A mathematical modelling tool for predicting survival of individual patients following resection of glioblastoma: a proof of principle

Abstract

The prediction of the outcome of individual patients with glioblastoma would be of great significance for monitoring responses to therapy. We hypothesise that, although a large number of genetic-metabolic abnormalities occur upstream, there are two 'final common pathways' dominating glioblastoma growth -net rates of proliferation (r) and dispersal (D). These rates can be estimated from features of pretreatment MR images and can be applied in a mathematical model to predict tumour growth, impact of extent of tumour resection and patient survival. Only the pre-operative gadolinium-enhanced T1-weighted (T1-Gd) and T2-weighted (T2) volume data from 70 patients with previously untreated glioblastoma were used to derive a ratio D/r for each patient. We developed a 'virtual control' for each patient with the same size tumour at the time of diagnosis, the same ratio of net invasion to proliferation (D/r) and the same extent of resection. The median durations of survival and the shapes of the survival curves of actual and 'virtual' patients subjected to biopsy or subtotal resection (STR) superimpose exactly. For those actually receiving gross total resection (GTR), as shown by post-operative CT, the actual survival curve lies between the 'virtual' results predicted for 100 and 125% resection of the T1-Gd volume. The concordance between predicted (virtual) and actual survivals suggests that the mathematical model is realistic enough to allow precise definition of the effectiveness of individualised treatments and their site(s) of action on proliferation (r) and/or dispersal (D) of the tumour cells without knowledge of any other clinical or pathological information.

Applying a patient-specific bio-mathematical model of glioma growth to develop virtual [18F]-FMISO-PET images

“…This model, studied by Swanson et al (2008) (Harpold et al, 2007), has proven to be an accurate predictor of anatomical changes that can be imaged by MRI in individual patients Szeto et al, 2009;Swanson et al, 2003Swanson et al, , 2008Rockne et al, 2009). Further, patient-specific PI model parameters for biological aggressiveness (D and ρ) can be estimated from routinely available pre-treatment MRIs (Harpold et al, 2007).…”

“…Further, patient-specific PI model parameters for biological aggressiveness (D and ρ) can be estimated from routinely available pre-treatment MRIs (Harpold et al, 2007). These patient-specific proliferation and invasion kinetic rates are prognostic of survival ) and response to therapy (Swanson et al, 2003(Swanson et al, , 2008Rockne et al, 2009) in individual patients. Although the PI model has been validated on both the population and patient-specific levels, it provides limited insight with regard to tumour activity at the molecular level.…”

Enforcing Monotonous Shape Growth or Shrinkage in Video Segmentation

“…The model assumes that changes of the core (visible in T1c) will occur within the larger edema regions (visible in T2 or FLAIR) and, hence, to only have class transitions from healthy to edema and from edema to core. As the tumor grows steadily [1,18], we can assume that negative volume changes stem from imaging artifacts. To this end we model the tumor volume to be either stable, regularizing the segmentation along time and suppressing noise, or to expand between any two time points.…”

Glioblastoma brain tumours: estimating the time from brain tumour initiation and resolution of a patient survival anomaly after similar treatment protocols

“…The results quantitatively confirm that gliomas always diffuse and cannot be cured by resection alone, surgically or radiologically, irrespective of the degree of malignancy. The developments of this model have proved medically illuminating and clinically practical [11,18].…”

“…Subsequent studies [13][14][15][16][17][18] refined the model for anatomically correct brains and certain predictions were confirmed by scans and often by autopsy. The results quantitatively confirm that gliomas always diffuse and cannot be cured by resection alone, surgically or radiologically, irrespective of the degree of malignancy.…”