ORIGINAL ARTICLE Optimal Equations for Describing the Relationship Between Prostate Volume, Number of Sources, and Total Activity in Permanent Prostate Brachytherapy Jesse N. Aronowitz, MD,* Jeff M. Michalski, MD,† Gregory S. Merrick, MD,‡ John E. Sylvester, MD,§ Juanita M. Crook, MD,¶ Wayne M. Butler, PhD,‡ Christie Mawson, RTT, David Pratt, MD,† Devi Naidoo, BSRT,§ and Kathryn Karolczuk, BA** Objectives: To determine whether there is an optimal type of mathematical equation for predicting seed and activity requirements for permanent prostate brachytherapy. Methods: Four institutions with extensive brachytherapy experience each submitted details of more than 40 implants. The data was used to generate power and linear equations to reflect the relationship between preimplant volume and the number of seeds implanted, and preimplant volume and the total implant activity. We compared the R 2 and standard error of the generated equations to determine which type of equation better fit the data. Results: For the limited range of prostate volumes commonly implanted (20 – 60 mL), power and linear equations predict seed and activity require- ments comparably well. Conclusions: Linear and power equations are equally suitable for generating institution-specific nomograms. Key Words: brachytherapy, prostatic neoplasms, dosimetry (Am J Clin Oncol 2010;33: 164 –167) C omputer dosimetry has revolutionized prostate brachyther- apy, allowing real-time intraoperative treatment planning and dosimetry. There remains, however, the need to predict seed requirements (both quantity and strength) so that an order can be placed in advance of the implant procedure. The published nomograms that could serve this purpose are generally based on a power equation, Seed number or total activity = a (volume b ) wherein a and b are regression fitting coefficients. 1–6 It has been proposed that a linear formula Seed number or total activity = a (volume)+b is also suitable. 7 Both linear and power formulas are easily gener- ated with common statistical or spreadsheet software, facilitating the formulation of institution-specific nomograms reflective of the in- stitution’s technique and implant philosophy. Although other equa- tion forms (particularly those with more than 2 fitting coefficients) may conform more closely to the data, we limited this investigation to equations that could be easily implemented in the surgical suite, on a pocket calculator. We are unaware of any published comparison of the efficacy of linear and power equations in predicting implant requirements. We obtained implant data from 4 institutions with extensive prostate brachytherapy experience to test whether their seed or activity usage are better expressed by a linear or power equation. MATERIALS AND METHODS Four institutions with extensive prostate brachytherapy ex- pertise and mature technique consented to share their implant philosophies (ie, seed distribution pattern, timing of planning) and data on 50 previously performed implants. There were 6 stipulations for submitted cases: • A wide array of prostate volumes (from 20 to 50 mL) were to be represented • Each institution was to supply data for iodine or palladium implants • The implants were intended to represent sole radiotherapy (with- out adjuvant beam therapy) • The implants’ quality had been deemed “satisfactory” by the brachytherapist, based on concordance of postimplant dosimetry with institutional guidelines • Implant data was to include planning ultrasound prostate volume, seed type and activity, number of seeds planned, the number actually implanted, and pre- and postplan D90 • The submitted data contain no information that would allow patient identification. Information regarding the use of androgen deprivation and seed model/manufacturer was not obtained. Individual cases that did not meet inclusion criteria (for example, implants intended to be combined with beam therapy) were excluded; after exclusions, there were be- tween 41 and 48 cases analyzed from each institution. This study was approved by the organizing institution’s review board, and participating brachytherapists were encouraged to obtain similar approval. Based on the supplied data, regression analyses were per- formed using JMP v7.0 software (SAS Institute, Cary, NC). Specif- ically, we generated both linear and power equations to reflect the relationship between: • Preimplant volume and number of seeds implanted • Preimplant volume and total implanted activity The R 2 and “Standard Error” (root mean square error) of these equations were then compared to determine which equation-type had superior “fit” (higher R 2 , but lower standard error, reflects superior fit). The number of extra seeds needed to account for uncertainties would be a multiple of the standard error. Graphing From the *Department of Radiation Oncology, University of Massachusetts Medical School, Worcester, MA; †Department of Radiation Oncology, Wash- ington University School of Medicine, St. Louis, MO; ‡Schiffler Cancer Center, Wheeling Jesuit University, Wheeling, WV; §Seattle Prostate Insti- tute, Seattle, WA; ¶Department of Radiation Oncology, University of To- ronto, Toronto, ON, Canada; Department of Radiation Medicine, Princess Margaret Hospital, Toronto, ON, Canada; and **Quality Assurance Review Center, Providence, RI. Reprints: Jesse Aronowitz, MD, 33 Kendall St, Worcester, MA 01605. E-mail: jaronowitz@comcast.net. Copyright © 2010 by Lippincott Williams & Wilkins ISSN: 0277-3732/10/3302-0164 DOI: 10.1097/COC.0b013e31819d3684 American Journal of Clinical Oncology • Volume 33, Number 2, April 2010 164 | www.amjclinicaloncology.com