The Harrod Model

As mentioned in the Introduction, Sect. 1.2, the objective of this book is twofold: to provide a personal specification of a business cycle model within the Kaldor–Kalecki framework (see Chap. 16) and to choose a chaotic specification of the Harrod model (Sportelli and Celi (Metroeconomica 62:459–493, 2011)) to prove that (1) real data can be obtained by a suitable calibration of model’s parameters and (2) the calibrated model confirms theoretical predictions (Orlando and Della Rossa (Mathematics 7:524, 2019)). In this chapter, we first explain the Domar model and the Harrod model separately, and then we describe the mathematical foundation to the Harrod’s instability principle that will be tested then in Chap. 18

Recurrent cutaneous leiomyosarcoma of the inner thigh

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Extramedullary Plasmacytoma Mimicking Pancreatic Cancer: An Unusual Presentation

Multiple myeloma is a plasma cell tumor that homes to and expands in the bone marrow and that, despite the new available drugs, remains incurable. Extramedullary plasmacytoma is a not frequent manifestation during the natural history of multiple myeloma and is frequently associated with plasma cell bone marrow infiltration. The most common locations for an EMP include the gastrointestinal tract, pleura, testis, skin, peritoneum, liver, endocrine glands, and lymph nodes. Primary involvement of the gallbladder fossa is exceedingly rare. In this report, we describe a patient with multiple myeloma who achieved a clinical and serological remission after autologous transplant but progressed rapidly at extramedullary site mimicking a second cancer (i.e., pancreatic or biliary cancer). In this case, the extramedullary localization was refractory to standard therapy, differently from bone marrow localization, but responded to lymphoma-like therapy. In this patient (i) the particular site of developing plasmacytoma is the gallbladder fossa, (ii) the timing of onset of this neoplasm is immediately after autologous transplant, and (iii) its disjunction from primary myeloma is that it appears in clinical and serological remission phase which may be confounding during the diagnostic approach simulating a different tumor (solid tumor)

Evidence of an interaction between FXR1 and GSK3β polymorphisms on levels of Negative Symptoms of Schizophrenia and their response to antipsychotics

Introduction: Genome Wide Association Studies (GWAS) have identified several genes associated with schizophrenia (SCZ) and exponentially increased knowledge on the genetic basis of the disease. Additionally, products of GWAS genes interact with neuronal factors coded by genes lacking association, such that this interaction may confer risk for specific phenotypes of this brain disorder. In this regard, FXR1 (Fragile-X mental-retardation-syndrome-related 1) gene has been GWAS associated with SCZ. FXR1 protein is regulated by Glycogen Synthase Kinase-3 (GSK3), which has been implicated in pathophysiology of SCZ and response to Antipsychotics (APs). rs496250 and rs12630592, two eQTLs of FXR1 and GSK3 respectively, interact on emotion stability and amygdala/PFC activity during emotion processing. These two phenotypes are associated with Negative Symptoms (NS) of SCZ suggesting that the interaction between these SNPs may also affect NS severity and responsiveness to medication. Methods: To test this hypothesis, in two independent samples of patients with SCZ, we investigated rs496250 by rs12630592 interaction on NS severity and response to APs. We also tested a putative link between APs administration and fxr1 expression, as already reported for GSK3 expression. Results: We found that rs496250 and rs12630592 interact on NS severity. We also found evidence suggesting interaction of these polymorphisms also on response to APs. This interaction was not present when looking at positive and general psychopathology scores. Furthermore, chronic olanzapine administration led to a reduction of FXR1 expression in mouse frontal cortex. Discussion: Our findings suggest that, like GSK3 , FXR1 is affected by APs while shedding new light on the role of the FXR1/GSK3 pathway for NS of SCZ

A new PET prototype for proton therapy: comparison of data and Monte Carlo simulations

Ion beam therapy is a valuable method for the treatment of deep-seated and radio-resistant tumors thanks to the favorable depth-dose distribution characterized by the Bragg peak. Hadrontherapy facilities take advantage of the specific ion range, resulting in a highly conformal dose in the target volume, while the dose in critical organs is reduced as compared to photon therapy. The necessity to monitor the delivery precision, i.e. the ion range, is unquestionable, thus different approaches have been investigated, such as the detection of prompt photons or annihilation photons of positron emitter nuclei created during the therapeutic treatment. Based on the measurement of the induced β+ activity, our group has developed various in-beam PET prototypes: the one under test is composed by two planar detector heads, each one consisting of four modules with a total active area of 10 × 10 cm2. A single detector module is made of a LYSO crystal matrix coupled to a position sensitive photomultiplier and is read-out by dedicated frontend electronics. A preliminary data taking was performed at the Italian National Centre for Oncological Hadron Therapy (CNAO, Pavia), using proton beams in the energy range of 93–112 MeV impinging on a plastic phantom. The measured activity profiles are presented and compared with the simulated ones based on the Monte Carlo FLUKA package

Online proton therapy monitoring: Clinical test of a Silicon-photodetector-based in-beam PET

Particle therapy exploits the energy deposition pattern of hadron beams. The narrow Bragg Peak at the end of range is a major advantage but range uncertainties can cause severe damage and require online verification to maximise the effectiveness in clinics. In-beam Positron Emission Tomography (PET) is a non-invasive, promising in-vivo technique, which consists in the measurement of the β+ activity induced by beam-tissue interactions during treatment, and presents the highest correlation of the measured activity distribution with the deposited dose, since it is not much influenced by biological washout. Here we report the first clinical results obtained with a state-of-the-art in-beam PET scanner, with on-the-fly reconstruction of the activity distribution during irradiation. An automated time-resolved quantitative analysis was tested on a lacrimal gland carcinoma case, monitored during two consecutive treatment sessions. The 3D activity map was reconstructed every 10 s, with an average delay between beam delivery and image availability of about 6 s. The correlation coefficient of 3D activity maps for the two sessions (above 0.9 after 120 s) and the range agreement (within 1 mm) prove the suitability of in-beam PET for online range verification during treatment, a crucial step towards adaptive strategies in particle therapy

Particle beam microstructure reconstruction and coincidence discrimination in PET monitoring for hadron therapy

Positron emission tomography is one of the most mature techniques for monitoring the particles range in hadron therapy, aiming to reduce treatment uncertainties and therefore the extent of safety margins in the treatment plan. In-beam PET monitoring has been already performed using inter-spill and post-irradiation data, i.e., while the particle beam is off or paused. The full beam acquisition procedure is commonly discarded because the particle spills abruptly increase the random coincidence rates and therefore the image noise. This is because random coincidences cannot be separated by annihilation photons originating from radioactive decays and cannot be corrected with standard random coincidence techniques due to the time correlation of the beam-induced background with the ion beam microstructure. The aim of this paper is to provide a new method to recover in-spill data to improve the images obtained with full-beam PET acquisitions. This is done by estimating the temporal microstructure of the beam and thus selecting input PET events that are less likely to be random ones. The PET detector we used was the one developed within the INSIDE project and tested at the CNAO synchrotron-based facility. The data were taken on a PMMA phantom irradiated with 72 MeV proton pencil beams. The obtained results confirm the possibility of improving the acquired PET data without any external signal coming from the synchrotron or ad-hoc detectors

The use of alteplase, although safe, does not offer clear clinical advantages when mild stroke is non-disabling

IntroductionIt is unknown whether alteplase is effective and safe in patients with mild acute ischemic stroke (AIS). Determining whether symptoms are “disabling” or not is a crucial factor in the management of these patients. This study aimed to investigate the efficacy and safety of alteplase in patients with mild, non-disabling AIS.MethodsWe included all consecutive patients admitted for AIS at our institution from January 2015 to May 2022 who presented a baseline NIHSS score of 0–5 and fit the criteria to receive intravenous thrombolysis. In order to select only subjects with non-disabling AIS, we excluded patients who scored more than 1 point in the following NIHSS single items: vision, language, neglect, and single limb. Patients who scored at least 1 point in the NIHSS consciousness item were excluded as well. This study is a retrospective analysis of a prospectively collected database.ResultsAfter the application of the exclusion criteria, we included 319 patients, stratified into patients receiving and not receiving alteplase based on non-disabling symptoms. The two groups were comparable regarding demographic and clinical data. Rates of a 3-month favorable outcome, defined as a 3-month mRS score of 0–1, were similar, being 82.3% and 86.1% in the treated and untreated patients, respectively. Hemorrhagic complications and mortality occurred infrequently and were not affected by alteplase treatment.DiscussionThis observational study suggests that the use of alteplase, although safe, is not associated with a better outcome in highly selected patients with non-disabling AIS

Localization of anatomical changes in patients during proton therapy with in-beam PET monitoring: a voxel-based morphometry approach exploiting Monte Carlo simulations

Purpose: In-beam positron emission tomography (PET) is one of the modalities that can be used for in vivo noninvasive treatment monitoring in proton therapy. Although PET monitoring has been frequently applied for this purpose, there is still no straightforward method to translate the information obtained from the PET images into easy-to-interpret information for clinical personnel. The purpose of this work is to propose a statistical method for analyzing in-beam PET monitoring images that can be used to locate, quantify, and visualize regions with possible morphological changes occurring over the course of treatment. Methods: We selected a patient treated for squamous cell carcinoma (SCC) with proton therapy, to perform multiple Monte Carlo (MC) simulations of the expected PET signal at the start of treatment, and to study how the PET signal may change along the treatment course due to morphological changes. We performed voxel-wise two-tailed statistical tests of the simulated PET images, resembling the voxel-based morphometry (VBM) method commonly used in neuroimaging data analysis, to locate regions with significant morphological changes and to quantify the change. Results: The VBM resembling method has been successfully applied to the simulated in-beam PET images, despite the fact that such images suffer from image artifacts and limited statistics. Three dimensional probability maps were obtained, that allowed to identify interfractional morphological changes and to visualize them superimposed on the computed tomography (CT) scan. In particular, the characteristic color patterns resulting from the two-tailed statistical tests lend themselves to trigger alarms in case of morphological changes along the course of treatment. Conclusions: The statistical method presented in this work is a promising method to apply to PET monitoring data to reveal interfractional morphological changes in patients, occurring over the course of treatment. Based on simulated in-beam PET treatment monitoring images, we showed that with our method it was possible to correctly identify the regions that changed. Moreover we could quantify the changes, and visualize them superimposed on the CT scan. The proposed method can possibly help clinical personnel in the replanning procedure in adaptive proton therapy treatments

In-vivo range verification analysis with in-beam PET data for patients treated with proton therapy at CNAO

Morphological changes that may arise through a treatment course are probably one of the most significant sources of range uncertainty in proton therapy. Non-invasive in-vivo treatment monitoring is useful to increase treatment quality. The INSIDE in-beam Positron Emission Tomography (PET) scanner performs in-vivo range monitoring in proton and carbon therapy treatments at the National Center of Oncological Hadrontherapy (CNAO). It is currently in a clinical trial (ID: NCT03662373) and has acquired in-beam PET data during the treatment of various patients. In this work we analyze the in-beam PET (IB-PET) data of eight patients treated with proton therapy at CNAO. The goal of the analysis is twofold. First, we assess the level of experimental fluctuations in inter-fractional range differences (sensitivity) of the INSIDE PET system by studying patients without morphological changes. Second, we use the obtained results to see whether we can observe anomalously large range variations in patients where morphological changes have occurred. The sensitivity of the INSIDE IB-PET scanner was quantified as the standard deviation of the range difference distributions observed for six patients that did not show morphological changes. Inter-fractional range variations with respect to a reference distribution were estimated using the Most-Likely-Shift (MLS) method. To establish the efficacy of this method, we made a comparison with the Beam's Eye View (BEV) method. For patients showing no morphological changes in the control CT the average range variation standard deviation was found to be 2.5 mm with the MLS method and 2.3 mm with the BEV method. On the other hand, for patients where some small anatomical changes occurred, we found larger standard deviation values. In these patients we evaluated where anomalous range differences were found and compared them with the CT. We found that the identified regions were mostly in agreement with the morphological changes seen in the CT scan