Miguel Angel Herrero

This work is concerned with bone remodeling, an intriguing and efficient biological process that ensures the optimal compliance of the human skeleton by screening and replacing any single piece of it on a recursive basis. We propose here that a class of algorithms, which are simple enough to be implemented at an individual cell level, suffices to account for the two main features of such homeostatic process: thorough screening of the whole skeleton on the one hand and destruction and subsequent replacement of any single bone piece on the other. This last process is accomplished at a microscopic scale by special groups of cells, assembled for that purpose, called Bone Multicellular Units (BMUs). Moreover, it is shown that the algorithms proposed are robust, i.e, they remain functional in a wide range of biomechanical environments, thus allowing for different remodeling rates at different places.

The protection induced by vaccines against infectious diseases such as malaria, dengue or hepatitis relies on a the creation of immune memory by T cells, key components of the human immune system. The induction of a strong T cell response leading to long lasting memory can be improved by using prime-boost (PB) vaccines, which consist in successive inoculations of appropriate vectors carrying target antigens that can be recognized by specific T cell clones. A problem faced by PB vaccines is the fact that T cell response is often biased towards a few clones that can identify only a small set of antigens, out of the many that could be displayed by the pathogen. This phenomenon, known as immunodominance, can significantly compromise the effectiveness of vaccination. In this work we will use mathematical modeling to better understand the role of T cell population dynamics in the onset of immunodominance in PB vaccines. In particular, we will use mathematical analysis and simulations to compare single-dose vaccines with PB ones, both for homologous (where the same antigen is used in every shot) and heterologous protocols (in which different antigens are used at each step).

Human skeleton undergoes constant remodeling during the whole life. By means of such process, which occurs at a microscopic scale, worn out bone is replaced by new, fully functional one. Multiple bone remodeling events occur simultaneously and independently throughout the body, so the whole skeleton is completely renewed about every ten years. Bone remodeling is performed by groups of cells called Bone Multicellular Units (BMU). BMUs consist of different cell types; some are specialized in destroying old bone, whereas others produce new bone to replace the former. The whole process is tightly regulated so that the amount of new bone produced exactly balances that of old one removed and bone microscopic structure is maintained. To date, many regulatory molecules involved in bone remodeling have been identified, but the precise mechanism of BMU operation remains to be fully elucidated. Given the complexity of the signaling pathways already known, the question arises of ascertaining whether such complexity is an inherent requirement of the process, or a consequence of operational redundancy. In this work we propose a minimal model of BMU function which involves a small number of signals and accounts for fully functional BMU operation. Our main assumptions are i) at any given time, any cell within a BMU can select only one among a reduced choice of decisions: divide, die, migrate or differentiate, ii) such decision is irreversibly determined by depletion of an appropriate internal inhibitor and iii) the dynamics of any such inhibitor is coupled to that of a few external mediators. It is shown that efficient BMU operation then unfolds as an emergent property, which results from individual decisions taken by cells in the BMU unit in the absence of any external planning. Author summary: Our skeleton is a living organ that is being renewed throughout our life. This task is accomplished by teams of bone cells termed as Bone Multicellular Units (BMUs) that are recruited when and where needed, to operate at places where bone has lost functionality either for an excess of mechanical stress or because loss of activity. Once assembled, BMU remove old bone and replace it by new one, and disband as soon as their mission has been accomplished. No single bone evades BMU screening, so that the whole human skeleton is completely renewed approximately every ten years. It is natural to wonder how such robust and fascinating process is regulated. Many signaling pathways involved in bone remodeling have been identified so far, but whether all of them are necessary for BMU operation remains unclear. In this work we show that just a reduced number of such signals could suffice for that purpose. This suggests that a large degree of redundancy might have been kept in place, perhaps as a consequence of different convergent strategies developed in the course of evolution.

The choice of any radiotherapy treatment plan is usually made after the evaluation of a few preliminary isodose distributions obtained from different beam configurations. Despite considerable advances in planning techniques, such final decision remains a challenging task that would greatly benefit from efficient and reliable assessment tools. For any dosimetric plan considered, data on dose-volume histograms supplied by treatment planning systems are used to provide estimates on planning target coverage as well as on sparing of organs at risk and the remaining healthy tissue. These partial metrics are then combined into a dose distribution index (DDI), which provides a unified, easy-to-read score for each competing radiotherapy plan. To assess the performance of the proposed scoring system, DDI figures for fifty brain cancer patients were retrospectively evaluated. Patients were divided in three groups depending on tumor location and malignancy. For each patient, three tentative plans were designed and recorded during planning, one of which was eventually selected for treatment. We thus were able to compare the plans with better DDI scores and those actually delivered. When planning target coverage and organs at risk sparing are considered as equally important, the tentative plan with the highest DDI score is shown to coincide with that actually delivered in 32 of the 50 patients considered. In 15 (respectively 3) of the remaining 18 cases, the plan with highest DDI value still coincides with that actually selected, provided that organs at risk sparing is given higher priority (respectively, lower priority) than target coverage. DDI provides a straightforward and non-subjective tool for dosimetric comparison of tentative radiotherapy plans. In particular, DDI readily quantifies differences among competing plans with similar-looking dose-volume histograms and can be easily implemented for any tumor type and localization, irrespective of the planning system and irradiation technique considered. Moreover, DDI permits to estimate the dosimetry impact of different priorities being assigned to sparing of organs at risk or to better target coverage.

This work is concerned with the sequence of events taking place during the first stages of bone fracture healing, from bone breakup until the formation of early fibrous callus (EFC). The latter provides a scaffold over which subsequent remodeling processes will eventually result in successful bone repair. Specifically, some mathematical models are proposed to estimate the time required for (1) the formation immediately after fracture of a fibrin clot, described in terms of a phase transition in a polymerization process, and (2) the onset of EFC which is produced when fibroblasts arising from differentiation of chemotactically recruited mesenchymal stem cells remodel a previous fibrin clot by releasing a collagen matrix over it. An attempt has been made to keep models as simple as possible, so that a explicit dependence of the estimates obtained on relevant biochemical parameters involved is obtained.

The main steps in planning radiotherapy consist in selecting for any patient diagnosed with a solid tumor (i) a prescribed radiation dose on the tumor, (ii) bounds on the radiation side effects on nearby organs at risk and (iii) a fractionation scheme specifying the number and frequency of therapeutic sessions during treatment. The goal of any radiotherapy treatment is to deliver on the tumor a radiation dose as close as possible to that selected in (i), while at the same time conforming to the constraints prescribed in (ii). To this day, considerable uncertainties remain concerning the best manner in which such issues should be addressed. In particular, the choice of a prescription radiation dose is mostly based on clinical experience accumulated on the particular type of tumor considered, without any direct reference to quantitative radiobiological assessment. Interestingly, mathematical models for the effect of radiation on biological matter have existed for quite some time, and are widely acknowledged by clinicians. However, the difficulty to obtain accurate in vivo measurements of the radiobiological parameters involved has severely restricted their direct application in current clinical practice. In this work, we first propose a mathematical model to select radiation dose distributions as solutions (minimizers) of suitable variational problems, under the assumption that key radiobiological parameters for tumors and organs at risk involved are known. Second, by analyzing the dependence of such solutions on the parameters involved, we then discuss the manner in which the use of those minimizers can improve current decision-making processes to select clinical dosimetries when (as is generally the case) only partial information on model radiosensitivity parameters is available. A comparison of the proposed radiation dose distributions with those actually delivered in a number of clinical cases strongly suggests that solutions of our mathematical model can be instrumental in deriving good quality tests to select radiotherapy treatment plans in rather general situations.

Tumor heterogeneity is widely considered to be a determinant factor in tumor progression and in particular in its recurrence after therapy. Unfortunately, current medical techniques are unable to deduce clinically relevant information about tumor heterogeneity by means of non-invasive methods. As a consequence, when radiotherapy is used as a treatment of choice, radiation dosimetries are prescribed under the assumption that the malignancy targeted is of a homogeneous nature. In this work we discuss the effects of different radiation dose distributions on heterogeneous tumors by means of an individual cell-based model. To that end, a case is considered where two tumor cell phenotypes are present, which we assume to strongly differ in their respective cell cycle duration and radiosensitivity properties. We show herein that, as a result of such differences, the spatial distribution of the corresponding phenotypes, whence the resulting tumor heterogeneity can be predicted as growth proceeds. In particular, we show that if we start from a situation where a majority of ordinary cancer cells (CCs) and a minority of cancer stem cells (CSCs) are randomly distributed, and we assume that the length of CSC cycle is significantly longer than that of CCs, then CSCs become concentrated at an inner region as tumor grows. As a consequence we obtain that if CSCs are assumed to be more resistant to radiation than CCs, heterogeneous dosimetries can be selected to enhance tumor control by boosting radiation in the region occupied by the more radioresistant tumor cell phenotype. It is also shown that, when compared with homogeneous dose distributions as those being currently delivered in clinical practice, such heterogeneous radiation dosimetries fare always better than their homogeneous counterparts. Finally, limitations to our assumptions and their resulting clinical implications will be discussed.