal/normal cells (A/N)
as well as of abnormal/abnormal cells (A/A). We believed that our
assumption of a `cross-sectional' frequency of chromosomal
mosaicism (A/N and A/A) of 60% in 2±8-cell embryos based on
the `extrapolation' of the FISH data of Table I in combination with
the reported WGA + CGH data was justi®ed.
We used the proportions of single monosomies and trisomies
among the homogeneous abnormalities in embryos of 0.30 and
0.233 respectively, as established by karyotyping of zygotes
(Almeida and Bolton, 1996). The slightly higher rate of monosomy
than of trisomy has also been encountered with the FISH and
WGA + CGH techniques (Munne et al., 1998; Voullaire et al.,
2002).
The values for non-mosaic and mosaic chromosome abnormalities in tissues after spontaneous abortion and induced abortion of a
vital pregnancy as well as those found at prenatal diagnosis in
chorionic villi are well established and need no further discussion.
We assumed, according to the observations of Sandalinas et al.
(2001), that cells with haploidy, polyploidy (>5n), monosomy
(other than monosomy X or 21), multiple trisomy (in most but not
all instances), extensive aneuploidy (chaotic chromosomal constitution) and severe structural chromosome rearrangements would
not survive cell cycle control beyond the 8-cell stage: lethal cells.
Cells with single and some with multiple trisomy, monosomy 21,
sex chromosomal aneuploidy, less severe structural chromosome
rearrangements, tetraploidy and triploidy were assumed to survive
81
F.J.Los, D.Van Opstal and C.van den Berg
Table I. Data from the literature on the cytogenetic conditions of the human embryo at various levels of development
Developmental stage
Cytogenetic investigation
Cytogenetics
Study
Non-mosaic
abnormal (%)
Mosaic
(A/N, A/A) (%)
Oocyte
Classical karyotyping
22±33 (26)a
±
Sperm
Classical karyotyping
9.6±10.4 (10)a
±
Fertilization
Classical karyotyping
8 (8)a
±
Arrested zygote
Classical karyotyping
65±90 (70)a
±
Cleavage stage embryo
(2±8 cells)
Classical karyotyping
13±20
2±26
FISH
(X, Y, 13/21, 18)
(X, Y, 15, 16, 17, 18)
(1, 4, 6, 7, 14, 15, 17, 18, 22)
(X, Y, 13, 14, 15, 16, 18, 21, 22)
(X, Y, 18/2, 7, 18/13, 16, 18, 21, 22)
12
16
38
32
45
56
31
30
35
Munne et al., 1995
Iwarsson et al., 1999
BahcËe et al., 1999
Gianarolli et al., 1999
Bielanska et al., 2002
CGH
8
67
Classical karyotyping
(calculated values)a
70±90
(60)a
70±90
Voullaire et al., 2000
Wells and Delhanty, 2000
21
40
24
25
56
(70)a
>3% +
(10% polyploidy )
32
52
32
35
(70)a
5% +
(23% polyploidy/2N)
Munne et al., 1994
Munne et al., 1995
BahcËe et al., 1999
Bielanska et al., 2002
Ruangvutilert et al., 2000
Classical karyotyping
>54 (54)a
36% +
(53% polyploidy/2N)
21% +
(70% polyploidy/2N)
>3 (3)a
Classical karyotyping
2.7
0.4
Classical karyotyping
2±5 (3)a
1±2.2 (2)a
Arrested embryo (2±8 cells)
FISH
(X, Y, 18)
(X, Y, 13/21, 18)
(1, 4, 6, 7, 14, 15, 17, 18, 22)
(X, Y, 18/2, 7, 18/13, 16, 18, 21, 22)
Blastocyst
Classical karyotyping
FISH
(X, Y, 13, 18, 21)
(X, Y, 18/2, 7, 18)
Spontaneous ®rst
trimester abortion
Induced abortion of
viable ®rst
trimester embryo
Viable pregnancies
at CVS
Plachot et al., 1988
Pellestor et al., 1991
Angell, 1997
Pellestor et al., 2002
Martin et al., 1987
Pellestor et al., 1991
Plachot et al., 1988
Zenzes et al., 1992
Wimmers and van der Merwe,
1988
Almeida and Bolton, 1996
Benkhalifa et al., 1996
Jamieson et al., 1994
Almeida and Bolton, 1996
Wimmers and van der Merwe,
1988
Michaeli et al., 1990
Pellestor et al., 1994
Almeida and Bolton, 1996
Clouston et al., 1997
Bielanska et al., 2002
Fritz et al., 2001
(pooled data of various studies)
Kajii et al., 1978
Ledbetter et al., 1992
Association of Clinical
Cytogeneticists, 1994
Pittalis et al., 1994
Leschot et al., 1996
Los et al., 1998b
Van den Berg et al., 2000
A/N and A/A stand for all possible combinations of mosaicism: A1/N, A1/A2/N, ¼ A1/A2/A3/A4/A5/A6/A7/N and A1/A2, A1/A2/A3, ¼A1/A2/A3/A4/A5/A6/A7/
A8.
aValues used for this study.
FISH = ¯uorescence in situ hybridization; CGH = comparative genomic hybridization; CVS = chorionic villus sampling.
82
Model of embryo development
cell cycle control and keep their ability of cell division: viable
cells.
Mosaicism in embryos at the 8-cell stage with 1 cell or 2 cells
that had become abnormal by (a) mitotic event(s) next to 7 or 6
original (normal or abnormal) cells was designated limited
mosaicism (Sandalinas et al., 2001). Mosaicism of >3 (daughter
cells of) mitotically changed cells next to <5 original (normal or
abnormal) cells was designated substantial mosaicism.
Mechanisms
Chromosomal abnormalities are of meiotic or mitotic origin or
both: a mitotic event might affect a normal as well as an abnormal
cell. A mitotic event might even hit a daughter cell of a previously
hit blastomere inducing a second change in the karyotype. We
considered three mechanisms for the induction of mitotic
chromosome errors: non-disjunction (ND), anaphase lagging
(AL) and `structural events' (SE) of DNA damage or chromatid/
chromosomal breakage causing structural chromosome rearrangements (translocations, deletions, duplications, marker or ring
chromosomes, etc.). Other possible mechanisms of chromosome
loss or damage, such as fragmentation or pulverization, were not
separately considered: we assumed that their effects of chromosome loss and/or induction of structural chromosome rearrangements were comprised in the mechanisms of AL and SE.
Blastomeres with complex chromosome abnormalities, also
known as chaotic cells and characteristic for preimplantation
embryos (Harper and Delhanty, 1996), were thought to have arisen
by ND (or sometimes by AL) involving multiple chromosomes
simultaneously: their effects were assumed to be comprised in the
mechanisms of ND (or AL). Finally, we considered only divisions
leading to two daughter cells for our model and discarded divisions
giving rise to three daughter cells, which might occur in cases of
three pronuclei (Kola et al., 1987).
ND results in two differently abnormal daughter cells, one cell
with loss of a chromosome and the other cell with the reciprocal
gain of that chromosome. When ND concerns two or multiple
chromosomes simultaneously, a random mixture of reciprocal
gains and losses of the various chromosomes in the daughter cells
can be expected. Special situations occur when cells displaying
single trisomy or monosomy are affected by ND involving only
that speci®c chromosome which then corrects one daughter cell to
normal disomy and makes the other tetrasomic or nullisomic.
These situations are known as trisomic zygote rescue (TZR) and
monosomic zygote rescue (MZR) respectively, and are characterized by uniparental disomy (UPD) in a proportion of the corrected
cases (Spence et al., 1988; Kalousek and Barret, 1994; Ledbetter
and Engel, 1995; Wolstenholme, 1995, 1996).
AL involves both chromatids of a chromosome in 36% of cases
and one chromatid in 64% of cases giving two identically
abnormal daughter cells or one abnormal and one unchanged
daughter cell respectively (Ford et al., 1988). In the case that AL
concerns two or multiple chromosomes and/or chromatids simultaneously, a random mixture of losses of the different chromosomes among the daughter cells can be expected, resulting in a few
unchanged daughter cells. Also the special situation of TZR can
occur, when AL corrects a cell with single trisomy to two normal
daughter cells or one normal and one original daughter cell.
Structural chromosome rearrangements by SE might involve
one chromatid or both chromatids of a single chromosome and
more chromosomes simultaneously (for instance in reciprocal
translocations). We assumed a 0.5:0.5 ratio for the situations of
one abnormal and one unchanged daughter cell versus two
identically abnormal daughter cells. Potential malsegregation of
the arisen derivative chromosome(s) among the daughter cells was
thought to be part of the SE mechanism.
The already mentioned very detailed studies by Wells and
Delhanty (2000) and Voullaire et al. (2000) comprising numerical
as well as unbalanced structural chromosomal abnormalities
tempted us to make an estimate of the relative frequencies of
these three mechanisms of mitotic events. In this estimate, the
minimum number of mitotic events needed to explain (or
`explain') the various, mitotically changed karyotypes in all the
analysed blastomeres was considered. Only zero or one mechanism per cell per division could be attributed. Sometimes,
simultaneous events in different cells during the same cell division
or consecutive events in subsequent cell divisions of already
mitotically changed cells had to be considered. We performed this
estimate according to the example given by the authors (Voullaire
et al., 2000). In our hands, the ratio of ND:AL:SE turned out to be
~5:5:2. There was a risk of underestimating the frequency of AL
and overestimating that of ND, because it was not always clear
whether a monosomy present in some cells of an embryo
originated from a normal embryo hit once by AL or represented
a case of MZR by ND. Furthermore, these two studies tempted us
to speculate on the ratio of single chromosome/chromatid versus
multiple chromosomes/chromatids involvement in mitotic events:
we established a ratio of 6:4. There were considerable differences
between the mechanisms on this point. SE involved a single
chromosome in all 5 events, AL in 10/11 events (91%) and ND in
3/14 events (21%). Because of the small involvement of multiple
chromosomes simultaneously in AL, we did not modify the abovementioned fractions of changed and unchanged daughter cells after
a mitotic event by AL concerning a single chromosome/chromatid
in the probability calculations for the model.
The mitotic events ND, AL and SE occurring in the relative
frequencies of 5:5:2, will result in a mean proportion of mitotically
changed cells with 2 identically abnormal daughter cells of 0.233
[0.3635/12 (AL) + 0.5032/12 (SE)] and with 1 abnormal and 1
original or 2 differently abnormal daughter cells of 0.767 [0.6435/
12 (AL) + 1.0035/12 (ND) + 0.5032/12 (SE)]. Mean proportions
of 0.35 [0.6435/12 (AL) + 0.5032/12 (SE)], 0.417 [1.0035/12
(ND)] and 0.233 [0.3635/12 (AL) + 0.5032/12 (SE)] will show 1
changed and 1 original daughter cell, 2 differently and 2
identically changed daughter cells respectively.
In a normal cell, ND concerning a single chromosome (21% of
the events) gives rise to 1 trisomic and 1 monosomic cell, the ®rst
being viable and the second lethal. ND concerning more chromosomes simultaneously (79% of the events) will result in only a few
viable cells (arbitrarily set at 5%) and a vast majority of lethal cells
(95%). Overall, 14.5% (0.2130.50 + 0.7930.05) of cells are
viable and 85.5% lethal following ND. AL leads to loss of
chromosomes; monosomy 21 and monosomy X are the only viable
conditions among the monosomies. These two monosomies are the
result of 7.6% of the AL events involving one chromosome
assuming that AL affects each chromosome equally [2:46
(autosomes), 0.532:46 (X chromosome in 46,XX) and 0.531:46
(Y chromosome in 46,XY)]. In the 9% of cases that AL involves
more chromosomes simultaneously, no viable cells are to be
83
F.J.Los, D.Van Opstal and C.van den Berg
expected. When AL affects normal cells, the fraction of lethal
daughter cells [0.913(1 ± 0.076)3(0.64 + 230.36) +
0.0931.0032] divided by the total of changed daughter cells
[0.913(0.64 + 0.3632) + 0.0932] delivers a ®gure of 93.4% for
the lethality rate. Concerning SE, no data are available. We
assumed that 50% of normal blastomeres mitotically changed by
SE would be lethal. The mean lethality rate of mitotically changed
cells from normal origin is 83.0%.
Abnormal cells affected by ND, AL and SE will show more
seriously abnormal karyotypes than normal cells. Therefore, we
assumed a 50% decrease in the fraction of viable cells for ND and
SE resulting in lethality rates of 0.927 for ND and 0.75 for SE. We
did not expect an abnormal cell to survive a hit by AL delivering a
lethality rate of 1.00. The mean lethality rate of mitotically
changed cells from abnormal origin is 92.5%. Mitotically changed
cells that were hit by a second or even a third mitotic event in a
subsequent cell division were supposed to be lethal in all instances.
In the two WGA + CGH studies of Wells and Delhanty (2000)
and Voullaire et al. (2000), we estimated the proportions of lethal
and viable cells among the mitotically changed cells according to
the de®nitions given in Cytogenetics above at 78 and 22%
respectively. Although the range of our theoretically calculated
lethality rate from 83.0 to 92.5% was not quite in agreement with
the `actual' estimated rate of 78%, we believed that our
assumptions on the mechanisms of ND, AL and SE were well
applicable to our model.
Calculations
For our hypothetical model, we assumed that a mitotic event could
hit any blastomere of a 1-, 2- or 4-cell embryo at random with a
certain probability (p) during mitosis. The probability that a
blastomere would not be hit was q (= 1 ± p). Such a situation could
be described by binomial probabilities (Zarr, 1999). We considered only the mitotic events that occurred in the ®rst three
mitotic cell divisions without full cell cycle control, allowing for
further cell division(s) of the majority of the karyotypically
changed cells. The formulae for binomial probability calculations
in these cell divisions are shown in Table II. Since we were for this
part of the calculations only interested in the number of embryos of
which >1 cells were hit by >1 mitotic events and not in that of the
unaffected embryos, this could be described by the formula (p +
q)n ± qn = (1)n ± (1 ± p)n = 1 ± (1 ± p)n delivering the formulae for
the ®rst, second and third cell division:
1-cell stage (n = 1): p
2-cell stage (n = 2): 1 ± (1 ± p)2
4-cell stage (n = 4): 1 ± (1 ± p)4.
Multiplication of probabilities by the numbers of embryos (= N)
would then deliver the numbers of embryos affected by (a) mitotic
event(s) at the various cell stages.
However, a mitotic event in the ®rst division might lead to
mosaicism in case of 2 differently changed daughter cells (A/A) or
1 changed and 1 original daughter cell (A/N or A/A), to
homogeneous abnormality in case of 2 identically changed
daughter cells and even to normality in case of TZR or MZR.
The chance of 2 different daughter cells after a mitotic event was
calculated at 0.767 (see Mechanisms above). So, the probability
that a mitotic event in the ®rst mitotic division would result in
mosaicism was 0.767p. In the second and third division, (a) mitotic
event(s) always would lead to mosaicsm; no further corrections
84
Table II. Formulae for binomial probability calculations in the ®rst, second
and third cell divisions
Cell
division
No. of
blastomeres
Binomial
Terms of
(p + q)n
(p + q)n
p
q
p2
2pq
q2
p4
4p3q
6p2q2
4pq3
q4
First
1
(p + q)1
Second
2
(p + q)2
Third
4
(p + q)4
No. of
(simultaneous)
mitotic events
1
0
2
1
0
4
3
2
1
0
were needed concerning this point. Mitotic events in the second
and/or third mitotic cell division of an embryo with mosaicism
already formed in (a) previous division(s), would not lead to a new
case of mosaicism but only to an aggravation of the existing
mosaicism. In the calculation of the number of mosaic cases
among the embryos undergoing mitotic events, N had to be
corrected by the subtraction of the number of already existing
cases of mosaicism. In the same way, a correction should be made
for the embryos lost by mitotic arrest. This last correction was
omitted because it would only lead to minor changes in values but
major problems in calculations. The value of 60% for mosaicism at
the 2±8-cell stage (see Cytogenetics section), N as the mean of the
N values at the 1-, 2- and 4-cell stages, the above-mentioned
formulae and corrections enabled us to describe the relation
between the `cross-sectional' value of 0.60 and p for our
longitudinal model in the following equation:
0.767pN + [1 ± (1 ± p)2](N ± 0.767pN) + [1 ± (1 ± p)4][N ±
0.767pN ± {1 ± (1 ± p)2}(N ± 0.767pN)] = 0.60N.
From the 8-cell stage onwards, the decay curves of the total
number of embryos as well as that of normal, homogeneously
abnormal and mosaic embryos separately were assumed to be
optically comprehensive curves. Therefore, estimations and calculations (multiplication, addition and subtraction) were conducted from the top (8-cell stage) downstream as well as from the
bottom (early fetus) upstream. This method was chosen because of
the lack of data on the cytogenetic condition of embryos between
the 8-cell stage and the level of recognized pregnancy (see
Cytogenetics section).
As mentioned in the Mechanisms section, a cell division of an
abnormal blastomere might accidentally deliver 2 normal daughter
cells or a mosaicism of 1 normal and 1 abnormal cell in case of
TZR or MZR. For monosomy corrected to nullisomy/disomy by
ND (MZR) assuming equal frequencies of all different monosomies, this value was given by the following product:
chance of (a) mitotic event(s) in the cell division of concern
3chance of a ND correction involving a single chromosome
(0.21 3 5/12 = 0.0875)
3 chance that the single chromosome involved was a speci®c
chromosome (22/23 3 1/45 (autosomes) + 1/231/2331/45 (45,X)
= 0.02174
Model of embryo development
Table III. The fate of the human embryo in relation to the cytogenetic condition
Developmental
stage
Condition(s) + event(s) causing,
changing or eliminating
chromosome abnormalities
N
Oocyte
Sperm
Meiotic errors
Meiotic errors
Fertilization
Syngamy, some cell cycle control
Arrested ®rst division
Mitotic errors ®rst division (12.7%)
100 000
100 000
100 000
100 000
±12 500
11 112
Omnipotent blastomeres, limited
cell cycle control
Arrested second division
Mitotic errors second division (23.8%)
87 500
Zygote
2-cell stage
4-cell stage
8-cell stage
8-cell stage/
morula
Free blastocyst
Hatched
blastocyst
Embryo
Fetus
Omnipotent blastomeres,
limited cell cycle control
Arrested third division
Mitotic errors third division (41.9%)
Expression of embryonic genome
(>8-cell stage):
arising of cell cycle control
(8±64-cell stage)
separation of trophoblast and ICM
(8±16-cell stage)
Arrested development
(8±64-cell stage)
Separation of epiblast and hypoblast
(64±128-cell stage)
Arrested development,
non-implantation
Recognized implantation
Occult abortion by developmental
arrest and implantation failure
Recognized pregnancy
®rst trimester spontaneous abortion
Viable pregnancy at CVS
(11±13 weeks)
Cytogenetics
Normal
(N)
Abnormal
(A)
74 000
(74%)
26 000
90 000
(90%)
10 000
Induction of abnormalities in 8%
61 000
(61%)
39 000
±3750
±8750
±2545
(N®A/N) 888
±3030
(N®A/A) ±2924
±1696
(N®A)
±21
+8
(A®N)*
±8
+1696
49 987
(57.1%)
28 993
Mosaic
(A/N, A/A)
(26%)
(10%)
±
±
(39%)
±
±
±
+ 2545
+ 3030
+ 2924
+ 21
8520
(N®A/N)
(N®A/A)
(A®A /A)
(A®A/N)*
(9.7%)
±397
380
1552
+ 11 376
+ 336
+ 6525
+ 49
26 409
(A/N®A/N)
(A/N, A/A®A/A)
(N®A/N)
(N®A/A)
(A®A/A)
(A®A/N)*
(31.1%)
±974
5414
5247
+ 15 413
+1
+ 8440
+ 63
49 352
(A/N®A/N)
(A/N, A/A®A/A)
(N®A/N)
(N®A/A)
(A®A/A)
(A®A/N)*
(59.8%)
±12 616
±7775
(A[1-2]/N[7-6]®N)
(A[1-2]/A[7-6]®A)
(A®A)
(A®A/A)
(A®A/N)*
(A®N)*
(N®A)
(33.1%)
±2500
20 218
±750
±11 376
±336
(N®A/N)
(N®A/A)
±1353
±6525
±49
(A®A/A)
(A®A/N)*
85 000
37 525
(44.1%)
21 066
(24.8%)
±2500
34 578
±750
±15 413
±1
(N®A/N)
(N®A/A)
±776
±8440
±63
(A®A/A)
(A®A/N)*
82 500
21 361
(25.9%)
11 787
(14.3%)
+ 12 616
(A/N®N)
+7775
(A/A®A)
±37 500
±4477
±8312
45 000
29 500
±8500
±1925
36 500
±7100
27 575
±1933
(75.5%)
7000
±3874
(19.2%)
1925
±1293
(5.3%)
29 400
±4400
25 000
25 642
±1892
23 750
(87.2%)
3126
±2376
750
(10.6%)
632
±132
500
(2.2%)
(65.6%)
11 250
±24 711
(25.0%)
±4250
(95%)
4250
(9.4%)
±2325
(3.0%)
(2.0%)
A/N, and A/A stand for all possible combinations of mosaicism: A1/N, A1/A2/N, ¼ A1/A2/A3/A4/A5/A6/A7/N and A1/A2, A1/A2/A3, ¼ A1/A2/A3/A4/A5/A6/A7/
A8.
*Correction by trisomic zygote rescue and monosomic zygote rescue.
CVS = chorionic villus sampling.
85
F.J.Los, D.Van Opstal and C.van den Berg
Table IV. Details of the numbers of embryos at the actual and virtual 8-cell stage, during the morula stage (16- and 32-cell stage) and arriving at the
blastocyst stage (64-cell stage)
Cell stage
Actual 8-cell stage before shift, A/N®N, A/A®A
Virtual 8-cell stage after shift, A/N®N, A/A®A
16-cell stage
32-cell stage
64-cell stage
N
82
82
67
55
45
Cytogenetics
500
500
500
500
000
Normal (N)
Abnormal (A)
Mosaic (A/N, A/A)
21
33
32
31
29
11
19
18
15
11
49 352
28 961
16 625
9250
4250
361
977
875
250
500
(25.9)
(41.2)
(48.7)
(56.3)
(65.6)
787
562
000
000
250
(14.3)
(23.7)
(26.7)
(27.0)
(25.0)
(59.8)
(35.1)
(24.6)
(16.7)
(9.4)
A/N and A/A stand for all possible combinations of mosaicism: A1/N, A1/A2/N, ¼ A1/A2/A3/A4/A5/A6/A7/N
and A1/A2, A1/A2/A3, ¼ A1/A2/A3/A4/A5/A6/A7/A8.
Values in parentheses are percentages.
Figure 1. Proportions of cytogenetically normal, abnormal and mosaic
embryos at different stages of embryonic development.
3 fraction of single monosomy among the homogeneous
abnormalities (0.30)
3 number of homogeneous abnormalities at the cell stage of
concern.
In the same way and under the assumption of equal frequencies
of all different trisomies, the calculation could be made for trisomy
corrected to trisomy/disomy or disomy by AL and tetrasomy/
disomy by ND (TZR):
chance of (a) mitotic event(s) in the cell division of concern
3 chance that a ND or AL correction involved a single
chromosome/chromatid [0.9135/12 (AL) + 0.2135/12 (ND) =
0.4667].
3 chance that the single chromosome involved was a speci®c
chromosome [22/23 3 3/47 (autosomes) + 231/431/2332/47
(47,XXY and 47,XYY) + 1/231/2333/47 (47,XXX) = 0.06337]
3 fraction of single trisomy among the homogeneous abnormalities (0.233)
3 number of homogeneous abnormalities at the cell stage of
concern.
All the discussed parameters and calculation methods needed
for the construction of the model are summarized below:
General: cell cycle control; de®nition of embryonic compartments.
86
Numbers: de®nition of starting point (100 000 zygotes); ®nal
number of viable fetuses at the beginning of the second trimester
of pregnancy (25 000); rate of zygotes developing into free
blastocysts (40±50%); rate of pregnancy loss after recognized
implantation (31%); numbers of embryos lost by mitotic arrest in
®rst (12 500), second (2500), and third (2500) cell division.
Cytogenetics: cytogenetic data at the various levels of embryonic development and used `mean' values for the model; de®nition
of lethal and viable cells under cell cycle control; de®nition of
limited mosaicism (A[<2]/N[>6] or A[<2]/A[>6]) and substantial
mosaicism (A[>3]/N[<5] or A[>3]/A[<5]).
Mechanisms: mechanisms and effects of the mitotic events (AL,
ND and SE); relative frequencies of AL:ND:SE = 5:5:2; ratios of 1
changed and 1 original (0.35), 2 differently changed (0.417) and 2
identically changed (0.233) daughter cells after mitotic events;
lethality rates of daughter cells of normal cell hit by ND (0.855),
AL (0.934) and SE (0.50); lethality rates of daughter cells of
abnormal cell hit by ND (0.927), AL (1.00) and SE (0.75);
mechanisms and effects of TZR and MZR.
Calculations: binomial probability calculations; equation for the
conversion of a cross-sectional into a longitudinal model; calculations for TZR and MZR.
Model for development of embryos
The model, which describes quantitatively the development of
chromosomally normal, abnormal and mosaic embryos, is presented in Table III and Figure 1. More details on the disappearance
of mosaic embryos and of mosaicism from surviving embryos are
shown in Table IV and on the levels of mosaicism at the 8-cell
stage in Figure 2. We will now explain the construction of the
model in detail.
With the abnormality rates in sperm (10%) and oocytes (26%)
and the rate of induction of abnormalities by the process of
fertilization (8%), the numbers of 61 000 normal and 39 000
abnormal zygotes could be calculated. Since 70% of the arrested
zygotes and 2±8-cell embryos showed cytogenetic abnormalities,
70% of the values for mitotic arrest were attributed proportionally
to abnormal and mosaic embryos. The total numbers of embryos
(N) at the 1-, 2- and 4-cell stage of development after subtraction
of the values of mitotic arrest were 87 500, 85 000 and 82 500
respectively. The mean N was 85 000 in the equation 0.767pN + [1
± (1 ± p)2](N ± 0.767pN) + [1 ± (1 ± p)4][N ± 0.767pN ± {1 ± (1 ±
Model of embryo development
Figure 2. Numbers of mosaic 8-cell stage embryos at each level of
mosaicism. A/N and A/A stand for all possible combinations of mosaicism:
A1/N, A1/A2/N, ¼ A1/A2/A3/A4/A5/A6/A7/N and A1/A2, A1/A2/A3, ¼ A1/
A2/A3/A4/A5/A6/A7/A8. The 133 cases of mosaicism due to trisomic and
monosomic zygote rescue consisting of the mosaicisms A (original)/N and A
(original)/A (mitotically changed)/N are not separately indicated in the group
of A/N mosaicism.
p)2}(N ± 0.767pN)] = 0.60N: the solution delivered p = 0.127 (and
q = 0.873). The probabilities of the occurrence of mitotic events in
the ®rst, second and third cell division were 0.127 (p), 0.238 [1 ±
(1± p)2] and 0.419 [1 ± (1 ± p)4] respectively.
Multiplication of these probabilities by the total numbers of
embryos at the 1-, 2- and 4-cell stages resulted in the numbers
of embryos hit by mitotic events. Multiplication of the numbers of
normal and abnormal zygotes (after subtraction of the values of
mitotic arrest) by 0.127 resulted in the numbers of arisen mosaic
embryos and of disappeared normal and abnormal embryos in the
®rst cell division. The implementation of the ratios of 1 and 2
(identically or differently) changed daughter cells and of the
calculations for TZR and MZR enabled the differentiation (N®A/
N, N®A/A, N®A, etc.) as shown in Table III. Subtraction and
addition then delivered the numbers of normal, abnormal and
mosaic embryos reaching the 2-cell stage. Multiplication of these
numbers of embryos (after subtraction of the numbers of mitotic
arrest) by 0.238 delivered the numbers of new mosaic cases arisen
from normal and abnormal embryos as well as the number of
aggravated mosaic cases arisen from mosaic embryos. The same
implementation of the ratios for changed daughter cells and the
calculations for TZR and MZR completed the values for the second
cell division. Subtraction and addition resulted in the numbers of
normal, abnormal and mosaic embryos arriving at the 4-cell stage.
The calculations at the 4-cell stage were performed in exactly the
same way as at the 2-cell stage, giving the various numbers for
the third cell division. The difference between the theoretical and
actually calculated numbers and fractions of mosaic embryos at
the 8-cell stage (51 000/85 000: 60.0% and 49 352/82 500: 59.8%)
was due to the omission of the correction for embryos lost by
mitotic arrest in the equation (see Calculations section).
With the substitution of p = 0.127 and q = 0.873 in the terms of
the binomial (p + q)2 of Table II, the numbers of normal, abnormal
and mosaic embryos undergoing 2, 1 and 0 (simultaneous) mitotic
events in the second cell division could be calculated out of the
numbers of surviving embryos that had undergone 1 and 0 mitotic
events in the ®rst cell division. The implementation of the relative
ratios of 1 and 2 (identically or differently) changed daughter cells
and the nature of the cell(s) (normal, abnormal or already
mitotically changed) hit by (a) mitotic event(s) further enabled
us to establish the levels of mosaicism within these numbers of
embryos. In the same way, the numbers of normal, abnormal and
mosaic embryos undergoing 4, 3, 2, 1 and 0 (simultaneous) mitotic
events in the third cell division could be calculated with the
probabilities of the terms of the binomial (p + q)4 and the numbers
of surviving embryos after 2, 1 and 0 events in the second cell
division. The relative ratios of changed daughter cells and the
nature of hit cells were implemented as in the second cell division.
These subsequent calculations resulted in the numbers of normal,
abnormal and mosaic embryos that had undergone all possible
combinations of 0, 1 or >2 (simultaneous and/or consecutive)
mitotic events in 1, 2 or all 3 of the ®rst 3 mitotic cell divisions.
The numbers of mosaic embryos at each level of mosaicism (A/N
and A/A) at the 8-cell stage are presented in Figure 2. The values
of mosaic embryos with even numbers of changed cells are higher
than with odd numbers. This can be explained by the fact that a cell
division of odd as well as even numbers of cells always leads to an
even number of daughter cells.
The numbers of the mosaic embryos that were hit by 1 and by
>2 consecutively and/or simultaneously occurring mitotic events
had become known: 32 285/49 352 (65.4%) and 17 067/49 352
(34.6%) respectively. Using the ratios of 1 and 2 (identically or
differently) changed daughter cells, we could calculate that 18 833/
49 352 (38.2%) of the mosaic embryos would show mosaicism of 2
and 30 519/49 352 (61.8%) of >3 cells/cell lines (multiple
mosaicism).
Mitotically changed lethal cells show mitotic arrest under cell
cycle control from the 8-cell stage onwards. Limited mosaicism of
1 or 2 lethal cells would then show the disappearance of these
cells, leaving only the original cells: a shift from mosaicism
towards normality (in case of A/N mosaicism) or homogeneous
abnormality (in case of A/A mosaicism) occurs during the morula
stage. We were aware of the fact that the dichotomous variable of
viability or lethality of the original cell line created a real and a
virtual component of this shift. It concerned those embryos hit
once or twice in the third cell division by a mitotic event delivering
1 or 2 lethally changed cells (A[1]/N[7], A[1]/A[1]/N[6], A[2]/N[6] or
A[1]/A[7], A[1]/A[1]/A[6], A[2]/A[6]). Additionally, it concerned
those embryos hit by 1 mitotic event in the second cell division
resulting in 1 lethal cell only (A[1]/N[3] or A[1]/A[3]) but not by a
second hit in the third cell division (thus becoming A[2]/N[6] or
A[2]/A[6] at the 8-cell stage) or hit consecutively in the third cell
division delivering 2 lethal cells (A[1]/A[1]/N[6], A[2]/N[6] or
A[1]/A[1]/A[6], A[2]/A[6] at the 8 cell-stage). We could calculate
that 83.0% of the A/N mosaics (12 616/15 209) and 93.0% of the
A/A mosaics (7775/8357) ful®lled these conditions using the
lethality rates of normal and abnormal cells hit by ND, AL and SE,
their relative frequencies and ratios of 1 and 2 (identically or
differently) changed daughter cells and the numbers of limited A/
N and A/A mosaics from Figure 2. The considerable fraction of
41.3% of the mosaic embryos [(12 616 + 7775)/49 352] turned
really or virtually back to normality or homogeneous abnormality
(Tables III and IV). Embryos with limited mosaicism of 1 or 2
viable cells (A[1]/N[7], A[2]/N[6] or A[1]/A[7], A[2]/A[6]) and of 1
87
F.J.Los, D.Van Opstal and C.van den Berg
viable and 1 lethal cell (A[1]/A[1]/N[6], or A[1]/A[1]/A[6]) continued
further development as mosaic embryos.
During the morula stage, a substantial proportion (37 500/82 500
= 45.5%) of embryos is lost by arrested development (Table IV).
The contributions of the normal, abnormal and mosaic embryos to
the combined values of embryo loss and shift from mosaicism
towards normality or homogeneous abnormality were established
using the values from the optically best-®tting decay curves.
Therefore, the virtual situation of localizing this complete shift at
the 8-cell stage was introduced: the virtual 8-cell stage (Table IV).
From this virtual 8-cell stage onwards, we searched for the best ®t
of the downstream and upstream values. Subtraction and addition
delivered the numbers of normal, abnormal and mosaic embryos
lost by non-implantation and those at the levels of recognized
implantation and recognized pregnancy (Tables III, IV and
Figure 1).
From the virtual 8-cell stage, only 1.7% of the mosaic embryos
(500/28 961) and 3.8% of the homogeneously abnormal embryos
(750/19 562) but as much as 69.9% of the normal embryos (23 750/
33 977) reached the stage of viable pregnancy (Tables III and IV).
At the actual 8-cell stage, the lowest level of chromosomally
normal embryos (25.9%) is associated with the highest level of
abnormal and mosaic embryos (74.1%) (Tables III and IV,
Figure 1).
As can be seen in Table III, eight normal and 133 mosaic cases
(A/N) have arisen in the ®rst three cell divisions due to accidental
TZR or MZR. The majority of the mosaic cases was derived from
trisomic conceptions (n = 122) and a minority from monosomic
conceptions (n = 11). The eight normal cases were all derived from
trisomic conceptions.
Discussion
The rates of homogeneous abnormalities (8%) and mosaicism
(67%) in cleavage stage embryos as found by Voullaire et al.
(2000) and Wells and Delhanty (2000) with WGA + CGH studies
give a total cytogenetic abnormality rate of 75%. This ®gure is
remarkably similar to the conceptional loss rate of 78% estimated
by Roberts and Lowe (1975). Our theoretical model combines the
development of 25 000 viable pregnancies out of 100 000 zygotes
with rates of 14.3% for homogeneous abnormalities and 59.8% for
mosaicism in embryos arrived at the 8-cell stage. This was
achieved by the conversion of the `mean' value for mosaicism
from cross-sectional studies in 2±8-cell embryos (60%) into a
longitudinal, developmental model on the arising of mosaicism in
the ®rst three mitotic cell divisions using binomial probability
calculations. The disappearance of mosaic embryos and mosaicism from surviving embryos during the morula stage involved the
implementation of the concept of lethality or viability of cells
under cell cycle control. Cells with cytogenetic abnormalities of
meiotic origin and/or induced by fertilization and/or mitotic events
during the ®rst three mitotic cell divisions could survive or nonsurvive cell cycle control from the fourth cell division onwards.
The cytogenetic conditions for this presumed surviving or nonsurviving of cells were given in the Cytogenetics section and the
cells were accordingly designated viable or lethal.
Our assumed low values for arrested development of the
preimplantation embryo in the early postzygotic cell divisions with
limited cell cycle control are consistent with a mathematical model
88
on developmental arrest of embryos in relation to cell death (Hardy
et al., 2001). According to this model, substantial cell death occurs
not before the 8-cell stage: ~50% of the embryos succumb during
the morula stage and the remaining 50% reach the blastocyst stage.
Also in our developmental model, the morula stage turned out to
be the predominant graveyard for embryos, especially mosaic
embryos. Not only in theoretical models but also in reality, it has
been established that the majority of mosaic cleavage stage
embryos does not reach the blastocyst stage (Evsikov and
Verlinsky, 1998; Sandalinas et al., 2001; Bielanska et al., 2002).
Uncontrolled passing on of numerical and structural chromosome abnormalities to daughter cells in the ®rst cell divisions
without full cell cycle control are the cause of mosaicism in the
preimplantation embryo (Delhanty and Handyside, 1995; Conn
et al., 1998; Bielanska et al., 2002). The activation of the
embryonic cell cycle control system from the 8-cell stage onwards
causes developmental arrest of many mosaic embryos and
eliminates previously formed mosaics during the morula stage.
The arising of further mosaics other than sporadic cases is
prevented since 83.0±92.5% of mitotically changed cells show
mitotic arrest. So, the number of mosaics is at its highest at the 8cell stage of embryonic development. An association of increasing
frequencies of mosaicism and increasing numbers of blastomeres
in cleavage stage embryos has been observed with FISH studies
(Bielanska et al., 2002).
Mosaic embryos with limited mosaicism of lethal cells (A[1,2]/
N[7,6] or A[1,2]/A[7,6]) have been proposed to continue further cell
divisions or to succumb as normal or homogeneously abnormal
embryos dependent on the lethality or viability of the original
cells. This phenomenon was called the shift of mosaicism towards
normality or homogeneous abnormality: this shift comprised a real
component (in case of embryo survival) and a virtual one (in case
of developmental arrest). Mosaic embryos with substantial
mosaicism of lethal cells (A[>3]/N[<5] or A[>3]/A[<5]) are nonviable irrespective of the lethality or viability of the original cells
and fail to reach the blastocyst stage (Sandalinas et al., 2001;
Voullaire et al., 2002). Mosaic embryos with limited or substantial
mosaicism of viable cells whilst the original cells are lethal
succumb during the morula stage. Mosaic embryos with limited or
substantial mosaicism of viable cells and viable original cells
(normal or abnormal) might continue further cell divisions but
might, dependent on the severity of the chromosomal abnormalities, show differences in growth velocities between the various
cell lines. Major differences might lead to irregularities in the
shape of the blastocyst or its ICM and hence in hampered or nonimplantation (Richter et al., 2001). After initially successful
implantation, minor differences in growth velocities might lead to
disturbances in embryo and further trophoblast development with
subsequent occult pregnancy loss. However, some cases of
mosaicism might be without lethal consequences for embryonic
and placental development and discovered later as generalized
mosaicism or CPM at prenatal diagnosis. Embryos with multiple
mosaicism (>3 different cells/cell lines) form the majority of
mosaic embryos (almost 62%) in our model. Such embryos display
limited or substantial mosaicism of different lethal, different
viable or a mixture of (different) viable and (different) lethal cells/
cell lines [next to the original (viable or lethal) cell or cell line].
Dependent on the fractions of the lethal and viable cells/cell lines
and their relative growth velocities, these embryos might theor-
Model of embryo development
etically have each of the described developmental prospects.
However, generalized mosaicism and/or CPM of >3 independent
cell lines are very rare: virtually all embryos displaying multiple
mosaicism are lost.
The above-hypothesized events explain the great decrease in
numbers as well as in fractions of mosaic cases in the cell divisions
during the morula stage. Such a decrease beyond the 8-cell stage
has actually been observed in a study of chromosomal mosaicism
in embryos throughout preimplantation development (Bielanska
et al., 2002). The increasing and decreasing frequency of
mosaicism prior to and beyond the 8-cell stage respectively, as
found by Bielanska et al. (2002) deliver the geometric shape of a
parabola with the top at the 8-cell stage and is consistent with our
model as shown in Figure 1. Furthermore, the above-hypothesized
events explain the non- or failed implantation of the majority of the
mosaic embryos that have reached the free or hatched blastocyst
stage.
Apart from the massive loss of mosaic embryos between the
virtual 8-cell stage and the free blastocyst stage, a substantial
number of homogeneously abnormal and a small number of
normal embryos are lost. Homogeneously abnormal embryos
consisting of lethal cells show mitotic arrest under cell cycle
control during the morula stage, whereas those consisting of viable
cells might continue further cell divisions. Apart from viability or
lethality of cytogenetically abnormal cells under cell cycle control,
other factors might cause mitotic arrest of cells during the morula
stage. Recently, the role of epigenetic reprogramming of the
preimplantation embryo has been reviewed as a possible cause of
developmental disturbances (De Rijcke et al., 2002). At the
blastocyst stage, disturbances in the uterine blastocyst signalling
may lead to non-implantation or failed implantation (Macklon
et al., 2002; Paria et al., 2002).
After successful implantation, disturbances in the development
of the embryo proper due to homogeneous chromosomal abnormalities or viable mosaicisms in some cases may lead to blighted
ovum, missed or spontaneous abortion (Boue and BoueÂ, 1976;
Byrne et al., 1985). Finally, factors not related to chromosomal
abnormalities can cause arrest of embryo development with
subsequent abortion.
In our model, randomness of all events and hence of the
occurrence of TZR and MZR has been assumed. Eight embryos
with a normal karyotype and 133 cases of mosaicism did arise by
TZR and MZR (see Table III). Accidental correction of 1 cell with
single trisomy or monosomy to 1 or 2 normal daughter cells
occurred in these cases in the ®rst, second or third mitotic cell
division. Assuming the same chances of survival for the eight
normal cases as for originally normal embryos at the 2-cell stage
(49 987 ± 8 = 49 979), a mean of four cases could be expected
among the 23 750 normal fetuses at the end of the ®rst trimester of
pregnancy. Two such rare cases have been discovered with DNA
and (molecular) cytogenetic investigations (Los et al., 1998a). The
mosaic embryos with trisomy/disomy mosaicism might have
better chances of survival than the whole group of mosaic embryos
since they represent a selected population affected by an accidentally selected mitotic event, as we will see below.
A number of CPM cases involving single trisomy shows UPD
(Robinson et al., 1997; EUCROMIC, 1999; Kotzot, 2002; Yong
et al., 2002). No CPM cases of monosomy/disomy mosaicism with
UPD of the disomic cell line have been reported (Kotzot, 2002).
Van Opstal et al. (1998) established prospectively the frequency of
UPD among cases of CPM III and/or I (investigation of the
trophoblast compartment of chorionic villi only) involving single
trisomy at 1/23 (4.3%) in a population of women that underwent
prenatal diagnosis. Since the proportion of CPM III and/or I among
the three types of CPM is 71% (Pittalis et al., 1994; Van den Berg
et al., 2000), we assumed a corrected incidence of UPD among all
CPM types involving single trisomy of 3.1%. The 33.3% risk for
UPD following TZR means that a theoretical proportion of 9.3% of
the CPM cases involving single trisomy has been subjected to
TZR. About 88% of the mosaic cases encountered in chorionic
villi concern CPM and the other 12% generalized mosaicism; 40%
of the CPM cases concern single trisomy (Pittalis et al., 1994;
Leschot et al., 1996; Phillips et al., 1996; Los et al., 1998b;
Van den Berg et al., 2000). So, 16.4 of the 500
(0.09330.8830.403500) mosaic cases at the level of viable
pregnancy of Table III could be regarded as CPM cases arisen by
TZR of a trisomic conception, of which 5.5 are expected to show
UPD. This means a UPD rate of 22 per 100 000 chorionic villus
samples. This value is close to the maximal UPD rate of 28±35 per
100 000 chorionic villus samples reported for the chromosomes 2,
3, 7, 8, 9, 15, 16 and 22 together (Wolstenholme, 1996;
EUCROMIC, 1999).
As already stated above, randomness of the occurrence of TZR
and MZR has been presumed in our model. Any trisomy has a
chance of 1.7% of being corrected by TZR to trisomy/disomy
mosaicism: 7048 of the abnormal zygotes undergoing the ®rst cell
division show single trisomy [0.233 (fraction of single trisomy)330 250] out of which ultimately 122 mosaic cases are
formed by TZR (1.7%). However, 10% of trisomy 16 conceptions
have been estimated to undergo TZR (Wolstenholme, 1995),
probably indicating some kind of a governing mechanism. From a
governing mechanism for TZR (and MZR), one would expect the
effects in the earliest possible postzygotic cell division(s) with a
suf®cient activity of the cell cycle control system. These are the
®rst division with the still strongest maternally derived control
system and the fourth division with the embryonic control system
becoming active. Furthermore, one would not expect a governing
mechanism to be active in only 1 cell per embryo, except in the
®rst cell division.
However, restricting the correction by TZR to 1 cell, we will
consider corrections in the different cell divisions by AL, the
mechanism mostly involved in TZR, more closely. Correction in
the ®rst cell division may result in N[16] or in the substantial
mosaicism A[8]/N[8] at the 16-cell stage. Corrections in the second,
third and fourth cell divisions result in the mosaicisms A[8,12]/
N[8,4], A[12,14]/N[4,2] and A[14,15]/N[2,1] at the 16-cell stage
respectively (Los et al., 1998a). Only the mosaicisms A[>12]/
N[<4] can become a CPM I of non-mosaic trisomy 16 or a CPM III
with non-mosaic trisomy 16 in trophoblast cells combined with a
mosaic or non-mosaic trisomy 16 in the mesenchymal core of
chorionic villi (EEM compartment). These types of CPM III and I
are the regular appearance of trisomy 16 mosaicism at prenatal
diagnosis (Wolstenholme, 1995, 1996). Also UPD cases of other
chromosomes show CPM III or I with high levels of mosaicism or
non-mosaicism (Wolstenholme, 1996; Robinson et al., 1997). This
means that the surviving mosaic embryos would be those that had
undergone TZR corrections as random events predominantly in the
third and corrections under control of a governing mechanism in
89
F.J.Los, D.Van Opstal and C.van den Berg
the fourth mitotic cell division. Under both circumstances, TZR
corrections in these cell divisions deliver inverted `limited
mosaicisms': the highest proportion of homogeneously (abnormal)
cells and the lowest proportion of mitotically changed (normal)
cells show apparently a higher rate of survival than the mosaic
population as a whole. These mosaicisms probably provide a
degree of homogeneity necessary for survival and successful
implantation. The allocation of normal cells only to the compartment of the embryo/fetus proper at the 128-cell stage favours
normal embryonic development after successful implantation.
The 16.4 CPM trisomy cases due to TZR in viable pregnancies
at the end of the ®rst trimester of pregnancy among 122 TZRderived mosaic trisomy (A/N) embryos give a survival rate of
13.4% (16.4/122). This is higher than that of the population of
mosaic embryos with A/N mosaicism at the virtual 8-cell stage of
~3.1% [<500/(28 536 ± 12 616)] (see Tables III, IV and Figure 2).
Almost all mosaic embryos at the end of the ®rst trimester of
pregnancy show A/N mosaicism. Not included in the calculation
of the survival rate are cases of generalized mosaicism of single
trisomy/disomy with UPD of the disomic cell line. These cases are
examples of a failed distribution of normal cells only to the
compartment of the embryo/fetus proper (Christian et al., 1996;
De Pater et al., 1997; Van den Berg et al., 1997; Los et al., 1998a).
The lack of data on the frequency of TZR cases among these
generalized mosaicisms prevents a fair estimate of the number of
such cases in our model. The occurrence of TZR and MZR as
random events in our model is compatible with the encountered
frequencies of CPM cases showing UPD in our opinion. However,
a governing mechanism of moderate ef®ciency (estimated to be
bene®cial to only 10% of the embryos with trisomy 16) cannot be
excluded.
PGD can be performed for inherited diseases and chromosomal
abnormalities with DNA or molecular cytogenetic techniques at
different levels of in vitro embryonic development. Polar body
biopsy for the investigation of the ®rst or ®rst and second polar
body has been successfully performed on the yet unfertilized or
fertilized oocyte (Verlinsky et al., 1996; Wells et al., 2002; Kuliev
et al., 2003). A limitation of PGD at the level of the polar body is
the fact that the complement of the maternal genetic/chromosomal
contribution to the embryo is investigated. Only the investigation
of both the ®rst and second polar body includes the complement of
abnormalities originating in maternal meiosis II and I (Kuliev
et al., 2003). Maternal meiotic errors, the major source of
numerical chromosome disorders in spontaneous abortion and live
birth, are the target of investigation. The problem of chromosomal
mosaicism, the predominant abnormality in cleavage stage
embryos and the main cause of developmental arrest before the
blastocyst stage cannot be encountered.
The most used method of PGD and PGD-AS is the blastomere
biopsy from cleavage stage embryos. The biopsy is preferentially
performed around the 8-cell stage of development (Handyside,
1998; Vandervorst et al., 2000; ESHRE PGD Consortium Steering
Committee, 2000). However, biopsies at a later stage (morula or
even blastocyst stage) have occasionally been carried out (Veiga
et al., 1997). A sample of 1 or 2 cells is taken from a mean 8-cell
(range: 4±12-cell) embryo at day 3 of in vitro development when it
consists out of <6 or >7 cells respectively (Munne et al., 1998;
Liebaers et al., 1998; Emiliani et al., 2000; Van de Velde et al.,
2000; Vandervorst et al., 2000; ESHRE PGD Consortium Steering
90
Figure 3. Probabilities of normal and abnormal results of 1-cell biopsies
taken from 8-cell embryos with various levels of mosaicism and the
compositions of the remaining post-biopsy embryos.
Figure 4. Probabilities of the results (N/N, A/N, A/A) of 2-cell biopsies
taken from 8-cell embryos with various levels of mosaicism and the
compositions of the remaining post-biopsy embryos.
Committee, 2002; Rubio et al., 2003). Various authors prefer the
2-cell biopsy to the biopsy of just 1 blastomere for a more reliable
diagnosis. The investigation of 2 cells carries a lower risk of
laboratory failure and is believed to be more representative for the
cytogenetic condition of the embryo in cases of chromosomal
mosaicism (Harper and Delhanty, 1996; Van de Velde et al., 2000;
Vandervorst et al., 2000; Wilton, 2002).
The theoretical probabilities of the cytogenetic status of 1-cell
biopsies (1 normal or 1 abnormal cell) and 2-cell biopsies (2
normal, 1 normal + 1 abnormal or 2 abnormal cells) from 8-cell
embryos with all possible levels of mosaicism are presented in
Figures 3 and 4. Furthermore, the cytogenetic conditions of the
remaining 7- or 6-cell post-biopsy embryos are given. The
multiplication of the numbers of normal, abnormal and mosaic
embryos at the 8-cell stage (Table III and Figure 2) by the
probabilities of biopsy and post-biopsy embryo compositions
(Figures 3 and 4) delivers the numbers of normal, abnormal and
mosaic post-biopsy embryos at each biopsy result (Table V).
Normal results are encountered in 47.9% of the 1-cell biopsies
(39 539/82 500) and in 40.1% of the 2-cell biopsies (33 063/
82 500). However, the predictive values of these normal results are
rather limited, since only 54.0% (21 361/39 539) and 64.6%
(21 361/33 063) of the normal biopsies represent a normal postbiopsy embryo in case of a 1-cell or a 2-cell biopsy respectively.
A minority of 43.9% of the mosaic (A/N) post-biopsy embryos
[11 830/(11 634 + 11 830 + 3494)] is correctly represented by a 2cell (A/N) biopsy whereas a 1-cell biopsy cannot represent
mosaicism. We have seen above that the majority of mosaic
embryos displays limited mosaicism of which a signi®cant part is
presumed to return to normality or homogeneous abnormality at
least when the embryo is not subjected to a biopsy procedure. An
abnormal or mosaic biopsy reduces or even eliminates the limited
Model of embryo development
Table V. Theoretical numbers of normal and abnormal 1-cell biopsies and of normal, mosaic and abnormal 2-cell biopsies from 8-cell embryos in relation to
the cytogenetic condition of the 7/6-cell post-biopsy embryos
Condition of post-biopsy
embryo
No. of cells per 7/6-cell embryo
Results of 1-cell biopsy
Results of 2-cell biopsy
A
N
N
A
N+N
A/N
Normal
Mosaic A/N
0
1
2
3
4
5
6
1±6/5
7/6
7/6
0±7/6
7/6
6/5
5/4
4/3
3/2
2/1
1
6/5±1
0
0
7/6±0
21 361
3806
8144
1012
4390
333
476
18 161
17
±
39 539
544
2715
607
4390
554
1426
122
9814
20 816
11 787
42 961
21 361
3263
5817
578
1881
95
±
11 634
68
±
33 063
1 087
4654
868
5018
475
815
±
11 830
35
±
12 952
Mosaic A/A
Abnormal
All
A+A, A/A
±
388
173
1881
317
1019
104
3494
20 816
11 787
36 485
A/N and A/A stand for all possible combinations of mosaicism: A1/N, A1/A2/N, ¼ A1/A2/A3/A4/A5/A6/A7/N and A1/A2, A1/A2/A3, ¼ A1/A2/A3/A4/A5/A6/A7/
A8
The values have been calculated using the values of normal and homogeneous abnormal embryos from Table III, those of mosaic embryos from Figure 2 and
the probabilities for biopsy and concomitant post-biopsy embryo composition from the Figures 3 and 4.
mosaicism from the embryo but decreases its chance for transfer.
In contrast, a normal biopsy aggravates the mosaicism in the
embryo but increases its chance for transfer. This risk of
aggravation of mosaicism is greater in the case of a 2-cell than a
1-cell biopsy because more normal blastomeres are removed in the
former situation. This problem concerns as many as 9080 (3263 +
5817) embryos of which a 2-cell biopsy was taken and 11 950
(3806 + 8144) embryos in case of a 1-cell biopsy (see Table V).
Mosaic (A/N) 2-cell biopsies change the pre-biopsy embryos with
the limited mosaicisms A[1]/N[7] and A[2]/N[6] into the post-biopsy
embryos N[6] (1087 cases) and A[1]/N[5] (4654 cases) (Table V). A
proportion of 83% of these cases would show mosaicism of 1 or 2
lethal cells (see Mechanisms) and turn to normality. Theoretically,
4950 of the 5741 (1087 + 0.8334654) embryos would be
transferable to the prospective mother of which 4765
[(0.833(1087 + 4654)] would have been recognized with the
biopsy (96.3%). So, 48.5% of the mosaic biopsies with a lethal cell
(4765/0.83311 830) could be expected to represent a viable
embryo. In the absence of embryos with normal biopsy results, one
might decide to transfer embryos with biopsies displaying
mosaicism of a lethal cell. The missing of mosaic cases but also
the rejection of potentially good embryos have been considered as
serious problems for PGD-AS (Cohen, 2002).
The 1-cell biopsy protocol allows for the transfer of 47.9% of
the embryos showing normal biopsy results with a predictive value
of 54.0%: for the 2-cell biopsy protocol these values are 40.1 and
64.6% respectively. In a PGD population with a mix of 1- and 2cell biopsy procedures, a rate of transferable embryos between
40.1 and 47.9% can be expected. In the population of PGD for
social sexing with a majority of fertile couples but an increased
average maternal age of 36 years, a percentage of 41% has been
encountered (ESHRE PGD Consortium Steering Committee,
2002). The implementation of the considerations on mosaic
biopsies would improve the 2-cell biopsy protocol, in which case
the transfer of 33 063 embryos with normal biopsies plus the 9819
(0.83311 830) with mosaicism of a lethal cell in the biopsy could
be considered. These 42 882 out of 82 500 biopsies (52.0%) would
show a predictive value of 60.9% [(21 361 + 4765)/42 882] (see
Table V). On the one hand, the 2-cell biopsy shows a higher
transfer rate with a slightly higher predictive value than the 1-cell
biopsy. On the other hand, the 2-cell biopsy carries a higher risk of
aggravation of mosaicism and would theoretically display more
adverse effects of the biopsy compared to the 1-cell biopsy.
However, embryo development seems not to be compromised to a
greater extent by the removal of 2 blastomeres instead of 1 at the 8cell stage (Hardy et al., 1990; Liu et al., 1993; Van de Velde et al.,
2000). The removal of a quarter of the blastomeres at the 4- or 5cell stage embryo might retard further cleavage (Tarin et al.,
1992).
From the data in Table V, the theoretical false-negative and
false-positive rates can easily be calculated: 22.0% [(18 161 + 17)/
82 500] and 12.6% [(544 + 9814)/82 500] in case of a 1-cell
biopsy; 14.2% [(11 634 + 68 + 35)/82 500)] and 6.0% [(1087 + 388
+ 3494)/82 500)] in case of a 2-cell biopsy. In the literature, the
sum of false-negative and false-positive rates in PGD-AS has been
designated type 1 error (Munne et al., 1998). In PGD studies using
FISH for six or nine chromosomes (X, Y, 13, 16, 18, 21, in some
cases additionally 14, 15 and 22), Munne et al. (1998) established
false-negative and false-positive rates of 4 and 14% respectively
(type 1 error rate of 18%). For the same chromosomes (X, Y, 13,
16, 18, 21, in some cases additionally 15 and 22), Silber et al.
(2003) established rates of 11.8 and 7.8% (type 1 error rate of
19.6%). A potential bias in the calculations of these error rates is
the fact that embryos with normal biopsy results are likely to be
transferred to the prospective mother and withdrawn from further
con®rmational investigations. This leads to an underestimate of
the false-negative rate and hence of the type 1 error rate in PGDAS studies. Notwithstanding this limitation, the encountered
values of false-negative and false-positive rates associated with
the detection of the numerical abnormalities of a set of six to nine
chromosomes ®t well into our theoretical values. Different
abnormal ®ndings in biopsies and remaining embryos in
91
F.J.Los, D.Van Opstal and C.van den Berg
con®rmational studies are designated type 2 errors (Munne et al.,
1998). In our model, these errors are included in the correct
diagnoses (A, A/N and A/A), since no diagnosis of mosaicism can
be made at all in case of a 1-cell biopsy and not of multiple
mosaicism in case of a 2-cell biopsy. The majority of mosaic
embryos (62%) has been shown to contain >3 different cells/cell
lines.
From a theoretical point of view, the 8-cell stage seems not the
most suitable level for PGD(-AS) as shown in the Tables III, IV
and Figure 1; the lowest rate of normal embryos and the highest
rate of abnormal and mosaic embryos are present at this stage. The
post-biopsy 6/7-cell embryo turned out to have a different prospect
of development than the pre-biopsy 8-cell embryo in the case of
limited mosaicism. This leads to the paradoxical effect of an
inverse relation between the developmental prospects of these
embryos and their chances for transfer. We hope to have
contributed to the understanding of the fate of normal, abnormal
and mosaic embryos with our theoretical model.
Acknowledgements
We would like to thank F.C.O.Los and M.F.J.Los for their help in the
many calculations. We also thank Professor M.F.Niermeijer for his
support and helpful discussions and Mrs J.Du Parand for preparing the
manuscript.
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