Cancer as a Model System for Testing Metabolic Scaling Theory

Alexander B Brummer,Van M Savage

doi:10.3389/fevo.2021.691830

Abstract

Biological allometries, such as the scaling of metabolism to mass, are hypothesized to result from natural selection to maximize how vascular networks fill space yet minimize internal transport distances and resistance to blood flow. Metabolic scaling theory argues two guiding principles—conservation of fluid flow and space-filling fractal distributions—describe a diversity of biological networks and predict how the geometry of these networks influences organismal metabolism. Yet, mostly absent from past efforts are studies that directly, and independently, measure metabolic rate from respiration and vascular architecture for the same organ, organism, or tissue. Lack of these measures may lead to inconsistent results and conclusions about metabolism, growth, and allometric scaling. We present simultaneous and consistent measurements of metabolic scaling exponents from clinical images of lung cancer, serving as a first-of-its-kind test of metabolic scaling theory, and identifying potential quantitative imaging biomarkers indicative of tumor growth. We analyze data for 535 clinical PET-CT scans of patients with non-small cell lung carcinoma to establish the presence of metabolic scaling between tumor metabolism and tumor volume. Furthermore, we use computer vision and mathematical modeling to examine predictions of metabolic scaling based on the branching geometry of the tumor-supplying blood vessel networks in a subset of 56 patients diagnosed with stage II-IV lung cancer. Examination of the scaling of maximum standard uptake value with metabolic tumor volume, and metabolic tumor volume with gross tumor volume, yield metabolic scaling exponents of 0.64 (0.20) and 0.70 (0.17), respectively. We compare these to the value of 0.85 (0.06) derived from the geometric scaling of the tumor-supplying vasculature. These results: (1) inform energetic models of growth and development for tumor forecasting; (2) identify imaging biomarkers in vascular geometry related to blood volume and flow; and (3) highlight unique opportunities to develop and test the metabolic scaling theory of ecology in tumors transitioning from avascular to vascular geometries.

Highlights

Since Max Kleiber’s finding of the remarkable biological pattern that organismal basal metabolic rate, B, scales with body mass, M, as B ∝ M3/4, scientists have worked to both understand and extend the phenomenon of metabolic scaling (Kleiber, 1932)
The standard uptake values (SUV) of glucose uptake are measured as SUV = r/(a′/w), where r is the concentration of radioactivity detected, a′ is the radioactivity of the full volume of injected radio-tracer adjusted for radioactive decay since injection, and w is the weight of the patient (g)
We found that estimates of metabolic scaling exponents, θ, based on SUVmax ∝ MTVθ are θ = 0.71 ± 0.07, with histologically specific values of θ = 0.73 ± 0.09 for adenocarcinomas (ADCs) and θ = 0.59 ± 0.10 for squamous cell carcinomas (SCCs)

Summary

Introduction

Since Max Kleiber’s finding of the remarkable biological pattern that organismal basal metabolic rate, B, scales with body mass, M, as B ∝ M3/4, scientists have worked to both understand and extend the phenomenon of metabolic scaling (Kleiber, 1932). Proposed theories that purport to explain the origins of metabolic scaling in vascular organisms fail to explain why the pattern persists in avascular organisms. To address these issues, we present simultaneous measurements of metabolic scaling in tumors derived from uptake of metabolic radio-tracers and of the vasculature that comprises and surrounds the tumors. Recent efforts to improve and expedite cancer diagnosis, treatment planning, and tracking responses have produced medical imaging and computer vision technologies that offer a unique lens with which to study metabolic scaling, within tissues that have undergone the avascular-to-vascular transition. We show that insight from metabolic scaling theory can be leveraged to derive vascular-based biomarkers of cancer, potentially introducing an ensemble of biomarkers indicative of tumor growth and the distribution and flow of blood

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