Medicine, Biology and Mathematics

Although mathematics finds large application in physical sciences, its use in the medical and biological field is less usual. Nevertheless, mathematical models can help in understanding many medical and biological phenomena and they can be a powerful tool in the designing process of many technological devices connected to the above mentioned phenomena. Of course, fundamental pre-requisite for building up a reliable mathematical model is the deep cooperation of different competences such as those of medical doctors, biologists, pharmacists and engineers. This paper deals with four different examples of mathematical models developed by our group and dealing with restenosis, enzyme action on two dimensional DNA brushes, oral delivery of drug in amorphous or nano-crystalline form and tumour cell behaviour

Plant respiration : Controlled by photosynthesis or biomass?

Abstract Two simplifying hypotheses have been proposed for whole-plant respiration. One links respiration to photosynthesis; the other to biomass. Using a first-principles carbon balance model with a prescribed live woody biomass turnover, applied at a forest research site where multidecadal measurements are available for comparison, we show that if turnover is fast the accumulation of respiring biomass is low and respiration depends primarily on photosynthesis; while if turnover is slow the accumulation of respiring biomass is high and respiration depends primarily on biomass. But the first scenario is inconsistent with evidence for substantial carryover of fixed carbon between years, while the second implies far too great an increase in respiration during stand development ? leading to depleted carbohydrate reserves and an unrealistically high mortality risk. These two mutually incompatible hypotheses are thus both incorrect. Respiration is not linearly related either to photosynthesis or to biomass, but it is more strongly controlled by recent photosynthates (and reserve availability) than by total biomass.Peer reviewe

Dissolution of an ensemble of differently shaped poly-dispersed drug particles undergoing solubility reduction: mathematical modelling

The aim of this theoretical paper is to develop a mathematical model for describing the dissolution process, in a finite liquid environment, of an ensemble of poly-dispersed drug particles, in form of sphere, cylinder and parallelepiped that can undergo solubility reduction due to phase transition induced by dissolution. The main result of this work consists in its simplicity as, whatever the particular particles size distribution, only two ordinary differential equations are needed to describe the dissolution process. This, in turn, reflects in a very powerful and agile theoretical tool that can be easily implemented in electronic sheets, a widespread tool among the research community. Another model advantage lies on the possibility of determining its parameters by means of common independent techniques thus enabling the evaluation of the importance of solid wettability on the dissolution process.</p

A physiologically-oriented mathematical model for the description of in vivo drug release and absorption

This paper focuses on a physiologically-oriented mathematical model aimed at studying the in vivo drug release, absorption, distribution, metabolism and elimination (ADME). To this purpose, the model accounts for drug delivery from an ensemble of non-eroding poly-disperse polymeric particles and the subsequent ADME processes. The model outcomes are studied with reference to three widely used drugs: theophylline, temazepam and nimesulide. One of the most important results of this study is the quantitative evaluation of the interplay between the release kinetics and the subsequent ADME processes. Indeed, it is usually assumed that in vivo drug release coincides with in vitro so that the effect exerted by the ADME processes is neglected. In addition, the proposed model may be an important tool for the design of delivery systems since, through proper changes, it could also account for different oral delivery systems

&quot;Delirium Day&quot;: A nationwide point prevalence study of delirium in older hospitalized patients using an easy standardized diagnostic tool

Background: To date, delirium prevalence in adult acute hospital populations has been estimated generally from pooled findings of single-center studies and/or among specific patient populations. Furthermore, the number of participants in these studies has not exceeded a few hundred. To overcome these limitations, we have determined, in a multicenter study, the prevalence of delirium over a single day among a large population of patients admitted to acute and rehabilitation hospital wards in Italy. Methods: This is a point prevalence study (called "Delirium Day") including 1867 older patients (aged 65 years or more) across 108 acute and 12 rehabilitation wards in Italian hospitals. Delirium was assessed on the same day in all patients using the 4AT, a validated and briefly administered tool which does not require training. We also collected data regarding motoric subtypes of delirium, functional and nutritional status, dementia, comorbidity, medications, feeding tubes, peripheral venous and urinary catheters, and physical restraints. Results: The mean sample age was 82.0 ± 7.5 years (58 % female). Overall, 429 patients (22.9 %) had delirium. Hypoactive was the commonest subtype (132/344 patients, 38.5 %), followed by mixed, hyperactive, and nonmotoric delirium. The prevalence was highest in Neurology (28.5 %) and Geriatrics (24.7 %), lowest in Rehabilitation (14.0 %), and intermediate in Orthopedic (20.6 %) and Internal Medicine wards (21.4 %). In a multivariable logistic regression, age (odds ratio [OR] 1.03, 95 % confidence interval [CI] 1.01-1.05), Activities of Daily Living dependence (OR 1.19, 95 % CI 1.12-1.27), dementia (OR 3.25, 95 % CI 2.41-4.38), malnutrition (OR 2.01, 95 % CI 1.29-3.14), and use of antipsychotics (OR 2.03, 95 % CI 1.45-2.82), feeding tubes (OR 2.51, 95 % CI 1.11-5.66), peripheral venous catheters (OR 1.41, 95 % CI 1.06-1.87), urinary catheters (OR 1.73, 95 % CI 1.30-2.29), and physical restraints (OR 1.84, 95 % CI 1.40-2.40) were associated with delirium. Admission to Neurology wards was also associated with delirium (OR 2.00, 95 % CI 1.29-3.14), while admission to other settings was not. Conclusions: Delirium occurred in more than one out of five patients in acute and rehabilitation hospital wards. Prevalence was highest in Neurology and lowest in Rehabilitation divisions. The "Delirium Day" project might become a useful method to assess delirium across hospital settings and a benchmarking platform for future surveys

The three-dimensional single-bin-size bin packing problem: combining metaheuristic and machine learning approaches

The Three-Dimensional Single-Bin-Size Bin Packing Problem is one of the most studied problem in the Cutting & Packing category. From a strictly mathematical point of view, it consists of packing a finite set of strongly heterogeneous “small” boxes, called items, into a finite set of identical “large” rectangles, called bins, minimizing the unused volume and requiring that the items are packed without overlapping. The great interest is mainly due to the number of real-world applications in which it arises, such as pallet and container loading, cutting objects out of a piece of material and packaging design. Depending on these real-world applications, more objective functions and more practical constraints could be needed. After a brief discussion about the real-world applications of the problem and a exhaustive literature review, the design of a two-stage algorithm to solve the aforementioned problem is presented. The algorithm must be able to provide the spatial coordinates of the placed boxes vertices and also the optimal boxes input sequence, while guaranteeing geometric, stability, fragility constraints and a reduced computational time. Due to NP-hard complexity of this type of combinatorial problems, a fusion of metaheuristic and machine learning techniques is adopted. In particular, a hybrid genetic algorithm coupled with a feedforward neural network is used. In the first stage, a rich dataset is created starting from a set of real input instances provided by an industrial company and the feedforward neural network is trained on it. After its training, given a new input instance, the hybrid genetic algorithm is able to run using the neural network output as input parameter vector, providing as output the optimal solution. The effectiveness of the proposed works is confirmed via several experimental tests

"Delirium Day": A nationwide point prevalence study of delirium in older hospitalized patients using an easy standardized diagnostic tool

Background: To date, delirium prevalence in adult acute hospital populations has been estimated generally from pooled findings of single-center studies and/or among specific patient populations. Furthermore, the number of participants in these studies has not exceeded a few hundred. To overcome these limitations, we have determined, in a multicenter study, the prevalence of delirium over a single day among a large population of patients admitted to acute and rehabilitation hospital wards in Italy. Methods: This is a point prevalence study (called "Delirium Day") including 1867 older patients (aged 65 years or more) across 108 acute and 12 rehabilitation wards in Italian hospitals. Delirium was assessed on the same day in all patients using the 4AT, a validated and briefly administered tool which does not require training. We also collected data regarding motoric subtypes of delirium, functional and nutritional status, dementia, comorbidity, medications, feeding tubes, peripheral venous and urinary catheters, and physical restraints. Results: The mean sample age was 82.0 \ub1 7.5 years (58 % female). Overall, 429 patients (22.9 %) had delirium. Hypoactive was the commonest subtype (132/344 patients, 38.5 %), followed by mixed, hyperactive, and nonmotoric delirium. The prevalence was highest in Neurology (28.5 %) and Geriatrics (24.7 %), lowest in Rehabilitation (14.0 %), and intermediate in Orthopedic (20.6 %) and Internal Medicine wards (21.4 %). In a multivariable logistic regression, age (odds ratio [OR] 1.03, 95 % confidence interval [CI] 1.01-1.05), Activities of Daily Living dependence (OR 1.19, 95 % CI 1.12-1.27), dementia (OR 3.25, 95 % CI 2.41-4.38), malnutrition (OR 2.01, 95 % CI 1.29-3.14), and use of antipsychotics (OR 2.03, 95 % CI 1.45-2.82), feeding tubes (OR 2.51, 95 % CI 1.11-5.66), peripheral venous catheters (OR 1.41, 95 % CI 1.06-1.87), urinary catheters (OR 1.73, 95 % CI 1.30-2.29), and physical restraints (OR 1.84, 95 % CI 1.40-2.40) were associated with delirium. Admission to Neurology wards was also associated with delirium (OR 2.00, 95 % CI 1.29-3.14), while admission to other settings was not. Conclusions: Delirium occurred in more than one out of five patients in acute and rehabilitation hospital wards. Prevalence was highest in Neurology and lowest in Rehabilitation divisions. The "Delirium Day" project might become a useful method to assess delirium across hospital settings and a benchmarking platform for future surveys

The Influence of Maturity Status on Anthropometric Profile and Body Composition of Youth Goalkeepers

The anthropometric profile assessment is an important aspect to consider during the growth stages of youth sport practitioners due to its usefulness in controlling maturity status and overall health. We performed an anthropometric profile evaluation in a sample of youth goalkeepers (n = 42) during a training camp, dividing them into three categories based on their years from peak height velocity (YPHV). We also checked if the selection of goalkeepers was associated with the birth quartile. The results showed that most of the participants’ anthropometric parameters followed the normal trend according to the maturation stages. However, several subjects showed an overweight/obese condition and/or high waist circumference. Non-optimal values were found, mostly in the group of goalkeepers around the PHV. In addition, no selection based on birth quartile was seen. Therefore, the anthropometric profile and body composition of youth goalkeepers are physiologically affected by maturity status. However, several subjects were found to be overweight/obese and at cardiometabolic risk, suggesting that children and adolescents, although practicing sport, should pay attention to potentially contributing factors such as the attainment of the recommended levels of physical activity, lowering sedentary time, and adopt a healthy lifestyle

Exploring the shape influence on melting temperature, enthalpy, and solubility of organic grug nanocrystals by a thermodynamic model

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.This paper focuses on a thermodynamic model built to predict the reduction of organic drug melting temperature and enthalpy with nanocrystal size decrease. Indeed, this valuable information enables us to evaluate the increase of drug solubility, an aspect of paramount importance for poorly water-soluble organic drugs since a solubility increase is reflected in a bioavailability enhancement. In particular, the model considers the effect of nanocrystals shape (spherical, cylindrical, and parallelepiped-shaped) and morphology (from platelet to needle nanocrystals) on the melting temperature and enthalpy reduction with crystal size decrease. Nimesulide, a typical nonsteroidal and poorly water-soluble drug with anti-inflammatory action, has been chosen as a model drug to test model reliability. Model outcomes suggest that the reduction of melting temperature and enthalpy mainly depends on the ratio between crystals surface area and volume, i.e., on the ratio between the number of surface and bulk molecules constituting the nanocrystal network. The obtained prediction of solubility enhancement and the successful comparison with the outcomes obtained from a molecular dynamics approach, in terms of melting temperature and enthalpy decrease, have confirmed the reliability of the proposed model