468
8 Morphogenesis
indicate that growth of the hemispheres depends on both chemical morphogens
and eCSF pressure. The following 3D model integrates biochemical effects with
mechanical growth laws (Garcia et al. 2019).
The model includes the telencephalon and hypothalamus, with initial geometry
approximating stage HH17 morphology (Fig. 8.54a). A recently measured eCSF
pressure of 15 Pa is applied to the inner surface, and the outer surface of the
hypothalamus is constrained by an elastic foundation representing external tissue.
Two morphogens known to affect growth in the forebrain are fibroblast growth
factor FGF8 and bone morphogenetic protein BMP4, which stimulate and inhibit
cell proliferation, respectively (Ohkubo et al. 2002). These chemicals are secreted
at two different locations: FGF8 at the anterior neural ridge and BMP4 at the roof
plate (Fig. 8.54a). Both morphogens diffuse through the BT with concentrations that
decay with distance from their sources. Approximate distributions are specified in
the model (Fig. 8.54a, right).
Geometric measurements show that the brain tube grows in both tangential and
radial directions, but only tangential growth depends on pressure (Garcia et al.
2019). This behavior is captured through the chemomechanical growth laws
˙
G = γ (a 0 + a σ ¯
σ )G
˙
G r = γ b 0 G r ,
(8.56)
where G = G φ = G θ , ¯
σ is given by Eq. (8.55), and a 0 and b 0 are constants.
The coefficients γ and a σ are assumed to depend on morphogens according to the
relations
γ = 1 − C BMP
a σ = α(1 + βC FGF ),
(8.57)
where 0 ≤ C BMP , C FGF ≤ 1 are normalized concentrations. These equations are
consistent with BMP4 and FGF8 inhibiting and promoting growth, respectively.
They also imply that no growth occurs in the roof plate, where C BMP = 1, in
agreement with findings that cell proliferation is greatly reduced in that region
(Gupta and Sen 2015; Garcia et al. 2019).
As the model grows, wall stress increases most in regions with the greatest radii
of curvature (by Laplace’s law), leading to increased growth rate and a further
increase in radius at these locations. Because the roof plate does not grow and stressinduced growth in the hypothalamus is restricted by external tissues, i.e., the elastic
foundation, this positive feedback produces the characteristic heart-shaped structure
of the forebrain at HH21 (Fig. 8.54b, right).
The realistic morphology given by the model offers tentative support for the
postulated growth law (8.56) 1 , which produces differential growth in response to
tangential stress. If growth is assumed to depend on eCSF pressure (or radial stress),
then the telencephalon and hypothalamus would grow uniformly, and the model
8 Morphogenesis
indicate that growth of the hemispheres depends on both chemical morphogens
and eCSF pressure. The following 3D model integrates biochemical effects with
mechanical growth laws (Garcia et al. 2019).
The model includes the telencephalon and hypothalamus, with initial geometry
approximating stage HH17 morphology (Fig. 8.54a). A recently measured eCSF
pressure of 15 Pa is applied to the inner surface, and the outer surface of the
hypothalamus is constrained by an elastic foundation representing external tissue.
Two morphogens known to affect growth in the forebrain are fibroblast growth
factor FGF8 and bone morphogenetic protein BMP4, which stimulate and inhibit
cell proliferation, respectively (Ohkubo et al. 2002). These chemicals are secreted
at two different locations: FGF8 at the anterior neural ridge and BMP4 at the roof
plate (Fig. 8.54a). Both morphogens diffuse through the BT with concentrations that
decay with distance from their sources. Approximate distributions are specified in
the model (Fig. 8.54a, right).
Geometric measurements show that the brain tube grows in both tangential and
radial directions, but only tangential growth depends on pressure (Garcia et al.
2019). This behavior is captured through the chemomechanical growth laws
˙
G = γ (a 0 + a σ ¯
σ )G
˙
G r = γ b 0 G r ,
(8.56)
where G = G φ = G θ , ¯
σ is given by Eq. (8.55), and a 0 and b 0 are constants.
The coefficients γ and a σ are assumed to depend on morphogens according to the
relations
γ = 1 − C BMP
a σ = α(1 + βC FGF ),
(8.57)
where 0 ≤ C BMP , C FGF ≤ 1 are normalized concentrations. These equations are
consistent with BMP4 and FGF8 inhibiting and promoting growth, respectively.
They also imply that no growth occurs in the roof plate, where C BMP = 1, in
agreement with findings that cell proliferation is greatly reduced in that region
(Gupta and Sen 2015; Garcia et al. 2019).
As the model grows, wall stress increases most in regions with the greatest radii
of curvature (by Laplace’s law), leading to increased growth rate and a further
increase in radius at these locations. Because the roof plate does not grow and stressinduced growth in the hypothalamus is restricted by external tissues, i.e., the elastic
foundation, this positive feedback produces the characteristic heart-shaped structure
of the forebrain at HH21 (Fig. 8.54b, right).
The realistic morphology given by the model offers tentative support for the
postulated growth law (8.56) 1 , which produces differential growth in response to
tangential stress. If growth is assumed to depend on eCSF pressure (or radial stress),
then the telencephalon and hypothalamus would grow uniformly, and the model