Efficacy of dose escalation on TCP, recurrence and second cancer risks: a mathematical study

OBJECTIVE

We investigated the effects of conventional and hypofractionation protocols by modelling tumour control probability (TCP) and tumour recurrence time, and examined their impact on second cancer risks. The main objectives of this study include the following: (a) incorporate tumour recurrence time and second cancer risks into the TCP framework and analyse the effects of variable doses and (b) investigate an efficient protocol to reduce the risk of a secondary malignancy while maximizing disease-free survival and tumour control.

METHODS

A generalized mathematical formalism was developed that incorporated recurrence and second cancer risk models into the TCP dynamics.

RESULTS

Our results suggest that TCP and relapse time are almost identical for conventional and hypofractionated regimens; however, second cancer risks resulting from hypofractionation were reduced by 22% when compared with the second cancer risk associated with a conventional protocol. The hypofractionated regimen appears to be sensitive to dose escalation and the corresponding impact on tumour recurrence time and reduction in second cancer risks. The reduction in second cancer risks is approximately 20% when the dose is increased from 60 to 72 Gy in a hypofractionated protocol.

CONCLUSION

Our results suggest that hypofractionation may be a more efficient regimen in the context of TCP, relapse time and second cancer risks. Overall, our study demonstrates the importance of including a second cancer risk model in designing an efficient radiation regimen.

ADVANCES IN KNOWLEDGE

The impact of various fractionation protocols on TCP and relapse in conjunction with second cancer risks is an important clinical question that is as yet unexplored.

Treatment of distal radial fractures with the DVR-A plate--the early Bristol experience

AIM

The aim of the study was to assess how adequately distal radial fracture reduction was reproduced and maintained with the distal volar radius anatomic DVR-A (Biomet, Inc) locking plate.

METHODS

We looked at a consecutive series of 111 patients treated with the DVR-A plate at our institution from 2007-2010. The preoperative, intra-operative, and postoperative films were reviewed. The AO and Frykman classification was recorded. The sagittal tilt, radial inclination, and radial length were measured on intra-operative X-rays and compared with final follow-up X-rays. The last recorded range of motion at follow-up and a functional assessment using the Disabilities of the Arm, Shoulder, and Hand (DASH) score was recorded.

RESULTS

At final follow-up a mean radial inclination of 22.22 degrees (11 to 38 degrees), radial height of 11.85 mm (6 to 18 mm), and sagittal tilt of 6.71 degrees volar (-9 to 19 degrees) was achieved. From initial post-operative films, to final follow-up X-rays there was a mean increase of 0.17 degrees in radial inclination, a mean loss of 0.36 mm radial height, and a mean loss of 2.17 degrees volar tilt. The mean extension was 46.8 degrees, flexion 48.3 degrees, pronation 77.4 degrees, supination 74.8 degrees, radial deviation 15.3 degrees and the ulnar deviation 19 degrees. The mean DASH score was 12.8 (0-68).

CONCLUSION

The DVR-A plate achieved a highly satisfactory reduction of radial length and radial inclination, with a small loss of volar sagittal tilt at final follow-up. A good functional outcome was reported, with a satisfactory range of motion achieved. The DVR-A plate is a safe and effective treatment for unstable and intra-articular displaced distal radius fractures, particularly in younger patients, in the short term.

Spatial invasion dynamics on random and unstructured meshes: implications for heterogeneous tumor populations

In this work we discuss a spatial evolutionary model for a heterogeneous cancer cell population. We consider the gain-of-function mutations that not only change the fitness potential of the mutant phenotypes against normal background cells but may also increase the relative motility of the mutant cells. The spatial modeling is implemented as a stochastic evolutionary system on a structured grid (a lattice, with random neighborhoods, which is not necessarily bi-directional) or on a two-dimensional unstructured mesh, i.e. a bi-directional graph with random numbers of neighbors. We present a computational approach to investigate the fixation probability of mutants in these spatial models. Additionally, we examine the effect of the migration potential on the spatial dynamics of mutants on unstructured meshes. Our results suggest that the probability of fixation is negatively correlated with the width of the distribution of the neighborhood size. Also, the fixation probability increases given a migration potential for mutants. We find that the fixation probability (of advantaged, disadvantaged and neutral mutants) on unstructured meshes is relatively smaller than the corresponding results on regular grids. More importantly, in the case of neutral mutants the introduction of a migration potential has a critical effect on the fixation probability and increases this by orders of magnitude. Further, we examine the effect of boundaries and as intuitively expected, the fixation probability is smaller on the boundary of regular grids when compared to its value in the bulk. Based on these computational results, we speculate on possible better therapeutic strategies that may delay tumor progression to some extent.

Characterization of brain cancer stem cells: a mathematical approach

OBJECTIVE

In recent years, support has increased for the notion that a subpopulation of brain tumour cells in possession of properties typically characteristic of stem cells is responsible for initiating and maintaining the tumour. Unravelling details of the brain tumour stem cell (BTSC) hierarchy, as well as interactions of these cells with various therapies, will be essential in the design of optimal treatment strategies.

MATERIALS AND METHODS

Motivated by this, we have developed a mathematical model of the BTSC hypothesis that may aid in characterization of brain tumours, as well as in prediction of effective therapeutic strategies, which can be further validated in experimental and clinical studies. At the level of a small number of cells, the model developed herein is stochastic. For larger populations of cancer cells, the model is handled from a deterministic approach.

RESULTS AND CONCLUSIONS

In the stochastic regime, importance of a relationship between the likelihoods of two distinct types of symmetric BTSC divisions in determining BTSC survival rates becomes apparent, consequently emphasizing the need for a set of biomarkers that are able to better characterize the BTSC hierarchy. At the large scale, we predict the importance of the aforementioned symmetric division rates in dictating brain tumour composition. Furthermore, we demonstrate possible therapeutic benefits of considering combination treatments of radiotherapy and putative BTSC inhibitors, such as bone morphogenetic proteins, while reinforcing the importance of developing novel treatment strategies that specifically target the BTSC subpopulation.

A poroelastic model of transcapillary flow in normal tissue

Starling's seminal work on the absorption of fluids from connective tissue spaces (and Starling's hypothesis that the energy for transcapillary flow lies in the difference between hydrostatic and osmotic pressures across the capillary wall) has long formed the basis of much of experimental physiology. Related recent experimental evidence points to a more active role of the interstitium in controlling interstitial fluid pressure (IFP) which has significant implications for clinical oncology. In light of these considerations, it is clearly of importance to reconsider the relationship between IFP and transcapillary transport, in addition to the regulation of IFP in normal tissue. In this paper, we adopt the Michel-Weinbaum viewpoint on the locality of Starling forces and model the capillary wall as a poroelastic solid using Biot's consolidation theory. However, the incorporation of the Michel-Weinbaum hypothesis requires an extension of Darcy's law to include the effects of oncotic pressure in the mechanism of filtration through the capillary wall. A unique feature of the model of transcapillary flow developed here is its ability to predict the stress and strain distribution across the capillary wall, which to our knowledge has not been attempted previously. We are optimistic that, with rapidly advancing technological capabilities, experimentalists will soon be able to test many of the model predictions.

Dynamics of tumor growth and combination of anti-angiogenic and cytotoxic therapies

Tumors cannot grow beyond a certain size (about 1-2 mm in diameter) through simple diffusion of oxygen and other essential nutrients into the tumor. Angiogenesis, the formation of blood vessels from pre-existing vessels, is a crucial and observed step, through which a tumor obtains its own blood supply. Thus, strategies that interfere with the development of this tumor vasculature, known as anti-angiogenic therapy, represent a novel approach to controlling tumor growth. Several pre-clinical studies have suggested that currently available angiogenesis inhibitors are unlikely to yield significant sustained improvements in tumor control on their own, but rather will need to be used in combination with conventional treatments to achieve maximal benefit. Optimal sequencing of anti-angiogenic treatment and radiotherapy or chemotherapy is essential to the success of these combined treatment strategies. Hence, a major challenge to mathematical modeling and computer simulations is to find appropriate dosages, schedules and sequencing of combination therapies to control or eliminate tumor growth. Here, we present a mathematical model that incorporates tumor cells and the vascular network, as well as their interplay. We can then include the effects of two different treatments, conventional cytotoxic therapy and anti-angiogenic therapy. The results are compared with available experimental and clinical data.

Mathematical modeling of brain tumors: effects of radiotherapy and chemotherapy

Gliomas, the most common primary brain tumors, are diffusive and highly invasive. The standard treatment for brain tumors consists of a combination of surgery, radiation therapy and chemotherapy. Over the past few years, mathematical models have been applied to study untreated and treated brain tumors. In an effort to improve treatment strategies, we consider a simple spatio-temporal mathematical model, based on proliferation and diffusion, that incorporates the effects of radiotherapeutic and chemotherapeutic treatments. We study the effects of different schedules of radiation therapy, including fractionated and hyperfractionated external beam radiotherapy, using a generalized linear quadratic (LQ) model. The results are compared with published clinical data. We also discuss the results for combination therapy (radiotherapy plus temozolomide, a new chemotherapy agent), as proposed in recent clinical trials. We use the model to predict optimal sequencing of the postoperative (combination of radiotherapy and adjuvant, neo-adjuvant or concurrent chemotherapy) treatments for brain tumors.

The constitutive properties of the brain parenchyma

In this paper we study several constitutive equations for the brain based on the strain energy density function. We use the polynomial function and hyper-elastic Ogden model for the strain energy and include the energy dissipation by a Prony series expansion. The models are compared with known unconfined compression experimental results of the human brain tissue to obtain the best fitted model and brain mechanical parameters. Finite element simulations are also performed using the given constitutive equations, and numerical solutions match the analytical results very closely. The results are compared with other analytical and numerical calculations.

The constitutive properties of the brain paraenchyma

Fractional models have proven to be very useful for studying viscoelastic materials. We consider the fractional Zener model (also called four-parameter model) to study both the relaxation function and creep compliance. The analytical results are compared with the known experimental results of the human brain tissue to obtain the best fit and brain mechanical parameters. The results are also compared to the non-fractional Zener model and four-parameter Burgers model, indicating that the four-parameter fractional model gives a substantially better fit for the all experimental data.

Mathematical modeling of ovarian cancer treatments: sequencing of surgery and chemotherapy

Ovarian cancer has long been one of the most common forms of cancer in women. The main treatment for ovarian cancer comprises a combination of surgery and chemotherapy. In an effort to improve treatment strategies, a variety of mathematical models have been developed in the literature. In this paper, we consider a simple mathematical model that incorporates tumor growth as well as the effects of chemotherapeutic and surgical treatments in ovarian cancer. We consider several growth models and combine them with different cell-kill hypotheses. Surgery is assumed to eliminate a fixed fraction of tumor cells instantaneously. We discuss how different models predict the optimal sequencing of chemotherapeutic and surgical treatments. This work has been carried out in the context of ovarian cancer; however, the results may also be useful for other kind of cancers.

Frequency dependence of complex moduli of brain tissue using a fractional Zener model

Brain tissue exhibits viscoelastic behaviour. If loading times are substantially short, static tests are not sufficient to determine the complete viscoelastic behaviour of the material, and dynamic test methods are more appropriate. The concept of complex modulus of elasticity is a powerful tool for characterizing the frequency domain behaviour of viscoelastic materials. On the other hand, it is well known that classical viscoelastic models can be generalized by means of fractional calculus to describe more complex viscoelastic behaviour of materials. In this paper, the fractional Zener model is investigated in order to describe the dynamic behaviour of brain tissue. The model is fitted to experimental data of oscillatory shear tests of bovine brain tissue to verify its behaviour and to obtain the material parameters.

Dynamical Morphology of the Brain's Ventricular Cavities in Hydrocephalus

Although interest in the biomechanics of the brain goes back over centuries, mathematical models of hydrocephalus and other brain abnormalities are still in their infancy and a much more recent phenomenon. This is rather surprising, since hydrocephalus is still an endemic condition in the pediatric population with an incidence of approximately 1–3 per 1000 births. Treatment has dramatically improved over the last three decades, thanks to the introduction of cerebrospinal fluid (CSF) shunts. Their use, however, is not without problems and the shunt failure at two years remains unacceptably high at 50%. The most common factor causing shunt failure is obstruction, especially of the proximal catheters. There is currently no agreement among neurosurgeons as to the optimal catheter tip position; however, common sense suggests that the lowest risk location is the place that remains larger after ventricular decompression drainage. Thus, success in this direction will depend on the development of a quantitative theory capable of predicting the ultimate shape of the ventricular wall. In this paper, we report on some recent progress towards the solution to this problem.

Brain biomechanics: mathematical modeling of hydrocephalus

The considerable amount of literature on mathematical models of hydrocephalus and other brain abnormalities is critically reviewed. These models have various degrees of mathematical sophistication, and have influenced not only the diagnosis of hydrocephalus, but also its treatment with CSF shunts. The mathematical models are classified into two classes, pressure-volume models, and consolidation models. Advantages and disadvantages of both types are pointed out with a view to removing the confusion frequently generated by the technical aspects of the subject. The conclusion is reached that, while none of the current models are good enough to be of immediate use to the neurosurgeon, mathematical models are likely in the future to be a powerful tool for the understanding and the treatment of hydrocephalus, as well as other conditions related to brain biomechanics. The amount of mathematics has been kept to the absolute minimum, but it is cited and appended for those who would like to dig further into this fascinating area of research.

Correlation of survival time with size of axonal swellings in diffuse axonal injury

Widespread damage to axons in the white matter of the brain is a well-recognised consequence of non-missile head injury. This diffuse axonal injury is characterised by a gradual swelling of the axon associated with an accumulation of cellular organelles and proteins. We have investigated the relationship between the size of the swellings of the damaged axon with survival time in post-mortem brain tissue. Sixty-six cases of head injury with known length of post-traumatic survival were selected for study, and immunohistochemistry for beta-amyloid precursor protein (betaAPP) was carried out. The minimum diameter of the betaAPP-immunolabelled damaged axons was measured in micrometers using the IBAS image analysis system. There was a strong, positive and significant relationship between the mean size of axonal swelling and survival time which plateaued at around 85 h post injury. With longer survival times the situation becomes more complex. betaAPP immunolabelling of damaged axons can contribute evidence about trauma and post-injury survival time in the forensic setting but should always be assessed with other evidence.

Death from diesel fumes

A rare fatality from inhalation of diesel motor exhaust fumes is reported and the toxicity of diesel fumes is discussed briefly.

Decapitation--a rare complication in hanging

Decapitation from hanging is rare and there appears to be a lack of reports in scientific literature. Two cases of this phenomenon are reported.

Medical evidence for the defence in homicide trials

The legal system for the investigation of major crime appears to be rather loose, in that there are no specific statutory provisions available to a defendant to present his or her case properly and adequately in court. There are no guidelines issued to the coroners nor are there any legal powers available to them to facilitate and authorize post-mortem examinations on behalf of the defence. This paper focuses attention on this legal dilemma, and attempts to suggest possible remedies.

Early detection of axonal injury after human head trauma using immunocytochemistry for beta-amyloid precursor protein

Severe non-missile head injury commonly results in a form of brain damage known as diffuse axonal injury (DAI). The histological diagnosis of DAI is made by silver staining for the presence of axonal retraction balls. This feature takes about 24 h to develop and does not allow for the early histological diagnosis of DAI. We have used immunocytochemistry for the beta-amyloid precursor protein (beta APP) as a marker for axonal injury in formalin-fixed, paraffin-embedded sections of human brain. Axonal beta APP immunoreactivity was present in all cases which had survived for 3 h or more. This was true even where the degree of head injury did not appear to be severe, supporting the theory that DAI is a severe form of a more common phenomenon of axonal injury which occurs after cerebral trauma. beta APP immunoreactivity was also found in some non-head injured cases and so cannot be considered to be a specific marker for trauma. The results show that beta APP immunocytochemistry may be useful in the detection of traumatic axonal injury in its early stages, before the formation of axonal retraction balls, provided care is taken to exclude other causes of such immunoreactivity.

Markers of axonal injury in post mortem human brain

beta-Amyloid precursor protein (beta APP) can be detected immunocytochemically at sites of axonal injury in the brain, and has recently been found to be a useful marker for injured axons in patients who survived for only 3 h after head trauma. It is transported by fast axonal transport and is thought to accumulate in detectable levels where the cytoskeleton breaks down. If this theory is correct, other substances should accumulate here in the same way, so we have used antibodies to other neuronal proteins to compare their efficacy as markers of axonal injury. SNAP-25, chromogranin A and cathepsin D also marked injured axons at all survival times studied (2.5 h-2 weeks), although they were not as sensitive or specific as beta APP. Immunolabelling for the 68-kDa neurofilament subunit (NF68) was present in most uninjured axons, and allowed axonal swellings to be seen in some cases. Synaptophysin, GAP-43, ubiquitin or tau did not label any normal or injured axons in this study. We, therefore, suggest that beta APP should be the immunocytochemical marker of choice for the detection of injured axons. This study also showed that microwave antigen retrieval significantly enhances the immunoreactivity of SNAP-25, chromogranin A, synaptophysin, GAP-43, ubiquitin and tau, in addition to that of beta APP, in formalin-fixed, paraffin-embedded tissue, and reveals NF68 antigenicity where it was not previously detectable.

Diphtheria with a difference--a rare Corynebacterium fatality with associated apoptotic cell death

A case of infection with Corynebacterium ulcerans (C. ulcerans), resulted in the sudden death of a previously healthy 73-year-old woman. Death from Corynebacterium diphtheriae (C. diphtheriae) infection is well-documented. Fatalities following infection with C. ulcerans are unreported; this would appear to be the first documented death due to such infection.

Aspiration of high-density barium contrast medium causing acute pulmonary inflammation--report of two fatal cases in elderly women with disordered swallowing

Two cases are reported in which accidental inhalation of barium contrast medium occurred owing to disordered swallowing in elderly women. In each case there was a pulmonary inflammatory reaction followed within a few hours by death. Experimental and clinical reports of barium inhalation are reviewed and the hazard of aspiration of high density barium preparations in elderly and debilitated patients with dysphagia is emphasised. It is concluded that particular care should be taken in the radiological examination of such patients, and a suggested method for performing a contrast swallow in those who are liable to aspirate is described.

Demonstration of myocardial infarction in putrefying bodies

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Catheteroticum. Fatal late complication following autoerotic practice

This article describes a report of a death resulting as a late consequence of autoerotic practice. The deceased died of bronchopneumonia due to renal failure following a bladder calculus which had formed around a coiled plastic tube, presumably self-introduced for autoerotic purposes.

Aqua-eroticum--a case of auto-erotic drowning

An unusual case of accidental death during auto-erotic practice, where partial drowning was used to produce partial asphyxia, is reported.

Ante-mortem injury or post-mortem?--Diagnosis using histamine as a marker

A relatively simple method for differentiating ante-mortem from post-mortem injuries is described. It involves the demonstration of an increase in free histamine at sites of injury by fluorescent microscopy on the basis that release of free histamine is a very early vital reaction to injury.

Curiosum eroticum--a case of fatal electrocution during auto-erotic practice

A fatal case of accidental electrocution occurring during auto-erotic experimentation with electricity is described and the dermal histological features of electrical injury emphasized.

Spinal cord damage in a case of non-accidental injury in children

An unusual injury discovered as an incidental finding in a child who received other fatal non-accidental injury is described in this paper. This injury might have presented a difficult diagnostic problem had the child survived. This was the presence of a spinal extradural haemorrhage together with microscopic haemorrhage into the spinal cord at the mid-thoracic level.