PMID: 9434986Jan 22, 1998Paper

An analytical approximation of the Bragg curve for therapeutic proton beams

Medical Physics
Thomas Bortfeld

Abstract

The knowledge of proton depth-dose curves, or "Bragg curves," is a fundamental prerequisite for dose calculations in radiotherapy planning, among other applications. In various cases it is desirable to have an analytical representation of the Bragg curve, rather than using measured or numerically calculated data. This work provides an analytical approximation of the Bragg curve in closed form. The underlying model is valid for proton energies between about 10 and 200 MeV. Its main four constituents are: (i) a power-law relationship describing the range-energy dependency; (ii) a linear model for the fluence reduction due to nonelastic nuclear interactions, assuming local deposition of a fraction of the released energy; (iii) a Gaussian approximation of the range straggling distribution; and (iv) a representation of the energy spectrum of poly-energetic beams by a Gaussian with a linear "tail." Based on these assumptions the Bragg curve can be described in closed form using a simple combination of Gaussians and parabolic cylinder functions. The resulting expression can be fitted to measurements within the measurement error. Very good agreement is also found with numerically calculated Bragg curves.

References

Oct 1, 1988·International Journal of Bio-medical Computing·C V LevinS Wynchank
Nov 1, 1983·Medical Physics·M Goitein, G T Chen
Jan 1, 1981·Annual Review of Biophysics and Bioengineering·G T ChenJ M Quivey
Aug 1, 1996·Physics in Medicine and Biology·L HongM Urie
Mar 1, 1961·The British Journal of Radiology·B LARSSON

❮ Previous
Next ❯

Citations

May 17, 2011·Australasian Physical & Engineering Sciences in Medicine·Z RiaziR Sadighi-Bonabi
Jul 11, 2001·Medical Dosimetry : Official Journal of the American Association of Medical Dosimetrists·U Oelfke, T Bortfeld
Oct 18, 2012·Physics in Medicine and Biology·Benjamin M ClasieHanne M Kooy
Feb 3, 2012·Physics in Medicine and Biology·Yupeng LiXiaodong Zhang
Oct 12, 2007·Medical Physics·Joanne H KangUwe Oelfke
Nov 7, 2012·Medical Physics·Hermann FuchsDietmar Georg
Feb 26, 2008·Medical Physics·Johanna Kempe, Anders Brahme
Dec 17, 2010·Medical Physics·David JetteWeimin Chen
Sep 8, 2007·Medical Physics·Dmitri NichiporovAndries Schreuder
Sep 6, 2014·Journal of Medical Physics·Keyvan Jabbari, Jan Seuntjens
Aug 27, 2014·Australasian Physical & Engineering Sciences in Medicine·Seung Hoon YooSung Yong Park
May 11, 2011·Radiation and Environmental Biophysics·Christoph GreubelJan J Wilkens
Jun 19, 2010·Strahlentherapie und Onkologie : Organ der Deutschen Röntgengesellschaft ... [et al]·Mark RickheyLudwig Bogner
Mar 12, 2013·Seminars in Radiation Oncology·Jacob Flanz, Thomas Bortfeld
Nov 22, 2011·International Journal of Radiation Oncology, Biology, Physics·Malte C FreseDavid J Carlson
Jul 5, 2011·Zeitschrift für medizinische Physik·Marita FalkingerJan J Wilkens
Jan 10, 2016·Medical Physics·Fatemeh S RasouliDavid Jette
Jun 29, 2010·Physica Medica : PM : an International Journal Devoted to the Applications of Physics to Medicine and Biology : Official Journal of the Italian Association of Biomedical Physics (AIFB)·Nobuyuki Kanematsu
Apr 13, 2010·International Journal of Radiation Oncology, Biology, Physics·Malte C FreseZahra Taheri-Kadkhoda
Apr 7, 2009·Physica Medica : PM : an International Journal Devoted to the Applications of Physics to Medicine and Biology : Official Journal of the Italian Association of Biomedical Physics (AIFB)·J Kempe, A Brahme
Oct 16, 2007·International Journal of Radiation Oncology, Biology, Physics·Jan J Wilkens, Uwe Oelfke
Nov 16, 2004·Radiotherapy and Oncology : Journal of the European Society for Therapeutic Radiology and Oncology·Lennart OlofssonMikael Karlsson
Apr 23, 2013·Radiotherapy and Oncology : Journal of the European Society for Therapeutic Radiology and Oncology·Gonzalo A Cabal, Oliver Jäkel
Feb 24, 2015·Nuclear Instruments & Methods in Physics Research. Section A, Accelerators, Spectrometers, Detectors and Associated Equipment·W Scott IngramSam Beddar
Oct 1, 2014·Zeitschrift für medizinische Physik·Sebastian Faby, Jan J Wilkens
Aug 10, 2011·Radiation Research·Robert D StewartDavid J Carlson
Apr 4, 2015·Medical Physics·P J DoolanE H Bentefour

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.