RESUMEN
5-Aminolevulinic Acid (5-ALA) is the only fluorophore approved by the FDA as an intraoperative optical imaging agent for fluorescence-guided surgery in patients with glioblastoma. The dosing regimen is based on rodent tests where a maximum signal occurs around 6 h after drug administration. Here, we construct a computational framework to simulate the transport of 5-ALA through the stomach, blood, and brain, and the subsequent conversion to the fluorescent agent protoporphyrin IX at the tumor site. The framework combines compartmental models with spatially-resolved partial differential equations, enabling one to address questions regarding quantity and timing of 5-ALA administration before surgery. Numerical tests in two spatial dimensions indicate that, for tumors exceeding the detection threshold, the time to peak fluorescent concentration is 2-7 h, broadly consistent with the current surgical guidelines. Moreover, the framework enables one to examine the specific effects of tumor size and location on the required dose and timing of 5-ALA administration before glioblastoma surgery.
Asunto(s)
Ácido Aminolevulínico , Neoplasias Encefálicas , Simulación por Computador , Glioblastoma , Conceptos Matemáticos , Modelos Biológicos , Protoporfirinas , Cirugía Asistida por Computador , Glioblastoma/cirugía , Glioblastoma/tratamiento farmacológico , Glioblastoma/patología , Glioblastoma/diagnóstico por imagen , Ácido Aminolevulínico/administración & dosificación , Humanos , Neoplasias Encefálicas/cirugía , Protoporfirinas/administración & dosificación , Protoporfirinas/metabolismo , Cirugía Asistida por Computador/métodos , Animales , Fármacos Fotosensibilizantes/administración & dosificación , Imagen Óptica/métodos , Colorantes Fluorescentes/administración & dosificaciónRESUMEN
Recent experiments demonstrate how a soluble body placed in a fluid spontaneously forms a dissolution pinnacle-a slender, upward pointing shape that resembles naturally occurring karst pinnacles found in stone forests. This unique shape results from the interplay between interface motion and the natural convective flows driven by the descent of relatively heavy solute. Previous investigations suggest these structures to be associated with shock formation in the underlying evolution equations, with the regularizing Gibbs-Thomson effect required for finite tip curvature. Here, we find a class of exact solutions that act as attractors for the shape dynamics in two and three dimensions. Intriguingly, the solutions exhibit large but finite tip curvature without any regularization, and they agree remarkably well with experimental measurements. The relationship between the dimensions of the initial shape and the final state of dissolution may offer a principle for estimating the age and environmental conditions of geological structures.