Development of Clinical Decision Support Systems based on Mathematical Models of Physiological Systems

In the last years of research, I focused my studies on different physiological problems. Together with my supervisors, I developed/improved different mathematical models in order to create valid tools useful for a better understanding of important clinical issues. The aim of all this work is to develop tools for learning and understanding cardiac and cerebrovascular physiology as well as pathology, generating research questions and developing clinical decision support systems useful for intensive care unit patients. I. ICP-model Designed for Medical Education We developed a comprehensive cerebral blood flow and intracranial pressure model to simulate and study the complex interactions in cerebrovascular dynamics caused by multiple simultaneous alterations, including normal and abnormal functional states of auto-regulation of the brain. Individual published equations (derived from prior animal and human studies) were implemented into a comprehensive simulation program. Included in the normal physiological modelling was: intracranial pressure, cerebral blood flow, blood pressure, and carbon dioxide (CO2) partial pressure. We also added external and pathological perturbations, such as head up position and intracranial haemorrhage. The model performed clinically realistically given inputs of published traumatized patients, and cases encountered by clinicians. The pulsatile nature of the output graphics was easy for clinicians to interpret. The manoeuvres simulated include changes of basic physiological inputs (e.g. blood pressure, central venous pressure, CO2 tension, head up position, and respiratory effects on vascular pressures) as well as pathological inputs (e.g. acute intracranial bleeding, and obstruction of cerebrospinal outflow). Based on the results, we believe the model would be useful to teach complex relationships of brain haemodynamics and study clinical research questions such as the optimal head-up position, the effects of intracranial haemorrhage on cerebral haemodynamics, as well as the best CO2 concentration to reach the optimal compromise between intracranial pressure and perfusion. We believe this model would be useful for both beginners and advanced learners. It could be used by practicing clinicians to model individual patients (entering the effects of needed clinical manipulations, and then running the model to test for optimal combinations of therapeutic manoeuvres). II. A Heterogeneous Cerebrovascular Mathematical Model Cerebrovascular pathologies are extremely complex, due to the multitude of factors acting simultaneously on cerebral haemodynamics. In this work, the mathematical model of cerebral haemodynamics and intracranial pressure dynamics, described in the point I, is extended to account for heterogeneity in cerebral blood flow. The model includes the Circle of Willis, six regional districts independently regulated by autoregulation and CO2 reactivity, distal cortical anastomoses, venous circulation, the cerebrospinal fluid circulation, and the intracranial pressure-volume relationship. Results agree with data in the literature and highlight the existence of a monotonic relationship between transient hyperemic response and the autoregulation gain. During unilateral internal carotid artery stenosis, local blood flow regulation is progressively lost in the ipsilateral territory with the presence of a steal phenomenon, while the anterior communicating artery plays the major role to redistribute the available blood flow. Conversely, distal collateral circulation plays a major role during unilateral occlusion of the middle cerebral artery. In conclusion, the model is able to reproduce several different pathological conditions characterized by heterogeneity in cerebrovascular haemodynamics and can not only explain generalized results in terms of physiological mechanisms involved, but also, by individualizing parameters, may represent a valuable tool to help with difficult clinical decisions. III. Effect of Cushing Response on Systemic Arterial Pressure. During cerebral hypoxic conditions, the sympathetic system causes an increase in arterial pressure (Cushing response), creating a link between the cerebral and the systemic circulation. This work investigates the complex relationships among cerebrovascular dynamics, intracranial pressure, Cushing response, and short-term systemic regulation, during plateau waves, by means of an original mathematical model. The model incorporates the pulsating heart, the pulmonary circulation and the systemic circulation, with an accurate description of the cerebral circulation and the intracranial pressure dynamics (same model as in the first paragraph). Various regulatory mechanisms are included: cerebral autoregulation, local blood flow control by oxygen (O2) and/or CO2 changes, sympathetic and vagal regulation of cardiovascular parameters by several reflex mechanisms (chemoreceptors, lung-stretch receptors, baroreceptors). The Cushing response has been described assuming a dramatic increase in sympathetic activity to vessels during a fall in brain O2 delivery. With this assumption, the model is able to simulate the cardiovascular effects experimentally observed when intracranial pressure is artificially elevated and maintained at constant level (arterial pressure increase and bradicardia). According to the model, these effects arise from the interaction between the Cushing response and the baroreflex response (secondary to arterial pressure increase). Then, patients with severe head injury have been simulated by reducing intracranial compliance and cerebrospinal fluid reabsorption. With these changes, oscillations with plateau waves developed. In these conditions, model results indicate that the Cushing response may have both positive effects, reducing the duration of the plateau phase via an increase in cerebral perfusion pressure, and negative effects, increasing the intracranial pressure plateau level, with a risk of greater compression of the cerebral vessels. This model may be of value to assist clinicians in finding the balance between clinical benefits of the Cushing response and its shortcomings. IV. Comprehensive Cardiopulmonary Simulation Model for the Analysis of Hypercapnic Respiratory Failure We developed a new comprehensive cardiopulmonary model that takes into account the mutual interactions between the cardiovascular and the respiratory systems along with their short-term regulatory mechanisms. The model includes the heart, systemic and pulmonary circulations, lung mechanics, gas exchange and transport equations, and cardio-ventilatory control. Results show good agreement with published patient data in case of normoxic and hyperoxic hypercapnia simulations. In particular, simulations predict a moderate increase in mean systemic arterial pressure and heart rate, with almost no change in cardiac output, paralleled by a relevant increase in minute ventilation, tidal volume and respiratory rate. The model can represent a valid tool for clinical practice and medical research, providing an alternative way to experience-based clinical decisions. In conclusion, models are not only capable of summarizing current knowledge, but also identifying missing knowledge. In the former case they can serve as training aids for teaching the operation of complex systems, especially if the model can be used to demonstrate the outcome of experiments. In the latter case they generate experiments to be performed to gather the missing data.

Econometric models of financial risks

The goal of this dissertation is to use statistical tools to analyze specific financial risks that have played dominant roles in the US financial crisis of 2008-2009. The first risk relates to the level of aggregate stress in the financial markets. I estimate the impact of financial stress on economic activity and monetary policy using structural VAR analysis. The second set of risks concerns the US housing market. There are in fact two prominent risks associated with a US mortgage, as borrowers can both prepay or default on a mortgage. I test the existence of unobservable heterogeneity in the borrower's decision to default or prepay on his mortgage by estimating a multinomial logit model with borrower-specific random coefficients.

Parametric Sensitivity Analysis of the Most Recent Computational Models of Rabbit Cardiac Pacemaking

The cellular basis of cardiac pacemaking activity, and specifically the quantitative contributions of particular mechanisms, is still debated. Reliable computational models of sinoatrial nodal (SAN) cells may provide mechanistic insights, but competing models are built from different data sets and with different underlying assumptions. To understand quantitative differences between alternative models, we performed thorough parameter sensitivity analyses of the SAN models of Maltsev & Lakatta (2009) and Severi et al (2012). Model parameters were randomized to generate a population of cell models with different properties, simulations performed with each set of random parameters generated 14 quantitative outputs that characterized cellular activity, and regression methods were used to analyze the population behavior. Clear differences between the two models were observed at every step of the analysis. Specifically: (1) SR Ca2+ pump activity had a greater effect on SAN cell cycle length (CL) in the Maltsev model; (2) conversely, parameters describing the funny current (If) had a greater effect on CL in the Severi model; (3) changes in rapid delayed rectifier conductance (GKr) had opposite effects on action potential amplitude in the two models; (4) within the population, a greater percentage of model cells failed to exhibit action potentials in the Maltsev model (27%) compared with the Severi model (7%), implying greater robustness in the latter; (5) confirming this initial impression, bifurcation analyses indicated that smaller relative changes in GKr or Na+-K+ pump activity led to failed action potentials in the Maltsev model. Overall, the results suggest experimental tests that can distinguish between models and alternative hypotheses, and the analysis offers strategies for developing anti-arrhythmic pharmaceuticals by predicting their effect on the pacemaking activity.

Subject-specific musculoskeletal models of the lower limbs for the prediction of skeletal loads during motion

The determination of skeletal loading conditions in vivo and their relationship to the health of bone tissues, remain an open question. Computational modeling of the musculoskeletal system is the only practicable method providing a valuable approach to muscle and joint loading analyses, although crucial shortcomings limit the translation process of computational methods into the orthopedic and neurological practice. A growing attention focused on subject-specific modeling, particularly when pathological musculoskeletal conditions need to be studied. Nevertheless, subject-specific data cannot be always collected in the research and clinical practice, and there is a lack of efficient methods and frameworks for building models and incorporating them in simulations of motion. The overall aim of the present PhD thesis was to introduce improvements to the state-of-the-art musculoskeletal modeling for the prediction of physiological muscle and joint loads during motion. A threefold goal was articulated as follows: (i) develop state-of-the art subject-specific models and analyze skeletal load predictions; (ii) analyze the sensitivity of model predictions to relevant musculotendon model parameters and kinematic uncertainties; (iii) design an efficient software framework simplifying the effort-intensive phases of subject-specific modeling pre-processing. The first goal underlined the relevance of subject-specific musculoskeletal modeling to determine physiological skeletal loads during gait, corroborating the choice of full subject-specific modeling for the analyses of pathological conditions. The second goal characterized the sensitivity of skeletal load predictions to major musculotendon parameters and kinematic uncertainties, and robust probabilistic methods were applied for methodological and clinical purposes. The last goal created an efficient software framework for subject-specific modeling and simulation, which is practical, user friendly and effort effective. Future research development aims at the implementation of more accurate models describing lower-limb joint mechanics and musculotendon paths, and the assessment of an overall scenario of the crucial model parameters affecting the skeletal load predictions through probabilistic modeling.

Development of control-oriented models of Dual Clutch Transmission systems

A control-oriented model of a Dual Clutch Transmission was developed for real-time Hardware In the Loop (HIL) applications, to support model-based development of the DCT controller. The model is an innovative attempt to reproduce the fast dynamics of the actuation system while maintaining a step size large enough for real-time applications. The model comprehends a detailed physical description of hydraulic circuit, clutches, synchronizers and gears, and simplified vehicle and internal combustion engine sub-models. As the oil circulating in the system has a large bulk modulus, the pressure dynamics are very fast, possibly causing instability in a real-time simulation; the same challenge involves the servo valves dynamics, due to the very small masses of the moving elements. Therefore, the hydraulic circuit model has been modified and simplified without losing physical validity, in order to adapt it to the real-time simulation requirements. The results of offline simulations have been compared to on-board measurements to verify the validity of the developed model, that was then implemented in a HIL system and connected to the TCU (Transmission Control Unit). Several tests have been performed: electrical failure tests on sensors and actuators, hydraulic and mechanical failure tests on hydraulic valves, clutches and synchronizers, and application tests comprehending all the main features of the control performed by the TCU. Being based on physical laws, in every condition the model simulates a plausible reaction of the system. The first intensive use of the HIL application led to the validation of the new safety strategies implemented inside the TCU software. A test automation procedure has been developed to permit the execution of a pattern of tests without the interaction of the user; fully repeatable tests can be performed for non-regression verification, allowing the testing of new software releases in fully automatic mode.

Spatio-temporal models of the functional architecture of the visual cortex

In this work I tried to explore many aspects of cognitive visual science, each one based on different academic fields, proposing mathematical models capable to reproduce both neuro-physiological and phenomenological results that were described in the recent literature. The structure of my thesis is mainly composed of three chapters, corresponding to the three main areas of research on which I focused my work. The results of each work put the basis for the following, and their ensemble form an homogeneous and large-scale survey on the spatio-temporal properties of the architecture of the visual cortex of mammals.

Su(3) lattice gauge theories and spin chains

I modelli su reticolo con simmetrie SU(n) sono attualmente oggetto di studio sia dal punto di vista sperimentale, sia dal punto di vista teorico; particolare impulso alla ricerca in questo campo è stato dato dai recenti sviluppi in campo sperimentale per quanto riguarda la tecnica dell’intrappolamento di atomi ultrafreddi in un reticolo ottico. In questa tesi viene studiata, sia con tecniche analitiche sia con simulazioni numeriche, la generalizzazione del modello di Heisenberg su reticolo monodimensionale a simmetria SU(3). In particolare, viene proposto un mapping tra il modello di Heisenberg SU(3) e l’Hamiltoniana con simmetria SU(2) bilineare-biquadratica con spin 1. Vengono inoltre presentati nuovi risultati numerici ottenuti con l’algoritmo DMRG che confermano le previsioni teoriche in letteratura sul modello in esame. Infine è proposto un approccio per la formulazione della funzione di partizione dell’Hamiltoniana bilineare-biquadratica a spin-1 servendosi degli stati coerenti per SU(3).

Standard intracranial in vivo animal models of delayed cerebral vasospasm

Animal models provide a basis for clarifying the complex pathogenesis of delayed cerebral vasospasm (DCVS) and for screening of potential therapeutic approaches. Arbitrary use of experimental parameters in current models can lead to results of uncertain relevance. The aim of this work was to identify and analyze the most consistent and feasible models and their parameters for each animal.

Automated detection of the osseous acetabular rim using three-dimensional models of the pelvis

An automated algorithm for detection of the acetabular rim was developed. Accuracy of the algorithm was validated in a sawbone study and compared against manually conducted digitization attempts, which were established as the ground truth. The latter proved to be reliable and reproducible, demonstrated by almost perfect intra- and interobserver reliability. Validation of the automated algorithm showed no significant difference compared to the manually acquired data in terms of detected version and inclination. Automated detection of the acetabular rim contour and the spatial orientation of the acetabular opening plane can be accurately achieved with this algorithm.

Population genomic tests of models of adaptive radiation in Lake Victoria Region cichlid fish

Adaptive radiation is usually thought to be associated with speciation, but the evolution of intraspecific polymorphisms without speciation is also possible. The radiation of cichlid fish in Lake Victoria (LV) is perhaps the most impressive example of a recent rapid adaptive radiation, with 600+ very young species. Key questions about its origin remain poorly characterized, such as the importance of speciation versus polymorphism, whether species persist on evolutionary time scales, and if speciation happens more commonly in small isolated or in large connected populations. We used 320 individuals from 105 putative species from Lakes Victoria, Edward, Kivu, Albert, Nabugabo and Saka, in a radiation-wide amplified fragment length polymorphism (AFLP) genome scan to address some of these questions. We demonstrate pervasive signatures of speciation supporting the classical model of adaptive radiation associated with speciation. A positive relationship between the age of lakes and the average genomic differentiation of their species, and a significant fraction of molecular variance explained by above-species level taxonomy suggest the persistence of species on evolutionary time scales, with radiation through sequential speciation rather than a single starburst. Finally the large gene diversity retained from colonization to individual species in every radiation suggests large effective population sizes and makes speciation in small geographical isolates unlikely.

Fastener-Based Computational Models of Cold-Formed Steel Shear Walls

Cold-formed steel (CFS) combined with wood sheathing, such as oriented strand board (OSB), forms shear walls that can provide lateral resistance to seismic forces. The ability to accurately predict building deformations in damaged states under seismic excitations is a must for modern performance-based seismic design. However, few static or dynamic tests have been conducted on the non-linear behavior of CFS shear walls. Thus, the purpose of this research work is to provide and demonstrate a fastener-based computational model of CFS wall models that incorporates essential nonlinearities that may eventually lead to improvement of the current seismic design requirements. The approach is based on the understanding that complex interaction of the fasteners with the sheathing is an important factor in the non-linear behavior of the shear wall. The computational model consists of beam-column elements for the CFS framing and a rigid diaphragm for the sheathing. The framing and sheathing are connected with non-linear zero-length fastener elements to capture the OSB sheathing damage surrounding the fastener area. Employing computational programs such as OpenSees and MATLAB, 4 ft. x 9 ft., 8 ft. x 9 ft. and 12 ft. x 9 ft. shear wall models are created, and monotonic lateral forces are applied to the computer models. The output data are then compared and analyzed with the available results of physical testing. The results indicate that the OpenSees model can accurately capture the initial stiffness, strength and non-linear behavior of the shear walls.

Quantification of atelectatic lung volumes in two different porcine models of ARDS

BACKGROUND: Cyclic recruitment during mechanical ventilation contributes to ventilator associated lung injury. Two different pathomechanisms in acute respiratory distress syndrome (ARDS) are currently discussed: alveolar collapse vs persistent flooding of small airways and alveoli. We compare two different ARDS animal models by computed tomography (CT) to describe different recruitment and derecruitment mechanisms at different airway pressures: (i) lavage-ARDS, favouring alveolar collapse by surfactant depletion; and (ii) oleic acid ARDS, favouring alveolar flooding by capillary leakage. METHODS: In 12 pigs [25 (1) kg], ARDS was randomly induced, either by saline lung lavage or oleic acid (OA) injection, and 3 animals served as controls. A respiratory breathhold manoeuvre without spontaneous breathing at different continuous positive airway pressure (CPAP) was applied in random order (CPAP levels of 5, 10, 15, 30, 35 and 50 cm H(2)O) and spiral-CT scans of the total lung were acquired at each CPAP level (slice thickness=1 mm). In each spiral-CT the volume of total lung parenchyma, tissue, gas, non-aerated, well-aerated, poorly aerated, and over-aerated lung was calculated. RESULTS: In both ARDS models non-aerated lung volume decreased significantly from CPAP 5 to CPAP 50 [oleic acid lung injury (OAI): 346.9 (80.1) to 96.4 (48.8) ml, P<0.001; lavage-ARDS: 245 17.6) to 42.7 (4.8) ml, P<0.001]. In lavage-ARDS poorly aerated lung volume decreased at higher CPAP levels [232 (45.2) at CPAP 10 to 84 (19.4) ml at CPAP 50, P<0.001] whereas in OAI poorly aerated lung volume did not vary at different airway pressures. CONCLUSIONS: In both ARDS models well-aerated and non-aerated lung volume respond to different CPAP levels in a comparable fashion: Thus, a cyclical alveolar collapse seems to be part of the derecruitment process also in the OA-ARDS. In OA-ARDS, the increase in poorly aerated lung volume reflects the specific initial lesion, that is capillary leakage with interstitial and alveolar oedema.

An integrated approach for reconstructing surface models of the proximal femur from sparse input data for surgical navigation

A patient-specific surface model of the proximal femur plays an important role in planning and supporting various computer-assisted surgical procedures including total hip replacement, hip resurfacing, and osteotomy of the proximal femur. The common approach to derive 3D models of the proximal femur is to use imaging techniques such as computed tomography (CT) or magnetic resonance imaging (MRI). However, the high logistic effort, the extra radiation (CT-imaging), and the large quantity of data to be acquired and processed make them less functional. In this paper, we present an integrated approach using a multi-level point distribution model (ML-PDM) to reconstruct a patient-specific model of the proximal femur from intra-operatively available sparse data. Results of experiments performed on dry cadaveric bones using dozens of 3D points are presented, as well as experiments using a limited number of 2D X-ray images, which demonstrate promising accuracy of the present approach.