Oedema-based model for diffuse low-grade gliomas: application to clinical cases under radiotherapy.

OBJECTIVES: Diffuse low-grade gliomas are characterized by slow growth. Despite appropriate treatment, they change inexorably into more aggressive forms, jeopardizing the patient's life. Optimizing treatments, for example with the use of mathematical modelling, could help to prevent tumour regrowth and anaplastic transformation. Here, we present a model of the effect of radiotherapy on such tumours. Our objective is to explain observed delay of tumour regrowth following radiotherapy and to predict its duration. MATERIALS AND METHODS: We have used a migration-proliferation model complemented by an equation describing appearance and draining of oedema. The model has been applied to clinical data of tumour radius over time, for a population of 28 patients. RESULTS: We were able to show that draining of oedema accounts for regrowth delay after radiotherapy and have been able to fit the clinical data in a robust way. The model predicts strong correlation between high proliferation coefficient and low progression-free gain of lifetime, due to radiotherapy among the patients, in agreement with clinical studies. We argue that, with reasonable assumptions, it is possible to predict (precision ~20%) regrowth delay after radiotherapy and the gain of lifetime due to radiotherapy. CONCLUSIONS: Our oedema-based model provides an early estimation of individual duration of tumour response to radiotherapy and thus, opens the door to the possibility of personalized medicine.

Modeling the role of water in Bacillus subtilis colonies.

We propose a simple cellular automaton model for the description of the evolution of a colony of Bacillus subtilis. The originality of our model lies in the fact that the bacteria can move in a pool of liquid. We assume that each migrating bacterium is surrounded by an individual pool, and the overlap of the latter gives rise to a collective pool with a higher water level. The bacteria migrate collectively when the level of water is high enough. When the bacteria are far enough from each other, the level of water becomes locally too low to allow migration, and the bacteria switch to a proliferating state. The proliferation-to-migration switch is triggered by high levels of a substance produced by proliferating bacteria. We show that it is possible to reproduce in a fairly satisfactory way the various forms that make up the experimentally observed morphological diagram of B. subtilis. We propose a phenomenological relation between the size of the water pool used in our model and the agar concentration of the substrate on which the bacteria migrate. We also compare experimental results from cutting the central part of the colony with the results of our simulations.

Improving the time-machine: estimating date of birth of grade II gliomas.

OBJECTIVES: Here we present a model aiming to provide an estimate of time from tumour genesis, for grade II gliomas. The model is based on a differential equation describing the diffusion-proliferation process. We have applied our model to situations where tumour diameter was shown to increase linearly with time, with characteristic diametric velocity. MATERIALS AND METHODS: We have performed numerical simulations to analyse data, on patients with grade II gliomas and to extract information concerning time of tumour biological onset, as well as radiology and distribution of model parameters. RESULTS AND CONCLUSIONS: We show that the estimate of tumour onset obtained from extrapolation using a constant velocity assumption, always underestimates biological tumour age, and that the correction one should add to this estimate is given roughly by 20/v (year), where v is the diametric velocity of expansion of the tumour (expressed in mm/year). Within the assumptions of the model, we have identified two types of tumour: the first corresponds to very slowly growing tumours that appear during adolescence, and the second type corresponds to slowly growing tumours that appear later, during early adulthood. That all these tumours become detectable around a mean patient age of 30 years could be interesting for formulation of strategies for early detection of tumours.

Quantitative analyses of GFRalpha-1 and GFRalpha-2 mRNAs and tyrosine hydroxylase protein in the nigrostriatal system reveal bilateral compensatory changes following unilateral 6-OHDA lesions in the rat.

Copy numbers of mRNAs for GFRalpha-1 and GFRalpha-2, the preferred receptors for glial cell line-derived neurotrophic factor (GDNF) and neurturin (NTN) were determined by real-time quantitative RT-PCR (QRT-PCR). Receptor expression was assessed in striatum (ST) and substantia nigra (SN) of normal rats and rats acutely or progressively lesioned by 6-OHDA injected into the medial forebrain bundle or ST, respectively. GFRalpha-1 mRNA was clearly detected in normal ST. In normal SN, significantly higher expression of both receptors was observed. At 4 weeks after acute lesion, GFRalpha-2 mRNA was markedly decreased in SN bilaterally, whereas GFRalpha-1 mRNA in SN and ST was not affected. A progressive lesion resulted in a progressive decrease of GFRalpha1 mRNA in ST bilaterally. In SN, levels of GFRalpha-1 mRNA were not significantly affected by a progressive lesion, whereas GFRalpha-2 mRNA was markedly decreased bilaterally. Quantitative western blotting standardized against tyrosine hydroxylase (TH) protein from PC12 cells revealed the expected decrease in TH protein in lesioned SN, but also significant increases in TH protein in contralateral, unlesioned SNs at 4 weeks after both acute and progressive lesions. These data suggest that previously unrecognized compensatory changes in the nigrostriatal system occur in response to unilateral dopamine depletion. Since the changes observed in receptor expression did not always parallel loss of dopamine neurons, cells in addition to the nigral dopamine neurons appear to be affected by a 6-OHDA insult and are potential targets for the neurotrophic factors, GDNF and NTN.

No correlation between aggregates of Cu/Zn superoxide dismutase and cell death in familial amyotrophic lateral sclerosis.

Aggregates of Cu/Zn superoxide dismutase (SOD) have been demonstrated in familial amyotrophic lateral sclerosis (FALS) and other neurodegenerative diseases; however, their role in disease pathogenesis is unclear. In this study, we investigated the presence of SOD aggregates in nerve growth factor (NGF)-differentiated PC12 cells and cell viability following: (i) transduction with replication-deficient recombinant adenoviruses (AdVs) expressing wild-type SOD (SODWT) or mutant SOD (SODMT, V148G or A4V); (ii) transfection of yellow fluorescent protein-tagged SODWT (SODWT-YFP) or SODMT (SODA4V-YFP, SODV148G-YFP). SOD aggregates were more prominent in cells following transduction of AdSODMT than AdSODWT and following treatment with H2O2, suggesting that mutant SOD leads to oxidation of cellular components. In addition, cells expressing SODMT-YFP yielded SOD aggregates that were significantly larger and more frequent than SOD aggregates in cells expressing SODWT-YFP. Proteasome inhibitors, but not cathepsin B inhibitors, increased aggregate formation but did not increase cell death. In addition, treatments that increased cell viability did not significantly decrease SOD aggregates. Taken together, our data demonstrate that there is no association between SOD aggregates and cell death in FALS.

Direct evidence for the link between monoaminergic descending pathways and motor activity: II. A study with microdialysis probes implanted in the ventral horn of the spinal cord.

In order to define precisely the relation between descending monoaminergic systems and the motor system, we measured in the ventral horn of spinal cord of adult rats the variations of extracellular concentrations of 5-HT, 5-HIAA, DA and MHPG. Measurements were performed during rest, endurance running on a treadmill, and a post-exercise period, with microdialysis probes implanted permanently for 45 days. We found a slight decrease in both 5-HT and 5-HIAA during locomotion with a more marked decrease during the post-exercise period compared to the mean of rest values. In contrast, the concentration of DA and MHPG increased slightly during the exercise and decreased thereafter. These results, when compared with those of a previous study, which measured monoamines in the spinal cord white matter [C. Gerin, D. Bécquet, A. Privat, Direct evidence for the link between monoaminergic descending pathways and motor activity: I. A study with microdialysis probes implanted in the ventral funiculus of the spinal cord, Brain Res. 704 (1995) 191-201], highlight the complex regulation of the release of monoamines that occurs in the ventral horn.

Evaluation of the function of microdialysis probes permanently implanted into the rat CNS and coupled to an on-line HPLC system of analysis.

The aim of the microdialysis technique is to reflect as closely as possible the status and fluctuations of substances contained in the extracellular space. Most often, microdialysis is performed with repetitively implanted probes. We have recently devised an experimental set-up which allows microdialysis to be performed in the spinal cord of unrestrained rats through chronically permanently implanted probes. In the present study, we have compared the in vitro recovery of a non-biogenic amine (DHBA) and of 5-HT, and the in vivo recovery of the former. Thus, we could extrapolate the in vivo recovery of endogenous 5-HT released. Moreover, we have found that the recovery does not vary irrespective of whether the animal is at rest or performing sustained physical exercise, and that it also remains stable with time, from 8 to 36 days after permanent implantation of the probe. We conclude that this simple method can be applied to standard experiments of microdialysis, and thus allow one to measure the actual rate of recovery for a given probe. Moreover, it permits control of the stability of dialysis parameters with time for long-term permanently implanted probes.

Direct evidence for the link between monoaminergic descending pathways and motor activity. I. A study with microdialysis probes implanted in the ventral funiculus of the spinal cord.

Monoaminergic projections to the spinal cord are involved in the modulation of motor, autonomic, and sensory functions. More specifically, the increase of electrical activity of serotonergic neurons in raphe obscurus has been correlated with locomotion in treadmill-trained cats [Jacobs, B.L. and Fornal, C., Trends Neurosci., 9 (1993) 346-352]. In order to test the direct correlation between locomotion and the release of monoamines, microdialysis probes were permanently implanted for 45 days into the ventral funiculus of the spinal cord (white matter) of adult rats. Eight days after implantation, these rats were subjected to an endurant exercise on a treadmill, and dialysis sessions were organized in such a way that microdialysate samples of 15 min duration were collected during pre-, per- and post-exercise periods. Measurements of serotonin, 5-hydroxyindoleacetic acid, dopamine and 3-methoxy-4-hydroxyphenylethylglycol concentration in the extracellular space showed significant increases during locomotion when compared with both pre- and post-exercise values. Histological analysis shows that serotonergic axons were present close to the dialysis probe. These results demonstrate that the implantation of a microdialysis probe in the ventral funiculus, close to a potential target of monoaminergic projections, is a suitable technique for the collection of neuromediators released during spontaneous running.

Study of 5-HT release with a chronically implanted microdialysis probe in the ventral horn of the spinal cord of unrestrained rats during exercise on a treadmill.

The ventral horn of the spinal cord is profusely innervated by serotonin (5-hydroxytryptamine, 5-HT) which presumably modulates locomotor activity through motoneurons. However, direct evidence of correlation between 5-HT release and activation of motoneurons is still lacking. In order to appreciate the functional characteristics of this innervation, we have used microdialysis to monitor the release of 5-HT in the spinal cord of rats spontaneously running on a treadmill. For this purpose, we developed an original surgical procedure adapted for the chronic implantation of a microdialysis probe in the lumbar spinal cord. The probe was kept in place for 40 days, and microdialysis experiments were carried out at days 8, 16, 20 and 32. 5-HT was detected with HPLC coupled to electrochemistry. This technique demonstrated that release of 5-HT is not increased during exercise. However, a significant decrease was measured during postexercise rest. 5-HT could still be detected 32 days after probe implantation. Detailed histological and immunocytochemical analysis based on glial fibrillary acidic protein and 5-HT immunocytochemistry showed minimal gliosis and the presence of serotonergic varicose fibers, respectively, at the probe contact. It thus appears that microdialysis can be performed through a probe implanted chronically in the spinal cord of unrestrained rat during an endurance running exercise.