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WIREs Syst Biol Med
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Mathematical modeling of the female reproductive system: from oocyte to delivery

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From ovulation to delivery, and through the menstrual cycle, the female reproductive system undergoes many dynamic changes to provide an optimal environment for the embryo to implant, and to develop successfully. It is difficult ethically and practically to observe the system over the timescales involved in growth and development (often hours to days). Even in carefully monitored conditions clinicians and biologists can only see snapshots of the development process. Mathematical models are emerging as a key means to supplement our knowledge of the reproductive process, and to tease apart complexity in the reproductive system. These models have been used successfully to test existing hypotheses regarding the mechanisms of female infertility and pathological fetal development, and also to provide new experimentally testable hypotheses regarding the process of development. This new knowledge has allowed for improvements in assisted reproductive technologies and is moving toward translation to clinical practice via multiscale assessments of the dynamics of ovulation, development in pregnancy, and the timing and mechanics of delivery. WIREs Syst Biol Med 2017, 9:e1353. doi: 10.1002/wsbm.1353

A schematic diagram of the structural, functional, and hormonal changes that occur through the menstrual cycle. During menses, the endometrial lining of the uterus is shed. Ovarian follicles develop from a stock of resting (primordial) follicles. The oocyte matures and companion cells (granulosa) proliferate to modulate the maturing oocyte's environment. During the proliferative phase, the uterine endometrium proliferates and becomes increasingly vascularized, with enlarged glandular structures, ovarian follicles continue to mature and fluid filled antrums enlarge. During this phase, a dominant follicle emerges. Following a hormonal surge, ovulation of the dominant follicle occurs approximately mid cycle, nondominant follicles enter atresia. The oocyte and its surrounding cells are transported through the fallopian tubes to the primed uterus in the secretory phase. A corpus luteum that forms at the site of the ovulated follicle secretes hormones that signal the uterine endometrium to undergo secretory differentiation. If pregnancy occurs, the corpus luteum is retained and hormone levels are elevated. If not it regresses, and the cycle begins again.
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The propagation of a solitary wave initiated at the fundus in an anatomical model of the uterus. This model illustrates one of two classes of uterine electrophysiology models, with excitation modeled using the FitzHugh‐Nagumu model. The same wave at three different time points is shown with white representing excited tissue and blue representing recovered tissue. (Reprinted with permission from Ref . Copyright 2011)
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(a) Transmission line and (b) geometrically accurate representations of the uterine vasculature. Transmission line models represent a network of vessels as 1D tubes characterized by their resistance (R), inductance (I), and capacitance (C) and use these data to characterize the impedance (Z) of the system. 3D fluid dynamics models are able to capture more realistic flow profiles within an individual vessel but are typically restricted to study of a small number of vessels. Panel (b) shows the main uterine artery (Uta) and a single branch from that artery with observation points (CoA and CoE), with different inlet characteristics (labeled b, c, d). (Reprinted with permission from: (a) Ref . Copyright 2009; (b) Ref . Copyright 2008)
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Typical model structure in three major classes of folliculogenesis model. (a) Modeling the population of follicles, where an initial large store of follicles is depleted by recruitment into maturation stages (at defined rates m1,…,mN), and subsequent follicle “death” (at rates d1,…,dN ). (b) Models based on a population of models acting under hormonal control, with follicle maturation based on local levels of hormones (LH and FSH) which in turn depend of follicle excreted oestradiol. (c) Models of follicular cell populations, where cells proliferate, differentiate, and enter apoptosis at defined rates. Each class of model was designed to answer specific questions regarding follicular population, but approaches are beginning to be merged as a drive toward multiscale modeling emerges.
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Models of Systems Properties and Processes > Mechanistic Models
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Jens Nielsen

Jens Nielsen
is a Professor in the Department of Biology and Biological Engineering at Chalmers University of Technology in Göteborg, Sweden. His research focus is on systems biology of metabolism. The yeast Saccharomyces cerevisiae is the lab’s key organism for experimental research, but they also work with Aspergilli oryzae.

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