Measure-based approach to mesoscopic modeling of optimal transportation networks

We propose a mesoscopic modeling framework for optimal transportation networks with biological applications. The network is described in terms of a joint probability measure on the phase space of tensor-valued conductivity and position in physical space. The energy expenditure of the network is given by a functional consisting of a pumping (kinetic) and metabolic power-law term, constrained by a Poisson equation accounting for local mass conservation. We establish convexity and lower semicontinuity of the functional on approriate sets. We then derive its gradient flow with respect to the 2-Wasserstein topology on the space of probability measures, which leads to a transport equation, coupled to the Poisson equation. To lessen the mathematical complexity of the problem, we derive a reduced Wasserstein gradient flow, taken with respect to the tensor-valued conductivity variable only. We then construct equilibrium measures of the resulting PDE system. Finally, we derive the gradient flow of the constrained energy functional with respect to the Fisher-Rao (or Hellinger-Kakutani) metric, which gives a reaction-type PDE. We calculate its equilibrium states, represented by measures concentrated on a hypersurface in the phase space

Self-regulated biological transportation structures with general entropy dissipations, part I: the 1D case

We study self-regulating processes modeling biological transportation networks as presented in \cite{portaro2023}. In particular, we focus on the 1D setting for Dirichlet and Neumann boundary conditions. We prove an existence and uniqueness result under the assumption of positivity of the diffusivity $D$. We explore systematically various scenarios and gain insights into the behavior of $D$ and its impact on the studied system. This involves analyzing the system with a signed measure distribution of sources and sinks. Finally, we perform several numerical tests in which the solution $D$ touches zero, confirming the previous hints of local existence in particular cases.Comment: 22 pages, 8 figure

Emergence of biological transportation networks as a self-regulated process

We study self-regulating processes modeling biological transportation networks. Firstly, we write the formal $L^2$-gradient flow for the symmetric tensor valued diffusivity $D$ of a broad class of entropy dissipations associated with a purely diffusive model. The introduction of a prescribed electric potential leads to the Fokker-Planck equation, for whose entropy dissipations we also investigate the formal $L^2$-gradient flow. We derive an integral formula for the second variation of the dissipation functional, proving convexity (in dependence of diffusivity tensor) for a quadratic entropy density modeling Joule heating. Finally, we couple in the Poisson equation for the electric potential obtaining the Poisson-Nernst-Planck system. The formal gradient flow of the associated entropy loss functional is derived, giving an evolution equation for $D$ coupled with two auxiliary elliptic PDEs.Comment: 16 page

C9ORF72 hexanucleotide repeat expansions in the Italian sporadic ALS population.

It has been recently reported that a large proportion of patients with familial amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD) are associated with a hexanucleotide (GGGGCC) repeat expansion in the first intron of C9ORF72. We have assessed 1757 Italian sporadic ALS cases, 133 from Sardinia, 101 from Sicily, and 1523 from mainland Italy. Sixty (3.7%) of 1624 mainland Italians and Sicilians and 9 (6.8%) of the 133 Sardinian sporadic ALS cases carried the pathogenic repeat expansion. None of the 619 regionally matched control samples (1238 chromosomes) carried the expansion. Twenty-five cases (36.2%) had behavioral FTD in addition to ALS. FTD or unspecified dementia was also detected in 19 pedigrees (27.5%) in first-degree relatives of ALS patients. Cases carrying the C9ORF72 hexanucleotide expansion survived 1 year less than cases who did not carry this mutation. In conclusion, we found that C9ORF72 hexanucleotide repeat expansions represents a sizeable proportion of apparent sporadic ALS in the Italian and Sardinian population, representing by far the most common mutation in Italy and the second most common in Sardinia

Genetic counselling in ALS: facts, uncertainties and clinical suggestions

The clinical approach to patients with amyotrophic lateral sclerosis (ALS) has been largely modified by the identification of novel genes, the detection of gene mutations in apparently sporadic patients, and the discovery of the strict genetic and clinical relation between ALS and frontotemporal dementia (FTD). As a consequence, clinicians are increasingly facing the dilemma on how to handle genetic counselling and testing both for ALS patients and their relatives. On the basis of existing literature on genetics of ALS and of other late-onset life-threatening disorders, we propose clinical suggestions to enable neurologists to provide optimal clinical and genetic counselling to patients and families. Genetic testing should be offered to ALS patients who have a first-degree or second-degree relative with ALS, FTD or both, and should be discussed with, but not offered to, all other ALS patients, with special emphasis on its major uncertainties. Presently, genetic testing should not be proposed to asymptomatic at-risk subjects, unless they request it or are enrolled in research programmes. Genetic counselling in ALS should take into account the uncertainties about the pathogenicity and penetrance of some genetic mutations; the possible presence of mutations of different genes in the same individual; the poor genotypic/phenotypic correlation in most ALS genes; and the phenotypic pleiotropy of some genes. Though psychological, social and ethical implications of genetic testing are still relatively unexplored in ALS, we recommend multidisciplinary counselling that addresses all relevant issues, including disclosure of tests results to family members and the risk for genetic discrimination

C9ORF72 hexanucleotide repeat expansions in the Italian sporadic ALS population

It has been recently reported that a large proportion of patients with familial amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD) are associated with a hexanucleotide (GGGGCC) repeat expansion in the first intron of . C9ORF72. We have assessed 1757 Italian sporadic ALS cases, 133 from Sardinia, 101 from Sicily, and 1523 from mainland Italy. Sixty (3.7%) of 1624 mainland Italians and Sicilians and 9 (6.8%) of the 133 Sardinian sporadic ALS cases carried the pathogenic repeat expansion. None of the 619 regionally matched control samples (1238 chromosomes) carried the expansion. Twenty-five cases (36.2%) had behavioral FTD in addition to ALS. FTD or unspecified dementia was also detected in 19 pedigrees (27.5%) in first-degree relatives of ALS patients. Cases carrying the . C9ORF72 hexanucleotide expansion survived 1 year less than cases who did not carry this mutation. In conclusion, we found that . C9ORF72 hexanucleotide repeat expansions represents a sizeable proportion of apparent sporadic ALS in the Italian and Sardinian population, representing by far the most common mutation in Italy and the second most common in Sardinia. © 2012 Elsevier Inc.

Genetic counselling in ALS: Facts, uncertainties and clinical suggestions

The clinical approach to patients with amyotrophic lateral sclerosis (ALS) has been largely modified by the identification of novel genes, the detection of gene mutations in apparently sporadic patients, and the discovery of the strict genetic and clinical relation between ALS and frontotemporal dementia (FTD), As a consequence, clinicians are increasingly facing the dilemma on how to handle genetic counselling and testing both for ALS patients and their relatives. On the basis of existing literature on genetics of ALS and of other late-onset life-threatening disorders, we propose clinical suggestions to enable neurologists to provide optimal clinical and genetic counselling to patients and families. Genetic testing should be offered to ALS patients who have a first-degree or second-degree relative with ALS, FTD or both, and should be discussed with, but not offered to, all other ALS patients, with special emphasis on its major uncertainties. Presently, genetic testing should not be proposed to asymptomatic at-risk subjects, unless they request it or are enrolled in research programmes. Genetic counselling in ALS should take into account the uncertainties about the pathogenicity and penetrance of some genetic mutations; the possible presence of mutations of different genes in the same individual; the poor genotypic/phenotypic correlation in most ALS genes; and the phenotypic pleiotropy of some genes. Though psychological, social and ethical implications of genetic testing are still relatively unexplored in ALS, we recommend multidisciplinary counselling that addresses all relevant issues, including disclosure of tests results to family members and the risk for genetic discrimination

Genetic counselling in ALS: facts, uncertainties and clinical suggestions

The clinical approach to patients with amyotrophic lateral sclerosis (ALS) has been largely modified by the identification of novel genes, the detection of gene mutations in apparently sporadic patients, and the discovery of the strict genetic and clinical relation between ALS and frontotemporal dementia (FTD). As a consequence, clinicians are increasingly facing the dilemma on how to handle genetic counselling and testing both for ALS patients and their relatives. On the basis of existing literature on genetics of ALS and of other late-onset life-threatening disorders, we propose clinical suggestions to enable neurologists to provide optimal clinical and genetic counselling to patients and families. Genetic testing should be offered to ALS patients who have a first-degree or second-degree relative with ALS, FTD or both, and should be discussed with, but not offered to, all other ALS patients, with special emphasis on its major uncertainties. Presently, genetic testing should not be proposed to asymptomatic at-risk subjects, unless they request it or are enrolled in research programmes. Genetic counselling in ALS should take into account the uncertainties about the pathogenicity and penetrance of some genetic mutations; the possible presence of mutations of different genes in the same individual; the poor genotypic/phenotypic correlation in most ALS genes; and the phenotypic pleiotropy of some genes. Though psychological, social and ethical implications of genetic testing are still relatively unexplored in ALS, we recommend multidisciplinary counselling that addresses all relevant issues, including disclosure of tests results to family members and the risk for genetic discrimination