  Most physical and other natural systems are complex entities composed of a
large number of interacting individual elements. It is a surprising fact that
they often obey the so-called scaling laws relating an observable quantity with
a measure of the size of the system. Here we describe the discovery of
universal superlinear metabolic scaling laws in human cancers. This dependence
underpins increasing tumour aggressiveness, due to evolutionary dynamics, which
leads to an explosive growth as the disease progresses. We validated this
dynamic using longitudinal volumetric data of different histologies from large
cohorts of cancer patients. To explain our observations we put forward
increasingly complex biologically-inspired mathematical models that captured
the key processes governing tumor growth. Our models predicted that the
emergence of superlinear allometric scaling laws is an inherently
three-dimensional phenomenon. Moreover, the scaling laws thereby identified
allowed us to define a set of metabolic metrics with prognostic value, thus
providing added clinical utility to the base findings.
