(312b) Modeling the Superovulation Stage in in-Vitro Fertilization (IVF)

Abstract

               In-vitro fertilization (IVF) is the most common
technique in assisted reproductive technology and in most cases the last resort
for infertility treatment. It has four basic stages: superovulation,
egg retrieval, insemination/fertilization and embryo transfer. Superovulation is a drug induced method to enable multiple
ovulation per menstrual cycle. The success of IVF majorly depends upon
successful superovulation, defined by the number and
similar quality of eggs retrieved in a cycle.

               The model is adapted from the theory of batch
crystallization. The aim of crystallization is to get maximum crystals of similar
size and purity, while superovulation aims at eggs of
similar quality and size. The rate of crystallization and superovulation
are both dependent on the process conditions and varies with time. Thus, model
formulation for multiple ovulation is on parallel lines to crystal formation in
a batch process and is modeled as such. The kinetics of follicle growth is
modeled as a function of injected hormones and the follicle properties are
represented in terms of the moments. Hence, modeling of this stage in terms of
distribution of eggs (oocytes) obtained per cycle
involving the chemical interactions of drugs used and the conditions imposed on
the patient during the process provides a basis for predicting the possible
outcome.  The results from the model prediction
were verified with the known data from Jijamata
Hospital Nanded, India. The predictions were found to
be in well matched with the actual observations.

               Thus, a phenomenon currently based on trial and error
will get a strong base in terms of a predictive model. It will help the patient
to decide whether to undergo superovulation or start
the IVF from donor eggs, which in turn would save the patient from financial
loss as well as emotional distress.

1. Introduction

               Around 80 million people in the
world are suffering from infertility issues. The rate of fertility is
constantly declining in the developed nations due to late marriages, postponed
childbearing and primary infertility. On the contrary, in the developing world
the reasons for infertility involve prevalence of sexually transmitted
diseases, infections which increase the rate of secondary infertility.
Childlessness is often stigmatized and leads to profound social suffering for women
in the developing nations (de Melo Martin, 1998).

1.1. In-vitro fertilization:

               It is a process by which oocytes or egg cells are fertilized by a sperm outside the
body in a laboratory simulating similar conditions in the body and then the
fertilized eggs are implanted back in the uterus for full term completion of
pregnancy.

Four stages in IVF:

i. Superovulation:
It is method to retrieve multiple eggs using drug induced stimulation. In
normal female body only one egg is ovulated per menstrual cycle, but with the
use of fertility drugs and hormones, more number of eggs can be ovulated per
cycle.

ii. Egg collection (retrieval):
On the maturation of the multiple eggs produced in the previous stage, the eggs
are retrieved through special techniques like ultrasonically guided transvaginal oocyte retrieval.

iii. In vitro fertilization (inseminaton/fertilization): Fertilization is done in
the incubator using the retrieved oocytes and sperms.
The conditions are maintained so as to mimic the invivo
environment.

iv. Embryo transfer: The
fertilized embryos are implanted into the uterus via a non-surgical technique
using ultrasound guidance.

               The
major cost of IVF is associated with the superovulation
stage where expensive drugs are used and almost daily monitoring is required.
Success of this stage in terms of number and quality of eggs affects the
outcome of IVF. In this work, we concentrated on modeling this stage and the
approach is presented in the next section.

1.2. Superovulation:

In
this work, we follow the analogy between batch crystallization and superovulation to model the process.

Analogy between Superovulation
and Batch crystallization:

               The moment model for follicle
number and size is adapted from the concept of batch crystallization (Q. Hu. et. al., 2005) based on the analogy between batch crystallization
and superovulation presented in Table 1.

Table
1: Analogy between batch crystallization and IVF superovulation
stage

               The superovulation
follicle growth model in general resembles greatly to the growth of seeded
batch crystals. Thus, the moment model for both the processes remain the same
the growth term which is a function of process variables like temperature and supersaturation in batch seeded crystallization will become
a function of medicinal dosage in case of superovulation
process.

2. Model details

               Due to ovarian stimulation using
externally injected hormones the number of follicles activated to enter into
the ovulation stage are more in number as compared to a single follicle in a
normal menstrual cycle. From the current data on successful superovulation
for patient 1, organized in Table 2; it can be observed that during FSH dosage
regime, as the time progresses the size of the eggs increase.

Table
2: Variation of Follicle size (diameter) with time and FSH dose

Size range (mm) dia Sr. No	Days	Day 1	Day 2	Day 5	Day 7	Day 9
1.	0-4	15	8	6	0	0
2.	4-8	3	6	4	2	0
3.	8-12	0	4	10	14	4
4.	12-16	0	0	0	2	11
5.	16-20	0	0	0	0	3
6.	20-24	0	0	0	0	0
	FSH dose	0	300	300	300	225

2.1. Model Assumptions:

               The rate expression for follicle
growth is dependent on FSH administered. Thus, we can write the growth term as;

G=kCfshα
                                                     (1)

               Assuming moment model, we
consider only the first seven moments; zeroth moment
corresponding to follicle number, the first moment corresponding to follicle
size and the other 5 moments. 1^st to 6^th moments are
being used since they help in recovering the size distributions more precisely
as against lower number of moments.

2.2. Model equations (Q. Hu.
et. al.,
2005):

μ0=constant
                                               (2)

dμ1dt=Gtμ0t           
                                (3)

dμ2dt=2Gtμ1t        
                                 (4)

dμ3dt=3Gtμ2t        
                                 (5)

dμ4dt=4Gtμ3t        
                                 (6)

dμ5dt=5Gtμ4t        
                                 (7)

dμ6dt=6Gtμ5t        
                                 (8)

               Conversion of the data available
on follicle number and size to moment using the expression given in literature
by Flood, 2002:

μi=nir,trinDri     
                          (9)

   Here, µ_i = i^th moment

               n_i(r,t) = number of follicles in bin of
mean radius 'r' at time 't'.

               r_i = mean radius of i^th bin

               Δr = range of radii variation in each bin

3. Results:

               We integrate the equations 2-8
for predicting the kinetic constants in the follicle growth expression. Later
we use non-linear optimization algorithm to predict the values of these kinetic
constants along with the integration constants obtained after integrating the
set of moment equations. In real practice, the model will be calibrated with
the first two days of data and then used for prediction of the complete cycle.

3.1. Model Validation:

               The
current moment model predicts the moment values, however our final output
desired is the follicle size distribution, thus in model validation the
approach to obtain follicle size distribution from moment values are shown. The
method is adapted from the literature by Flood 2002; where he shows the method
to recover particle size distribution from moments in batch crystallization. Using
the model predicted moment values we evaluate n(r,t)
and compare with the actual data to check the model accuracy. We
plot the follicle size distribution for four patients for various days. The
experimental size distribution is shown by symbols while the continuous curve
shows the model predicted values after using the inversion method. 

4.
Conclusion:

The moment model developed for IVF superovulation predicts the follicle size distribution
which is in well agreement with the actual size distribution seen in the IVF
cycle data.  The model can be used to
predict the outcome. This will reduce the almost daily requirement of testing.
The model can also provide a basis for predicting the optimum dosage for the
desired outcome from the superovulation stage. The
model used here is a very basic model and the complexities present in the
patient are not considered. Later, we aim to include these complexities and
model the system uncertainties, using more data for analysis, modeling and
validation.

Fig 1. Follicle size
distribution  for four patients

References

de Melo-Martin, I., 1998. "Ethics and
Uncertainty: In Vitro Fertilization and Risks to Women's Health" Risk:
Health, Safety & Environment 201.

Flood, A. E., 2002. "Thoughts on recovering
particle size distributions from the moment form of the population
balance." Dev. Chem. Eng. Mineral
Process, Vol. 10, No. 5/6, pp. 501-519.

Q. Hu, S. Rohani, A. Jutan, 2005. ?Modelling and
optimization of seeded batch crystallizers? Computers and Chemical Engg. Vol. 29, pp. 911-918.