Biogeography and Biological Optimization

Using a geometric model of shell morphology, it is demonstrated that biconvex brachiopods occupy only a small region of the potential geometric space available to organisms with planispiral exoskeletons composed of two articulated valves. Measurements taken for a sample of 324 genera of the articulate orders Pentamerida, Rhynchonellida, Spiriferida, and Terebratulida were analyzed using a simple geometric model of shell form and ontogeny. The frequency distribution of brachiopod shell morphologies exhibited by the four orders represents the biological optimization of the spatial relationships between area and volume. Biconvex brachiopods develop shells which are designed to minimize shell surface area while maximizing internal shell volume. The means by which optimization is achieved is related directly to the effects of increase in absolute size during ontogeny. The boundaries upon shell geometries utilizable by biconvex brachiopods are determined by (1) limitations of articulation, and (2) limitations of surface and volume.

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Risk-Adaptive Volumetric Modulated Arc Therapy Using Biological Objective Functions for Subvolume Boosting in Radiotherapy

Computational and Mathematical Methods in Medicine ◽

10.1155/2012/348471 ◽

2012 ◽

Vol 2012 ◽

pp. 1-7 ◽

Cited By ~ 2

Author(s):

Nicholas Hardcastle ◽

Wolfgang A. Tome

Keyword(s):

Prostate Cancer ◽

Normal Tissue ◽

Volumetric Modulated Arc Therapy ◽

Simultaneous Integrated Boost ◽

Tumor Control ◽

Objective Functions ◽

Arc Therapy ◽

Integrated Boost ◽

Dose Constraints ◽

Biological Optimization

Objectives. Simultaneous integrated boost (SIB) for prostate cancer allows increases in tumor control probability while respecting normal tissue dose constraints. Biological optimization functions that optimize based on treatment outcome can be used to create SIB prostate plans. This study investigates the feasibility of biologically optimized volumetric modulated arc therapy (VMAT) for SIB prostate radiotherapy.Methods. Five prostate cancer patients with diffusion-weighted MR images were selected for analysis. A two-step VMAT optimization was performed, which consisted of an initial biological optimization of a static gantry angle delivery followed by conversion of the static delivery to a single arc VMAT plan. A dosimetric analysis was performed on the resulting plans.Results. The VMAT plans resulted in a ΔEUD between the prostate and the boost volume of between 15.1 Gy and 20.3 Gy. Rectal volumes receiving 75.6 Gy ranged from 4.5 to 9.9%. Expected rectal normal tissue complication probabilities were between 8.6% and 21.4%. Maximum bladder doses ranged from 73.6 Gy to 75.8 Gy. Estimated treatment time was 120 s or less.Conclusions. The presented biological optimization method resulted in deliverable VMAT plans that achieved sufficient modulation for SIB without violating rectal and bladder dose constraints.Advances in knowledge. This study presents a method for creating simultaneous integrated boost VMAT treatments using biological outcome objective functions.

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