The upregulation of low-density lipoprotein (LDL) transporters in tumour cells has been exploited to deliver a sufficient amount of gadolinium/boron/ligand (Gd/B/L) probes for neutron capture therapy, a binary chemio-radiotherapy for cancer treatment. The Gd/B/L probe consists of a carborane unit (ten B atoms) bearing an aliphatic chain on one side (to bind LDL particles), and a Gd(III)/1,4,7,10-tetraazacyclododecane monoamide complex on the other (for detection by magnetic resonance imaging (MRI)). Up to 190 Gd/B/L probes were loaded per LDL particle. The uptake from tumour cells was initially assessed on cell cultures of human hepatoma (HepG2), murine melanoma (B16), and human glioblastoma (U87). The MRI assessment of the amount of Gd/B/L taken up by tumour cells was validated by inductively coupled plasma-mass-spectrometric measurements of the Gd and B content. Measurements were undertaken in vivo on mice bearing tumours in which B16 tumour cells were inoculated at the base of the neck. From the acquisition of magnetic resonance images, it was established that after 4-6 hours from the administration of the Gd/B/L-LDL particles (0.1 and 1 mmol kg(-1) of Gd and (10)B, respectively) the amount of boron taken up in the tumour region is above the threshold required for successful NCT treatment. After neutron irradiation, tumour growth was followed for 20 days by MRI. The group of treated mice showed markedly lower tumour growth with respect to the control group.

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Tumour metabolism is an outstanding topic of cancer research, as it determines the growth rate and the global activity of tumours. Recently, by combining the diffusion of oxygen, nutrients, and metabolites in the extracellular environment, and the internal motions that mix live and dead cells, we derived a growth law of solid tumours which is linked to parameters at the cellular level 1 . Here we use this growth law to obtain a metabolic scaling law for solid tumours, which is obeyed by tumours of different histotypes both in vitro and in vivo, and we display its relation with the fractal dimension of the distribution of live cells in the tumour mass. The scaling behaviour is related to measurable parameters, with potential applications in the clinical practice.R ecently we derived a growth law for solid tumours 1 , where growth depends on the distribution of live cells in the tumour mass. The model was suggested by the results of computer simulations 2 , and it has been validated using data from in vitro experiments. In this model the inter-vascular micro-regions of solid tumours contain both live and dead cells, and the fraction of live cells is exponentially smaller as the distance from the sources of nutrients and oxygen increases. Although the decay length l is weakly dependent on tumour size, we found that an effective, size-independent l works nearly as well, and that l has values mostly in the range 50-150 mm. Notably, this is also the distance from the nearest blood vessel where the interstitial pO 2 assumes hypoxic and anoxic values and pH drops to acidic values in the micro-regions of vascularized tumours 3 , and corresponds to the typical thickness of the viable tumour cell layer around blood vessels 4 . Here we show how the growth law can be combined with basic metabolic parameters to yield a seemingly universal metabolic scaling law for tumours, that holds both in vitro and in vivo.We start from the tumour growth law, that can be expressed as a differential equation for tumour volume, and combines proliferation of live cells in the tumour with the gradual shrinking of dead cells 1whereis the fraction of live cells in the tumour, derived from the assumption of exponential decay of the density of live cells, so that the total volume of live cells is V a 5 F(V)V, and where the parameter a defines the individual cell proliferation rate, while the parameter d is the shrinking rate of dead cells. The tumour volume is proportional to x 3 , where x is some characteristic length of the tumour, i.e., V 5 Ax 3 . In the case of spherical tumours A 5 4p/3 < 4.2, and x is the tumour radius, but here we consider the possibility of departure from a spherical shape. Still, we assume that the tumour keeps roughly the same shape as it grows, so that x can be chosen as a substitute for radius, e.g., as the length of a given chord between two fixed, recognizable surface features of the tumour shape. We note that A is one of the factors that set the rate of tumour growth, at least for large tumour sizes, since in that c...

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