Joubert syndrome (JS) is a complex medical condition characterized by a pathognomonic midbrain-hindbrain malformation visible on brain imaging, which is known as the “molar tooth sign” (MTS). The presence of the MTS in the brain is the defining diagnostic criterion for JS. Individuals with JS commonly exhibit a developmental delay, hypotonia, and abnormal eye movements. In addition, neonatal breathing dysregulation is observed in about half of the cases. Midline brain defects associated with JS can lead to pituitary hormone abnormalities, thereby manifesting as multiple pituitary insufficiencies in the neonatal period, such as hypoglycemia and, in male patients, a micropenis with undescended testes. Although JS is a well-researched genetic condition, there is minimal information on the endocrinological aspects of JS. This manuscript aims to emphasize the spectrum of endocrinologic findings in JS through the retrospective evaluation of four cases characterized by combined pituitary dysfunctions, including secondary hypothyroidism, growth hormone deficiency, and panhypopituitarism. Highlighting these treatable aspects of JS is crucial, as continuous endocrinological monitoring can positively impact a patient's well-being, particularly in managing secondary adrenal and thyroid insufficiencies.
Citation: Elżbieta Marczak, Maria Szarras-Czapnik, Małgorzata Wójcik, Agata Zygmunt-Górska, Jerzy Starzyk, Karolina Czyżowska, Anna Szymańska, Katarzyna Gołąb-Jenerał, Agnieszka Zachurzok, Elżbieta Moszczyńska. Hypopituitarism—A rare manifestation in Joubert syndrome: about 4 cases[J]. AIMS Medical Science, 2024, 11(3): 318-329. doi: 10.3934/medsci.2024022
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Joubert syndrome (JS) is a complex medical condition characterized by a pathognomonic midbrain-hindbrain malformation visible on brain imaging, which is known as the “molar tooth sign” (MTS). The presence of the MTS in the brain is the defining diagnostic criterion for JS. Individuals with JS commonly exhibit a developmental delay, hypotonia, and abnormal eye movements. In addition, neonatal breathing dysregulation is observed in about half of the cases. Midline brain defects associated with JS can lead to pituitary hormone abnormalities, thereby manifesting as multiple pituitary insufficiencies in the neonatal period, such as hypoglycemia and, in male patients, a micropenis with undescended testes. Although JS is a well-researched genetic condition, there is minimal information on the endocrinological aspects of JS. This manuscript aims to emphasize the spectrum of endocrinologic findings in JS through the retrospective evaluation of four cases characterized by combined pituitary dysfunctions, including secondary hypothyroidism, growth hormone deficiency, and panhypopituitarism. Highlighting these treatable aspects of JS is crucial, as continuous endocrinological monitoring can positively impact a patient's well-being, particularly in managing secondary adrenal and thyroid insufficiencies.
Adrenocorticotropic hormone;
Central adrenal insufficiency;
Continuous positive airway pressure;
Dehydroepiandrosterone-sulfate;
Follicle stimulating hormone;
Free triiodothyronine;
Free thyroxine;
Gas chromatography–mass spectrometry;
Growth hormone deficiency;
Insulin-like growth factor 1;
Insulin-like growth factor binding protein 3;
Intramuscular injection;
Joubert syndrome;
Luteinizing hormone;
Magnetic resonance imaging;
Mass spectrometry;
Molar tooth sign;
Not applicable;
Pituitary stalk interruption syndrome;
Recombinant human growth hormone;
Testosterone enanthate;
Thyroid stimulating hormone;
Thyroid hormones
The definition of impulsive semi-dynamical system and its properties including the limit sets of orbits have been investigated [1,9]. The generalized planar impulsive dynamical semi-dynamical system can be described as follows
{dxdt=P(x,y),dydt=Q(x,y),(x,y)∉M,△x=a(x,y),△y=b(x,y),(x,y)∈M, | (1) |
where
I(z)=z+=(x+,y+)∈R2, x+=x+a(x,y), y+=y+b(x,y) |
and
Let
C+(z)={Π(z,t)|t∈R+} |
is called the positive orbit of
M+(z)=C+(z)∩M−{z}. |
Based on above notations, the definition of impulsive semi-dynamical system is defined as follows [1,9,23].
Definition 1.1. An planar impulsive semi-dynamic system
F(z,(0,ϵz))∩M=∅ and Π(z,(0,ϵz))∩M=∅. |
Definition 1.2. Let
1.
2. for each
It is clear that
Definition 1.3. Let
Denote the points of discontinuity of
Theorem 1.4. Let
In 2004 [2], the author pointed out some errors on Theorem 1.4, that is, it need not be continuous under the assumptions. And the main aspect concerned in the paper [2] is the continuality of
In the following we will provide an example to show this Theorem is not true for some special cases. Considering the following model with state-dependent feedback control
{dx(t)dt=ax(t)[1−x(t)K]−βx(t)y(t)1+ωx(t),dy(t)dt=ηβx(t)y(t)1+ωx(t)−δy(t),}x<ET,x(t+)=(1−θ)x(t),y(t+)=y(t)+τ,}x=ET. | (2) |
where
Define four curves as follows
L0:x=δηβ−δω; L1:y=rβ[1−xK](1+ωx); |
L2:x=ET; and L3:x=(1−θ)ET. |
The intersection points of two lines
yET=rβ[1−ETK](1+ωET), yθET=rβ[1−(1−θ)ETK](1+ω(1−θ)ET). |
Define the open set in
Ω={(x,y)|x>0,y>0,x<ET}⊂R2+={(x,y)|x≥0,y≥0}. | (3) |
In the following we assume that model (2) without impulsive effects exists an unstable focus
E∗=(xe,ye)=(δηβ−δω,rη(Kηβ−Kδω−δ)K(ηβ−δω)2), |
which means that model (2) without impulsive effects has a unique stable limit cycle (denoted by
In the following we show that model (2) defines an impulsive semi-dynamical system. From a biological point of view, we focus on the space
Further, we define the section
y+k+1=P(y+k)+τ=y(t1,t0,(1−θ)ET,y+k)+τ≐PM(y+k), and Φ(y+k)=t1. | (4) |
Now define the impulsive set
M={(x,y)| x=ET,0≤y≤YM}, | (5) |
which is a closed subset of
N=I(M)={(x+,y+)∈Ω| x+=(1−θ)ET,τ≤y+≤P(yθET)+τ}. | (6) |
Therefore,
According to the Definition 1.3 and topological structure of orbits of model (2) without impulsive effects, it is easy to see that
However, this is not true for case (C) shown in Fig. 2(C). In fact, for case (C) there exists a trajectory (denoted by
If we fixed all the parameter values as those shown in Fig. 3, then we can see that the continuities of the Poincaré map and the function
Theorem 2.1. Let
Note that the transversality condition in Theorem 2.1 may exclude the case (B) in Fig. 2(B). In fact, based on our example we can conclude that the function
Recently, impulsive semi-dynamical systems or state dependent feedback control systems arise from many important applications in life sciences including biological resource management programmes and chemostat cultures [5,6,10,12,17,18,19,20,21,22,24], diabetes mellitus and tumor control [8,13], vaccination strategies and epidemiological control [14,15], and neuroscience [3,4,7]. In those fields, the threshold policies such as
The above state-dependent feedback control strategies can be defined in broad terms in real biological problems, which are usually modeled by the impulsive semi-dynamical systems. The continuity of the function
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