Between β-Emitting Isotopes and α-Emitters Regarding Their Effects on Cancer Cells

(1)

Tumor (cell) dimensions:

Assume a “typical” tumor cell of spherical shape with r = 5 μ radius.

The volume of this cell v = 4/3 × π × r³ = 4 × 125 μ³ = 5 × 10⁻¹⁰ cm³.

${\text {With an assumed specific density of}}\; 1 {\text{ gram}}/{\text{cm}}^{ 3} ,{\text{ the weight of this cell equals 5 }} \times { 1}0^{ - 10} {\text{grams}}$

(2)

Isotope ( ²¹³Bi) need for tumor kill:

For pharmacokinetic reasons we distinguish between two typical kinds of cancer occurrence where αRIT may be of particular use:

(a) Blood-borne cancers and

(b) Micro-metastases.

(a) Blood-borne cancers are relatively easy to access for systemically administered therapy. Also, they are aggressive, like AML, with very rapid growth rates, they cannot be excised by surgery, and are relatively insensitive to total body γ-radiation. Therefore, they can grow up to a load of the order of 1 kg before treatment can be arranged.

Therefore, assume a “typical” tumor load in a patient of 1000 grams. And assume the tumor(s) to consist for 50 % of cancer cells and the other 50 % of physically associated fluid, directly around the cells. This “typical” tumor load, then, will have a total cancer cell weight of 500 grams and, therefore contains (Eq. 2): 500/5 × 10⁻¹⁰ = 10¹² tumor cells. This load will be distributed within the blood pool.

We assume an average of 10 ²¹³Bi ions needed for effective total cell kill. For blood-borne cancers like AML we furthermore assume these to reach the cancer cells without appreciable loss, so a total of 10 ²¹³Bi ions must be administered per tumor cell to be killed. This implies an effective therapeutic isotope dose of 10 × 10¹² ²¹³Bi ions, or (with Eq. 1), in terms of activity, 10 × 10¹²/1,45 × 10¹⁴ curie or, In practical terms,

$\, \approx \, 75 \, mCi \, \left( {millicuries} \right) \, of \;^{213} Bi \, to \, kill \, 1000 \, grams \, of \, tumor \, tissue$

(3)

This agrees well with the amount of isotope used by MSKCC to treat AML patients within the scope of the clinical Phase I/II study. Patients had up to 1 kg of leukemia, which would call for a therapeutic dose of 75 mCi of ²¹³Bi—or 1 mCi per kg body weight of the patient. This amount was not available and patients were pretreated with Cytarabine which allowed for sufficient debulking and reaching full remission when sufficient ²¹³Bi was subsequently given.

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