Leukaemia cells circulate singly in the bone marrow

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Nuclear medicine, dosimetry and radiotherapy · Nuclear medicine, dosimetry and radiotherapy

The Nucleus Resolved, Ch What it is used for: medicine, dating and analysis

Problem

Leukaemia cells circulate singly in the bone marrow, dispersed among healthy marrow cells that must be spared as far as possible: there is no solid tumour mass to give useful cross-fire, only isolated targets. Model every marrow cell, healthy or malignant, as a sphere of diameter

10\,\mu\mathrm{m}

. An antibody that binds a leukaemia-specific surface marker can be labelled with one of three particle emitters:

^{90}\mathrm{Y}

\beta^-

, maximum range in tissue

11\,\mathrm{mm}

^{213}\mathrm{Bi}

\alpha

particles, range in tissue

80\,\mu\mathrm{m}

T_{1/2} = 45.6\,\mathrm{min}

^{125}\mathrm{I}

: an Auger-electron emitter (electron capture); its Auger electrons travel less than about

1\,\mu\mathrm{m}

in tissue, but only deposit a lethal dose if the decay occurs inside, or very close to, the cell's nucleus. ((a)) Express each particle's range as a number of cell diameters, and use these numbers to rank the three emitters by how much dose they give to the healthy cells surrounding a single labelled leukaemia cell. ((b)) State the practical caveat on using

^{125}\mathrm{I}

, and hence say which emitter is the sound practical choice if the antibody is known not to be internalised into the cell. ((c)) List two decisions here forced by a nuclear property and one that is not.

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