Little is known about the growth mechanics of the developing mammalian diaphragm or the abnormalities that result in congenital diaphragmatic hernia. In particular, tissue and cell morphometrics and parameters of mitotic activity will be required to understand diaphragm morphogenesis. Treating pregnant rats and mice with the herbicide nitrofen can produce a posterior diaphragmatic defect reminiscent of that seen in human cases of CDH . To what extent this rodent model is germane to the human clinical anomaly is unknown. Recent analysis of the embryonic diaphragm in the nitrofen model has defined a posterior defect in the PPF that seems to be a natural antecedent for development of the adult defect (Fig. 6) [8,10].
Our goal here has been two-fold. First, we introduce computer simulation modeling as a means for studying normal and abnormal development of the diaphragm. In doing so, we apply a novel method combining experimental data and simulated objects – the "Roger Rabbit" method. Second, we investigate specific patterns of mitotic activity and active (short-range) cell migration in simulations of normal and altered development in the nitrofen CDH model.
Logic of simulations
We have sought to combine morphological data with simple postulates to model both normal development and the altered development of CDH. We have built our model in a stepwise fashion so that the effect of individual changes can be appreciated (Table 2). We have also limited our postulates to simple and reasonable mechanisms that are applied broadly to large, homogeneous cell populations, i.e. simple cell programs.
We begin with a homogeneous pattern of growth as a simulation "ground state." This pattern does not accurately reproduce either normal development or growth of the nitrofen-induced embryonic PPF defect into the large posterior defect of the older embryo and adult (Simulation I – Fig. 11). Evidence suggests that the mid-portion of each side of the evolving muscular diaphragm differentiates before those portions nearer the edges [8,17]. Comparable edge-based or edge-biased growth is an established pattern of mitotic activity in vertebrate embryogenesis [18,19]. We therefore institute an edge-growth pattern in which centrally located cells become post-mitotic (Simulation II – Fig. 12). In our model, this fails to generate the degree of circumferential extension noted in vivo. Adding a trophic effect of the body wall, whereby cells in proximity to the body wall tend to remain mitotically active, is a partial improvement (Simulation III – Fig. 13). If mitotically active non-edge cells (in essence, those cells affected by the body wall trophism) migrate toward the body wall as well, a greater degree of extension is produced (Simulation IV – Fig. 14). Similar patterns of "convergence-extension" are found extensively in early embryonic morphogenesis . Here, addition of this process generates a respectable normal diaphragm, but fails to reproduce the experimental CDH finding of a large posterior defect with a normal ipsilateral anterior diaphragm. The latter can be achieved if we postulate two different cell populations within the PPF, each with a slightly different (and clonally-derived) movement pattern (Simulation V – Fig. 15). Indeed, our attempts to achieve this anterior-posterior dichotomy without some intrinsic difference in the action of anterior and posterior progenitors have not been successful. Within the context of this simulation strategy, the combination of an enlarging posterior defect and a normal anterior diaphragm does not appear possible if anterior and posterior PPF progenitors are not either (1) intrinsically distinct populations, and/or (2) responding to different environmental signals.
Propagation of a tissue defect
Our model serves to highlight issues related to one generic component of morphogenesis – propagation of a hole or tissue defect. The defect in the early embryo PPF [8,10] seems a natural antecedent for the larger defect in the later embryo and adult. But defects do not grow of themselves; they represent the absence of surrounding tissue. As the surrounding tissue grows, the effect is to lessen and eliminate, rather than propagate, the defect. As an example, one can consider a torus (donut) of cells. As these cells divide, the natural result will be a closing of the central hole, eventually yielding a disc rather than a larger donut. To produce a larger donut (with a correspondingly larger hole) requires specific cellular interactions (Fig 16). Possible interactions include (i) active radial (centrifugal) cell migration, (ii) position-dependent cell death, and (iii) enlargement of an obstacle or boundary that forms or delineates the hole. In the simulations presented here, active migration is used. Programmed cell death has not been reported as a significant feature of diaphragm development. It has been suggested that in the rat nitrofen model, fetal liver growth within the evolving defect may contribute to enlarging the defect (the obstacle option) , but liver is found only occasionally in human CDH defects.
Of mice and men
The classic description of the location of the defect in human CDH is postero-lateral (Fig. 1) [1,4]. There is large variation in the size and extent of the defect and large defects may extend beyond the posterolateral region and appear to involve the entire posterior aspect of the hemi-thorax. However, typically there is a posteromedial rim of diaphragm (large in the case of small defects and small to grossly non-existent in the case of large defects). This rim of posterior diaphragm is most prominent medially and fades away laterally such that the defect itself abuts the posterolateral chest wall (Fig. 2). This can be seen most clearly in moderate size defects. Very large defects may appear to have almost no posteromedial rim and thus simply seem posterior (see footnote 7); and very small defects also occur, in which the defect is completely surrounded by diaphragm without abutting the chest wall .
There is also considerable variation in the size of the defect in the rodent nitrofen model and, as in the human, large defects may extend across the entire posterior hemi-thorax as well as anteriorly (Fig. 5) . However, the nitrofen-induced rodent defect has been described as postero-medial  (see footnote 8). This view is not without dissent. Indeed, many experienced investigators have described teratogen-induced defects [10,23], and similar defects generated by genetic  or nutritional  manipulation, as posterolateral (or, equivalently, as "dorsolateral").
The distinction between "posterolateral" and "posteromedial" is more than semantic to the extent that it reveals something of the embryology. Here, posterolateral is understood to describe human-type defects that generally abut the posterolateral body wall and that have a persistent posteromedial rim of diaphragm. The "morphogenic plan" that, when defective, yields such a posterolateral defect must include formation of the posteromedial rim with some degree of independence. This is not required in a plan that, when defective, yields a posteromedial defect (i.e. no posteromedial rim). Identification of this distinction should not be taken as neglect of the very real size variation that creates visual overlap at large sizes (after all, a very large medial defect will encroach laterally and a very large lateral defect will encroach medially). Published figures of rodent-type defects (Figs. 5, 17) generally do not fit the above description of posterolateral as defined in humans (Fig. 2). However, a detailed comparative analysis of the morphology of human and rodent-type defects currently is lacking, so the degree of overlap remains an open question.
The embryological origin of the human diaphragm is poorly understood . The classic multi-component theory is based solely on descriptive studies and may or may not withstand scrutiny with current methods (Fig. 3) [4-6].
In contrast, the rodent provides an opportunity to create a rich experimental embryology of mammalian diaphragm development. There is now an evolving data set related to the embryology of the rodent diaphragm that targets both normal and various abnormal forms [7-11,23-27]. Thus we use findings in the rodent as a basis for our simulations. We also make the tacit assumption that differences between the mouse and the rat will be small and interchange results between these species.
According to recent studies, the rodent muscular diaphragm is formed almost exclusively from the PPF [8,10]. This contrasts with the above multi-component view of human diaphragm development. Earlier workers had described the PPF as likely a more important contributor to the diaphragm in some non-human mammals than in man . It is not known whether experimental findings in the rodent indicate that the classic view of human diaphragm development is in error or whether an actual species difference exists.
The muscular diaphragm surrounds a non-muscular central tendon (Figs. 1, 4). If we consider observations in the rodent, then one feature of diaphragm morphogenesis is a circumferential extension of the PPF anteriorly along the lateral body wall. In order to generate this feature in our model (Figs. 14, 15), we programmed cells in close proximity to the body wall to remain mitotically active (a trophic effect) and to migrate toward the body wall (a tropic effect). However, if the anterolateral body wall does indeed contribute to the diaphragm in man, then this aspect of PPF extension may be unnecessary or more limited. Likewise, if in the human case a separate diaphragm component is derived from the dorsal mesentery and posteromedial body wall, then the observed posterior rim in human CDH may represent the remnant of this component, now isolated from the remainder of the diaphragm by the CDH defect (compare human CDH in Fig. 2 to rodent CDH in Fig. 5). Although differences between the human and rodent defects may reflect different pathways of pathogenesis, an alternative is that the same pathogenesis (e.g. the PPF defect previously described [10,11]) is superimposed on a slightly different underlying morphogenic plan. We find this possibility intriguing – it would link the distinct schemes for diaphragm development (multi-component in humans vs. PPF-dominated in rodents) with the disparate CDH findings (posterolateral defect with posterior rim in humans vs. posteromedial defect in rodents). Further analysis along these lines awaits a more detailed experimental analysis of human diaphragm development.
The study of morphogenesis and pattern formation has a rich history of computer simulation modeling. Simulated tissue may be modeled as a homogeneous field in diffusion and reaction-diffusion models [28-31]. Tissues may also be partitioned into mathematically useful, but not biologically defined, elements as in finite-element models and certain lattice and cellular automata models [32-35]. Although these approaches are mathematically powerful, it may be difficult to translate experimental findings into appropriate simulation parameters. Alternatively, a tissue may be partitioned into elements designed to represent actual biological cells. These latter models allow experimental findings to be more readily translated into simulations. For example, the experimental finding that a cell in a given location divides with a certain orientation is smoothly incorporated into a model that "understands" a physically defined cell, but would require some recasting to be inserted into a finite-element model and may not have a clear counterpart in a reaction-diffusion model. Cell-based models include those in which a rigid "checkerboard" [36,37] or less constrained polygonal [38-40] decomposition is used. These models usually lack the concept of extracellular space and may require ad hoc procedures to simulate cell division and intermingling of cells. The Nudge++™ model and its brethren [41,42] treat cells as independent entities. This addresses the experiment-to-simulation translation issue and readily incorporates a full range of cell "behaviors." Although different modeling strategies may be more-or-less useful in different settings, independent cell-based systems are very plastic and well suited for studying mammalian morphogenesis.
When computer modeling is used to simulate morphogenesis of a tissue or organ, we generally model the tissue in isolation from the surrounding embryo. Although this may be more-or-less valid when naturally bounded organs are modeled , we may miss important constraints and effects if we impose artificial boundaries or none at all. We have therefore developed the "Roger Rabbit" methodology for fusing experimental data with simulation modeling. This allows us to model certain features of the system (here, cells) in the context of other, non-modeled features (here, boundaries). In a clinical setting not related to morphogenesis, a similar strategy has been used to combine non-invasive imaging with finite-element modeling [43,44].
Computer simulation modeling becomes more valuable as more data are accumulated. With limited extant data on the morphogenesis of the mammalian diaphragm, we are so limited (or rather, so unconstrained in possibilities) that it is difficult to select relevant modeling strategies and parameters. Put otherwise, certainly we can build a diaphragm in silico, but relevance to the diaphragm in vivo depends on our ability to link the two through experimental data. Current morphometric data on the developing mouse diaphragm include gross tissue outlines in normal animals and animals with diaphragm defects after a variety of experimental manipulations [24,27,45,46].
We limit our simulations to the time-slice between E11.5 and E13 in the mouse. These stages are chosen to bracket the events leading from the presumed anlagen (PPF)  to a morphologically defined (but still immature) diaphragm. We do not examine initial creation of the normal PPF or the defective PPF seen in the nitrofen model.
We have sought to model the muscular diaphragm because most of the data relate to this component. Recent studies have suggested that there may be an important, independent, non-muscular (mesenchymal) component . Indeed, the CDH defect may be primary to this non-muscular component, with the muscular diaphragm following in a more passive role. Of course, we would prefer to model the determining cell population(s) but detailed information concerning the nature of the non-muscular component and its relationship to the muscular component currently is limited. Our simulations can be "redefined" to model this other component if further research focuses attention in that direction.
The topography, orientation and timing of mitotic activity within the developing diaphragm are generally unknown, although the more internal areas appear to differentiate before those nearer the edges . We have therefore selected mundane cell division patterns: homogeneous and edge-based topography are compared, cell division orientation remains random, and cell cycle times are homogeneous throughout the tissue but increase slowly over time. We have not added cell death as a factor since apoptosis has not been described in the developing diaphragm. Although cell death has been described in the nitrofen model , it probably involves early myogenic precursors and may not be relevant to the time-space window of our simulations. Myogenic precursors, having migrated to the brachial plexus region from the cervical somites, then appear to migrate into the PPF . Active cell migration within the developing diaphragm has not been described. We have therefore been cautious in postulating only limited, short-range movements occurring in proximity to the body wall and suggestive of the well-established process of convergence-extension .
Limitations imposed by the lack of experimental data beg the question of what type of data would be most useful and how simulation modeling can suggest avenues of experimental investigation. Embryogenesis is a period of profound growth. We believe that one of the shortcomings in understanding and modeling morphogenesis is an under-appreciation of the fact that patterning occurs not on a static field, but rather on a field undergoing tumultuous growth and remodeling. We have sought to address this in our simulations – the very boundaries of the simulations (the body wall and dorsal mesentery) change over time. In order to understand growth of the diaphragm, details of tissue morphometrics and the topography of mitotic activity over time must be determined; standard histological and immunohistochemical methods should suffice. The current simulations suggest an edge-type pattern of growth – experimental verification would strengthen the current model, non-verification would suggest a different set of simulations. Edge growth also is associated with a specific clonal pattern  that can be investigated in mammalian muscle tissue with current methods . Such analysis would also be expected to shed light on the possible role of convergence-extension .
We are acutely aware of the limitations of our highly schematized model in representing the subtle complexity of mammalian morphogenesis, and have treated these issues in some detail elsewhere . One particular issue is that of modeling a three-dimensional (3D) structure in two dimensions (2D). Although Nudge++™ is capable of 3D modeling, we favor first trying to construct a 2D model of any system. Two-dimensional simulations generally are easier to construct from experimental data, are computationally less complex, and are easier to understand in terms of output. This does require that the biological system be amenable to this simplification. For example, the liver might be a structure for which this is not appropriate. As essentially a 2D sheet embedded in three-space, the diaphragm seems suitable for this approach. However, some caveats must be maintained. Although the mature diaphragm may be viewed as a sheet, it is multi-cellular in thickness and more than one type of cell forms the structure. As our knowledge of the system increases, it may become evident that including this multi-cellular thickness is essential for an adequate model. Also, we have derived the 2D outline of the PPF used in our model from sections of the 3D structure. Defects in the PPF in the nitrofen model have now been defined in 3D (Fig. 6) . As our knowledge of diaphragm development increases, it may become necessary to incorporate this dimensionality into the model as well.
The above uncertainties notwithstanding, computer simulations can allow us to understand morphogenesis of the normal mammalian diaphragm and the events that underlie the abnormal development of CDH and other anomalies. In particular, they can act as proving grounds for various theories of development and as a means of understanding the results of the complex interactions that underlie mammalian development.