Tumour growth control: analysis of alternative approaches.

In this work we address the problem of tumour growth control by properly exploiting a low-dimensional model that grounds on the Chemical Reaction Network (CRN) formalism. Originally conceived to work both in deterministic and stochastic frameworks, it is shown that, except for the case of very low number of tumour cells, the deterministic approach is appropriate to characterize the system behaviour, especially for control planning purposes. Two alternative control approaches are here investigated. One trivially assumes a constant infusion of external drug administration, the other is designed according to a state-feedback control scheme, with complete or partial knowledge of the state. Pros and cons of both control laws are investigated, showing that the tumour size at the beginning of the therapy plays a role of paramount importance for fixed infusion therapies, whilst only state-feedback laws can eradicate arbitrarily large tumours.

Modeling continuous glucose monitoring with fractional differential equations subject to shocks.

Continuous Glucose Monitoring (CGM) produces long time-series of noisy observations of a single variable (tissue glucose concentration), whose evolution may be explained by a dynamical model. In order to represent the unknown mixture of possible control mechanisms of different orders affecting the measured variable, a fractional differential approach seems justified. In any case, variations in food intake and/or physical activity ought to be taken into account if a plausible interpretation of the dynamics is to be obtained. In the present work, the mathematical construction and the numerical implementation of a Fractional Differential Equations (FDE) initial value problem are systematically reviewed, with the intent of offering the reader a concise and mathematically rigorous description of this approach. An FDE model for CGM is formulated: the model includes compartments for stomach and intestinal glucose contents and for blood and tissue (subcutaneous) glucose concentrations, as well as the shock effects of food ingestion and of increased glucose consumption due to physical activity. The model parameters, including the (non-integer) order of differentiation, are estimated from CGM observations on six Type 1 diabetic patients. The best-fit fractional orders for the six subjects range from 1.59 to 2.13. For comparison, best fits have also been computed for all subjects using an average fractional order of 1.9 and integer orders of 1 and 2.The results indicate that in the case of CGM the fractional differential model, which should be physiologically more appropriate, in fact fits the data much better than the first-order model and also better than the 2nd-order model.

A quasi-equilibrium reduced model of pancreatic insulin secretion.

Much attention has been devoted in the last few decades to mathematical models of insulin secretion, in order to better understand the regulation of glycemia and its derangements. The glucose-insulin homeostatic mechanism is so complex and gives rise to such diverse behavior following perturbations that different models had been published, which reproduced the results of single experiments. More recently, a unifying model of pancreatic insulin secretion was proposed, which is able to account, with a single value of the (meta)parameters, for the wide array of clinically observed behavior. This model explicitly represented the pulsatile nature of the many pancreatic hormone-secreting firing units: the price to pay for its flexibility and performance is the very high dimensionality (hundreds of thousand equations) of the corresponding dynamical system. Clearly, it would be desirable to reduce this model to a much simpler form while retaining its power to reproduce heterogeneous phenomena. The present work reviews the qualitative behavior of this pancreas pulsatile model and offers some insight into its reduction in equilibrium and quasi-equilibrium conditions, also considering single-shot (non-repeated) glucose jumps from an approximately resting condition (such as would occur in standard Intra-Venous bolus dosing of glucose during diabetes diagnostic maneuvers). The resulting quasi-steady-state model can be further endowed with additional lower-order dynamics to also approximate transient behavior. Although a more accurate reduction of the original pulsatile model is left to further investigation, numerical results confirm the biomedical applicability of the formulation already obtained.

Optimal design of lock-down and reopening policies for early-stage epidemics through SIR-D models.

The diffusion of COVID-19 represents a real threat for the health and economic system of a country. Therefore the governments have to adopt fast containment measures in order to stop its spread and to prevent the related devastating consequences. In this paper, a technique is proposed to optimally design the lock-down and reopening policies so as to minimize an aggregate cost function accounting for the number of individuals that decease due to the spread of COVID-19. A constraint on the maximal number of concomitant infected patients is also taken into account in order to prevent the collapse of the health system. The optimal procedure is built on the basis of a simple SIR model that describes the outbreak of a generic disease, without attempting to accurately reproduce all the COVID-19 epidemic features. This modeling choice is motivated by the fact that the containing measurements are actuated during the very first period of the outbreak, when the characteristics of the new emergent disease are not known but timely containment actions are required. In fact, as a consequence of dealing with poor preliminary data, the simplest modeling choice is able to reduce unidentifiability problems. Further, the relative simplicity of this model allows to compute explicitly its solutions and to derive closed-form expressions for the maximum number of infected and for the steady-state value of deceased individuals. These expressions can be then used to design static optimization problems so to determine the (open-loop) optimal lock-down and reopening policies for early-stage epidemics accounting for both the health and economic costs.

Mixture distributions in a stochastic gene expression model with delayed feedback: a WKB approximation approach.

Noise in gene expression can be substantively affected by the presence of production delay. Here we consider a mathematical model with bursty production of protein, a one-step production delay (the passage of which activates the protein), and feedback in the frequency of bursts. We specifically focus on examining the steady-state behaviour of the model in the slow-activation (i.e. large-delay) regime. Using a formal asymptotic approach, we derive an autonomous ordinary differential equation for the inactive protein that applies in the slow-activation regime. If the differential equation is monostable, the steady-state distribution of the inactive (active) protein is approximated by a single Gaussian (Poisson) mode located at the globally stable fixed point of the differential equation. If the differential equation is bistable (due to cooperative positive feedback), the steady-state distribution of the inactive (active) protein is approximated by a mixture of Gaussian (Poisson) modes located at the stable fixed points; the weights of the modes are determined from a WKB approximation to the stationary distribution. The asymptotic results are compared to numerical solutions of the chemical master equation.

Ten Years' Experience in Robotic-Assisted Thoracic Surgery for Early Stage Lung Cancer.

BACKGROUND: This study analyzed the short- and long-term outcomes of robotic-assisted thoracic surgery (RATS) for early stage non-small cell lung cancer (NSCLC). METHODS: From November 2006 to December 2016, we performed 363 RATS procedures. This study retrospectively reviewed 339 patients who underwent RATS for clinical stages I (n = 318) or II (n = 21) NSCLC. RESULTS: Twenty-nine patients underwent segmentectomy, 307 lobectomy, and 3 pneumonectomy. Conversion occurred in 22 patients (6.5%): 15 (4.4%) due to technical issues, 4 (1.2%) for oncological reasons, and 3 (0.9%) for bleeding. The median number of N1 and N2 stations resected was 2 and 3, respectively, and the median number of N1 and N2 lymph nodes resected was 9 and 6, respectively. Median operative time was 192 minutes for lobectomy, 172 minutes for segmentectomy, and 275 minutes for pneumonectomy. Median length of hospital stay was 5 days (2-191). The most common postoperative complication was prolonged air leak (12.1%). Major complications occurred in eight patients (2.4%). The 30-day and 90-day operative mortality was 0% and 0.3%, respectively. Two and 5-year cancer-specific survival rate was 96.1% and 91.5%, respectively. Five-year survival rate was 96.2% for patients who underwent segmentectomy, and 89.1% for lobectomy. All three patients who underwent pneumonectomy were alive at 5 years with no disease. CONCLUSIONS: Besides the well-known short-term outcomes showing very low morbidity and mortality rates, mediastinal lymph node dissection during RATS adequately assesses lymph node stations detecting occult lymph node metastasis and leading to excellent oncologic results. However, these results await longer follow-up studies.

Efficacy and safety of Innoseal for air leak after pulmonary resection: a case-control study.

BACKGROUND: Prolonged air leak is one of the most common complications after lung surgery and the cause of prolonged hospital stay frequently associated with major postoperative morbidity and thus responsible for even higher hospital costs. This case-control study was designed to test the sealing efficacy and safety of Enable-Innoseal TP4 in patients undergoing pulmonary resection for lung cancer. METHODS: This was a case-control trial enrolling patients with primary or single site metastatic lung cancer scheduled for elective anatomic or nonanatomic pulmonary resection presenting intraoperative grade 1 or 2 air leak at water submersion test; the study group population was then matched 1:1 according to surgical procedure, male/female ratio, preoperative FEV1, and age. RESULTS: In the study population, 21 patients (70.0%) presented intraoperative grade 1 air leak and 9 patients grade 2 (30.0%) air leak; after comparison with the control group, we observed a significant shorter time for chest drain removal in the study population (P = 0.0050), whereas no difference was registered in terms of number of days needing for discharge (P = 0.0762). CONCLUSIONS: Enable-Innoseal TP4 was effective in treating limited intraoperative air leaks after pulmonary resection and preventing prolonged postoperative air leaks in patients receiving either anatomic or nonanatomic lung resections. Further randomized double-arm studies are required to confirm the efficacy of Enable-Innoseal TP4 demonstrated by this pilot study.

A glycemia-structured population model.

Structured models are population models in which the individuals are characterized with respect to the value of some variable of interest, called the structure variable. In the present paper, we propose a glycemia-structured population model, based on a linear partial differential equation with variable coefficients. The model is characterized by three rate functions: a new-adult population glycemic profile, a glycemia-dependent mortality rate and a glycemia-dependent average worsening rate. First, we formally analyze some properties of the solution, the transient behavior and the equilibrium distribution. Then, we identify the key parameters and functions of the model from real-life data and we hypothesize some plausible modifications of the rate functions to obtain a more beneficial steady-state behavior. The interest of the model is that, while it summarizes the evolution of diabetes in the population in a completely different way with respect to previously published Monte Carlo aggregations of individual-based models, it does appear to offer a good approximation of observed reality and of the features expected in the clinical setting. The model can offer insights in pharmaceutical research and be used to assess possible public health intervention strategies.

Chest wall resection and reconstruction for locally recurrent breast cancer: From technical aspects to biological assessment.

INTRODUCTION: Breast cancer is the leading cause of cancer death among women in the industrialized countries. The incidence of local recurrences after mastectomy and breast-conserving therapy varies between 5% and 40% depending on risk factors and primary therapy. METHODS: From April 1999 to April 2011, 40 patients underwent chest wall resection and reconstruction for locally recurrent breast carcinoma with chest wall invasion. The main goal of surgery was local disease control to palliate clinical symptoms. RESULTS: Local radical resection was achieved in 26 patients (65%). One, 2 and 5 year overall survival rates were 94.4%, 82.0% and 68.5%; 1, 2 and 5 year disease-free survival rates were 94.4%, 73.6% and 45.5% respectively. Univariate analysis indicated age (p = 0.002) and synchronous distant metastases (p = 0.020) as factors having a negative impact on overall survival; multivariate analysis disclosed age (p = 0.052) and synchronous metastases (p = 0.059) as factors with a slight negative impact on overall survival. Older age was associated with improved overall survival. Univariate analysis indicated synchronous distant metastases (p = 0.029) and the need of post resectional additional treatments (p = 0.022) as factors adversely conditioning disease-free survival or time to progression; multivariate analysis disclosed the need of post resectional additional treatments (p = 0.036) as the only factor adversely conditioning disease-free survival or time to progression. CONCLUSIONS: Chest wall resection and reconstruction for locally recurrent breast cancer is a feasible and safe procedure providing adequate local disease control and an excellent palliation of very disabling symptoms in a selected group of patients.

Simulation of Trauma Incidents : Modelling the Evolution of Patients and Resources.

Mathematical modeling and simulation with medical applications has gained much interest in the last few years, mainly due to the widespread availability of low-cost technology and computational power. This paper presents an integrated platform for the in-silico simulation of trauma incidents, based on a suite of interacting mathematical models. The models cover the generation of a scenario for an incident, a model of physiological evolution of the affected individuals, including the possible effect of the treatment, and a model of evolution in time of the required medical resources. The problem of optimal resource allocation is also investigated. Model parameters have been identified according to the expertise of medical doctors and by reviewing some related literature. The models have been implemented and exposed as web services, while some software clients have been built for the purpose of testing. Due to its extendability, our integrated platform highlights the potential of model-based simulation in different health-related fields, such as emergency medicine and personal health systems. Modifications of the models are already being used in the context of two funded projects, aiming at evaluating the response of health systems to major incidents with and without model-based decision support.

Perioperative blood transfusion practices in oncologic thoracic surgery: when, why, and how.

INTRODUCTION: Available information on perioperative blood transfusion practices in oncologic thoracic surgery is scant and outdated. The purpose of this study was to investigate transfusion requirements in patients undergoing curative resection for lung cancer and to identify possible factors predictive of perioperative blood transfusion in our cohort of patients. METHODS: From 1st January 2009 to 31st December 2009, 317 patients underwent anatomic pulmonary resection. Patients who received at least 1 unit of red blood cells comprised the "transfused" group. Each case in this group was matched for surgical procedure with a control subject who did not require blood transfusion and was operated on during the same year; these patients comprised the "not transfused" group. RESULTS: A total of 75 patients (23.6%) received at least 1 unit of red blood cells during the perioperative period. Factors conditioning perioperative blood transfusion were: preoperative hemoglobin level (p < 0.0001); procedure duration (p = 0.017); body mass index (p < 0.001); induction therapies (p = 0.017); redo procedure (p = 0.021). Age, sex, histology, stage, ASA score, side, intraoperative blood loss, and fluid infusion did not affect perioperative blood transfusion practices. CONCLUSIONS: Preoperative hemoglobin level is the major risk factor for perioperative blood transfusion practices in oncologic thoracic surgery; procedure duration, body mass index, induction therapies, and redo procedure may condition transfusional needs, although they were actually not predictive on multivariate analysis.

Characterizing Fractal Genetic Variation in the Human Genome from the Hapmap Project.

Over the last decades, the exuberant development of next-generation sequencing has revolutionized gene discovery. These technologies have boosted the mapping of single nucleotide polymorphisms (SNPs) across the human genome, providing a complex universe of heterogeneity characterizing individuals worldwide. Fractal dimension (FD) measures the degree of geometric irregularity, quantifying how "complex" a self-similar natural phenomenon is. We compared two FD algorithms, box-counting dimension (BCD) and Higuchi's fractal dimension (HFD), to characterize genome-wide patterns of SNPs extracted from the HapMap data set, which includes data from 1184 healthy subjects of eleven populations. In addition, we have used cluster and classification analysis to relate the genetic distances within chromosomes based on FD similarities to the geographical distances among the 11 global populations. We found that HFD outperformed BCD at both grand average clusterization analysis by the cophenetic correlation coefficient, in which the closest value to 1 represents the most accurate clustering solution (0.981 for the HFD and 0.956 for the BCD) and classification (79.0% accuracy, 61.7% sensitivity, and 96.4% specificity for the HFD with respect to 69.1% accuracy, 43.2% sensitivity, and 94.9% specificity for the BCD) of the 11 populations present in the HapMap data set. These results support the evidence that HFD is a reliable measure helpful in representing individual variations within all chromosomes and categorizing individuals and global populations.

ARDS after Pneumonectomy: How to Prevent It? Development of a Nomogram to Predict the Risk of ARDS after Pneumonectomy for Lung Cancer.

(1) Background: The cause of ARDS after pneumonectomy is still unclear, and the study of risk factors is a subject of debate. (2) Methods: We reviewed a large panel of pre-, peri- and postoperative data of 211 patients who underwent pneumonectomy during the period 2014−2021. Univariable and multivariable logistic regression was used to quantify the association between preoperative parameters and the risk of developing ARDS, in addition to odds ratios and their respective 95% confidence intervals. A backward stepwise selection approach was used to limit the number of variables in the final multivariable model to significant independent predictors of ARDS. A nomogram was constructed based on the results of the final multivariable model, making it possible to estimate the probability of developing ARDS. Statistical significance was defined by a two-tailed p-value < 0.05. (3) Results: Out of 211 patients (13.3%), 28 developed ARDS. In the univariate analysis, increasing age, Charlson Comorbidity Index and ASA scores, DLCO < 75% predicted, preoperative C-reactive protein (CRP), lung perfusion and duration of surgery were associated with ARDS; a significant increase in ARDS was also observed with decreasing VO2max level. Multivariable analysis confirmed the role of ASA score, DLCO < 75% predicted, preoperative C-reactive protein and lung perfusion. Using the nomogram, we classified patients into four classes with rates of ARDS ranking from 2.0% to 34.0%. (4) Conclusions: Classification in four classes of growing risk allows a correct preoperative stratification of these patients in order to quantify the postoperative risk of ARDS and facilitate their global management.

Predicting prolonged air leak after standard pulmonary lobectomy: computed tomography assessment and risk factors stratification.

BACKGROUND: Prolonged air leak after pulmonary lobectomy is a common time- and cost-consuming complication. Its prevention may significantly reduce hospitalization length and costs offering patients a standard uneventful postoperative course. The aim of the present study is to identify predictors of prolonged postoperative air leak and to stratify preoperative risk factors. METHODS: From July 2004 to December 2007 241 consecutive standard lobectomies were performed with curative intent for lung cancer. After excluding patients not fulfilling the inclusion criterion, 58 patients were enrolled in the "prolonged air leak" group and 63 patients were enrolled in the "standard outcome" group. RESULTS: Total lung capacity (p=0.0038) and percentage emphysema (p=0.0050) calculated by computed tomography were both significantly related to prolonged postoperative air leak; the values of 4773cc and 0.4% showed the highest predictive value in terms of sensitivity (84.5% and 75.9% respectively). Multivariate logistic regression disclosed that male sex (p=0.0006), right side of operation (p=0.0010) and age (p=0.0082) were significantly related to prolonged postoperative air leak. Preoperative chemotherapy (p=0.0940) did not affect air leak status. CONCLUSIONS: Computed tomography quantification of emphysema is the best predictor of prolonged air leak. Age, male sex and right side lobectomy are correlated to this complication. Preoperative chemotherapy is not an additional risk factor.

A comparison among three maximal mathematical models of the glucose-insulin system.

The most well-known and widely used mathematical representations of the physiology of a diabetic individual are the Sorensen and Hovorka models as well as the UVAPadova Simulator. While the Hovorka model and the UVAPadova Simulator only describe the glucose metabolism of a subject with type 1 diabetes, the Sorensen model was formulated to simulate the behaviour of both normal and diabetic individuals. The UVAPadova model is the most known model, accepted by the FDA, with a high level of complexity. The Hovorka model is the simplest of the three models, well documented and used primarily for the development of control algorithms. The Sorensen model is the most complete, even though some modifications were required both to the model equations (adding useful compartments for modelling subcutaneous insulin delivery) and to the parameter values. In the present work several simulated experiments, such as IVGTTs and OGTTs, were used as tools to compare the three formulations in order to establish to what extent increasing complexity translates into richer and more correct physiological behaviour. All the equations and parameters used for carrying out the simulations are provided.

Laparoscopic vaginal lateral suspension: technical aspects and initial experience.

BACKGROUND: Pelvic organ prolapse (POP) etiology is a combination of anatomical, physiological, genetic, lifestyle, and reproductive factors determine pelvic floor dysfunction. POP is very common across all ages women worldwide and has become an increasing socioeconomic problem with public health consequences, with symptoms that could lead to a significant decrease in quality of life. METHODS: This study retrospectively analyzes a small case series of our initial experience of laparoscopic vaginal suspension with mesh focusing on the technical aspects of the technique. Although sacrocolpopexy and sacrohysteropexy are the most performed surgical techniques, they are associated with serious complications. Laparoscopic vaginal suspension appears reproducible and safe to learn. RESULTS: Between November 2017 and January 2020, fifteen patients underwent laparoscopic vaginal suspension for pelvic organ prolapse repair. Despite the small number, for a minimally invasive skilled surgeon, we notice a significative reduction of the learning curve to become proficient in this procedure. CONCLUSIONS: The diagnosis and management of pelvic organ prolapse are further complicated by what is considered "successful" treatment. Laparoscopic vaginal suspension is a feasible surgical procedure for one-stage treatment of pelvic organ prolapse.

A mathematical model of cardiovascular dynamics for the diagnosis and prognosis of hemorrhagic shock.

A variety of mathematical models of the cardiovascular system have been suggested over several years in order to describe the time-course of a series of physiological variables (i.e. heart rate, cardiac output, arterial pressure) relevant for the compensation mechanisms to perturbations, such as severe haemorrhage. The current study provides a simple but realistic mathematical description of cardiovascular dynamics that may be useful in the assessment and prognosis of hemorrhagic shock. The present work proposes a first version of a differential-algebraic equations model, the model dynamical ODE model for haemorrhage (dODEg). The model consists of 10 differential and 14 algebraic equations, incorporating 61 model parameters. This model is capable of replicating the changes in heart rate, mean arterial pressure and cardiac output after the onset of bleeding observed in four experimental animal preparations and fits well to the experimental data. By predicting the time-course of the physiological response after haemorrhage, the dODEg model presented here may be of significant value for the quantitative assessment of conventional or novel therapeutic regimens. The model may be applied to the prediction of survivability and to the determination of the urgency of evacuation towards definitive surgical treatment in the operational setting.

A revised Sorensen model: Simulating glycemic and insulinemic response to oral and intra-venous glucose load.

In 1978, Thomas J. Sorensen defended a thesis in chemical engineering at the University of California, Berkeley, where he proposed an extensive model of glucose-insulin control, model which was thereafter widely employed for virtual patient simulation. The original model, and even more so its subsequent implementations by other Authors, presented however a few imprecisions in reporting the correct model equations and parameter values. The goal of the present work is to revise the original Sorensen's model, to clearly summarize its defining equations, to supplement it with a missing gastrio-intestinal glucose absorption and to make an implementation of the revised model available on-line to the scientific community.

Diagnostic biomarkers for lung cancer prevention.

Lung cancer is the leading cause of death for neoplasm. Lung cancer mortality is frequently associated with late diagnosis, therefore an early diagnosis is a key factor to significantly improve overall survival in high risk populations of asymptomatic patients. Conventional cancer screenings (low-dose computed tomography or chest x-ray) today offer early detection but are invasive and expensive. Previously these studies evaluated the solid and topographic cancer structure and morphology. Today the concept of tumor has been remodelled, being defined as a disease that has its own genetic, biological and metabolic identity; it is on this new awareness that we should base new screening methods. Recent research has shown great reliability of new tests such as exhaled breath analysis, serum biomarkers and urine analysis in early diagnosis of lung cancer. Analysis of new biomarkers associated with the high specificity of these new screening methods, which are non-invasive, safe, inexpensive and simple to perform, could allow a non-invasive approach to determine a big change in the early diagnosis of cancer and its survival rate. Furthermore, these new techniques put the patient at the core of a non-invasive diagnostic process and ensure a better quality of life during medical diagnosis. In this article, we want to analyze the possible benefits of these new and promising methods, suggesting a possible combination between them to ensure, as soon as possible, an early and effective diagnosis of lung cancer with a special focus on the patient, in a new era of personalized medicine.