Dose calculation algorithms are usually performed by computers but more simple penandpaper methods are available. They allow the isodose chart to be adjusted to account for tissue inhomogeneities.
Correction Based Algorithms
Correction algorithms are the easiest to calculate but also the least accurate.
Tissue Air Ratio (TAR) Method
The TAR method adjusts the dose beyond an inhomogeneity based by assuming that the inhomogeneity of density $\delta$I and thickness dI causes attenuation of the beam equivalent to water (density $\delta$W) of thickness dW. The correction from the inhomogeneity density to water density is based on the inhomogeneity in question. The TAR method does not take into account changes in scatter caused by an inhomogeneity.
Batho Power Law Method
Similar to the TAR method, the Batho Power Law method applies a correction factor based on the electron density of the inhomogeneity. It only takes into account incoherent scattering effects.
Equivalent Tissue Air Ratio (ETAR) method
The ETAR method was developed to account for alterations in scattering that occur when an inhomogeneity is present. This is not predicted at all with the TAR method that is mainly useful for primary radiation. The ETAR method uses a weighted density, the sum of the density of each pixel in the inhomogeneity, to adjust scattered dose. This method is much lengthier than the TAR method but provides more accurate isodose corrections.
Isodose Shift Method
Instead of performing numerous calculations, the isodose shift method adjusts the isodose distribution by moving the lines a shift factor of n coupled with the thickness of the inhomogeneity. This shifts isodose lines superficially for bony inhomogeneity or deeper for air gaps or lung.
Summary of Correction Based Algorithms
The correction based methods may be performed with pen, paper and a calculator. They calculate scatter poorly (if at all) and as such are the least accurate of the dose correction algorithms.
Model Based Algorithms
Model based algorithms are far more complex and must be performed by a high end computer.
SuperpositionConvolution
This method calculates the primary and scattered radiation separately. For each point in a volume (voxel), the attenuation coefficient is calculated and the primary radiation beam is attenuated by that amount. A kernel, representing the average distribution of scatter from that point, is then applied to each voxel, weighted according to the amount of primary radiation that was attenuated at that point. By summing the primary radiation and scattered radiation arising from each voxel, an accurate dose distribution is generated.
The accuracy of this method is dependent on the resolution of the images used and the design of the kernels. More complex methods tend to be more accurate but also take longer to calculate. Superpositionconvolution performs inferiorly to Monte Carlo methods around inhomogeneities.
Monte Carlo
Monte Carlo simulations were first coined by nuclear researchers attempting to predict the likelihood of a chain reaction occurring in a nuclear reactor. Given an uncertainty, the simulation is run multiple times to estimate the probability of a particular outcome.
In dose calculation, Monte Carlo simulations determine the fate of single xray photons as they enter the phantom or patient. Scattering and attenuation of the photon and resulting electrons are taken into account based on the physical features of each voxel. By mapping out the paths of thousands (or millions) of photons, an average dose distribution is created.
Monte Carlo is the most accurate method of dose calculation that is in use. It is limited by the lengthy computing time needed to perform the numerous simulations.
Clarkson Segmental Integration
This method is used to adjust monitor units for irregular field shapes. It involves dividing the field into radii of 10o each, radiation out from a central point. The distance along each radius is measured and compared with a table of scatterair ratios for a circular field of that radius. By summing the scatterair ratios of each radius, and then dividing the result by the number of radii, and equivalent field size is generated. This can then be used to adjust monitor units so that an accurate dose is delivered.
Links

11: Treatment Planning And Delivery
 11.01  Simulation
 11.02  ICRU Reports 50 and 62
 11.03  2D And 3D Planning
 11.04  Principles Of IMRT
 11.05  Patient Data Acquisition
 11.06  Choice of beam and modifiers
 11.07  Field Junctioning
 11.08  Calculation Of Monitor Units
 11.09  Dose Calculation Algorithms

11.10  Accuracy Of Treatment Planning And Delivery
 11.10.1  Patient Immobilisation And Monitoring
 11.10.2  Image Guided Radiotherapy
 11.10.3  Consistency Of Contours During Treatment
 11.10.4  Accuracy And Tolerance
 11.10.5  Determination Of Accuracy
 11.10.6  Types Of Errors
 11.10.7  Avoidance And Detection Of Dose Delivery Errors
 11.10.8  Errors Due To Computer Control
 11.10.9  In Vivo Dosimetry