Methods for evaluating treatments that consist of multiple datasets

2.3.1 Cumulative dose

In an adaptive treatment, re-plans are based on recent images of patient anatomy which reflect any variation that has occurred since previous acquisitions and which modify the projected dose distribution of the initial plan. One method for synthesizing data from multiple time-points is to sum individual dose distributions to a single reference image[32]

using a mapping established by deformable image registration. This method of evaluation has various

advantages: 1) cumulative dose is directly comparable to the original plan which likewise corresponds to a single image, 2) dose-response data is largely based on projected cumulative metrics,[33]

and 3) ambiguities related to comparing volume-based parameters (e.g. V20) in the presence of volumetric variation[34]

are avoided if a common reference is utilized for both. Dose accumulation utilizes mappings between imaging data to warp dose distributions to a given reference image. Inaccuracies in image registrations will likewise affect deformed

distributions, thus reliable dose accumulation depends on accurate mappings between image data. In this work consistency between images and mappings is achieved by generating synthetic

displacement vector fields (DVF) using a PCA model and then warping the primary dataset to create images resulting in self-consistent images, contours, and mappings that correspond to intermediate time points (see chapter 3).

In cases where DVFs accurately map dose, any time-point may serve as a valid reference for dose accumulation assuming that mass is conserved between images. In cases where mass is

not conserved, different images represent distinct structures as opposed to distinct poses of anatomy which presents a subtlety in reference image selection. The following discussion illustrates this point.

2.3.1.1 Cumulative dose in the presence of mass loss

Consider an image Ia that consists of a single voxel Va acquired at time-point ta and that receives an initial fraction of radiation. Assuming mass loss occurs as a result of the delivered radiation, the cellular population represented in Va may be divided into a group that survives and persists, denoted by S, and a group that is killed or otherwise cleared from the voxel, denoted by

K. After the initial irradiation, a second image Ib consisting of a single voxel Vb, and containing the surviving fraction, is acquired at time-point tb, and an additional fraction of radiation is delivered to population S. The scenario is illustrated in Fig. 2.2.

Dose delivered to the cellular population represented in Va at time ta considering separate populations of surviving and non-surviving cells is given by:

(2.1)

where Es and Ek are the absorbed energy at a given time point for surviving and non-surviving fractions respectively, and ms and mk are the masses of the respective population. Dose delivered to voxel Vb at time tb is as follows:

(2.2)

Cumulative dose using image Ia as reference is then given by:

(2.3)

and incorporating equation (2.2 this becomes:

D_V a = E_s

( )

( )

( )

( )

( )

( )

( )

(2.4)

Cumulative dose using Ib as reference is given by:

(2.5)

and assuming that

(2.6)

equation (2.5 may be written as

(2.7)

Fig. 2.2. Dose accumulation in the presence of mass loss. Voxels Va and Vb are irradiated at times ta and tb respectively.

The surviving fraction of cells is denoted as S and the fraction that does not survive is denoted as K. Dose accumulation is facilitated by a mapping between the two images Ia and Ib either of which may be selected as the reference image.

Equation(2.4 is consistent with a literal interpretation of cumulative dose, i.e. cumulative dose is equal to the actual mean dose received by the cellular population contained in the voxel. In this case, cells that receive less dose because they are eradicated and cleared from the voxel decrease the reported cumulative dose. One may argue, that summing dose in this way may lead

CDI_a = DV_a+ DV_b ms m_s+ m_k = DVa+ DVb mV_b m_V a CD_I b = E_s

( )

( )

( )

( )

to an erroneous conclusion that coverage was compromised throughout treatment when in reality coverage was maintained and mass-loss occurred. An alternative then is to report the mean dose that would be received if all cells were to persist throughout treatment. In this case cumulative dose reflects the dose received by surviving cells in each fraction as opposed to the actual dose received by all cells represented in the earlier image. Using the latter definition, cumulative dose reported on the earlier image is equivalent to that reporter on the later image.

These subtleties highlight the limitations inherent in using a static image to summarize dose delivered to dynamic structures that experience mass loss which result from the

compression of temporal data to a single time-point. Such considerations motivate development of history-based methods to compliment assessments based on cumulative dose.

2.3.2 History-based assessment methods

As highlighted in the previous section, cumulative dose represents a compression of data which obscures the temporal details associated with treatment delivery, i.e. the dose distributions associated with each fraction are compressed to a single time-point.

Temporal sequences of dose metrics, plotted as a function of treatment fraction, are presented here as a complimentary method to accumulating dose for evaluating and informing adaptive plans. It is hypothesized that preserving the temporal course of metrics throughout treatment will provide insight into the dynamics of adaptive benefit i.e. Patterns and trends in temporal signals (e.g. changes in volume, mass, tumor centroid, etc.) may indicate advantageous times to adapt or serve to classify patients that benefit from an adaptive planning approach.

Greater clarity and accuracy in evaluation methods are necessary to relate details of treatment delivery to clinical outcome;[35]

likewise, it is anticipated that temporal tracking of relevant metrics will provide valuable perspective on treatment delivery and outcome and may

allow patient specific estimates of response through a correlation of various temporal signals (e.g. mass and cumulative dose), though correlative analysis of delivery metrics and response are not addressed in this thesis.