Development of a silicon photomultiplier based innovative and low cost positron emission tomography scanner.

The Silicon Photomultiplier (SiPM) is a state-of-the-art semiconductor photodetector consisting of a high density matrix (up to 104) of independent pixels of micro-metric dimension (from 10 \u3bcm to 100 \u3bcm) which form a macroscopic unit of 1 to 6 mm2 area. Each pixel is a single-photon avalanche diode operated with a bias voltage of a few volts above the breakdown voltage. When a charge carrier is generated in a pixel by an incoming photon or a thermal effect, a Geiger discharge confined to that pixel is initiated and an intrinsic gain of about 106 is obtained. The output signal of a pixel is the same regardless of the number of interacting photons and provide only a binary information. Since the pixels are arranged on a common Silicon substrate and are connected in parallel to the same readout line, the SiPM combined output response corresponds to the sum of all fired pixel currents. As a result, the SiPM as a whole is an analogue detector, which can measure the incoming light intensity. Nowadays a great number of companies are investing increasing efforts in SiPM detector performances and high quality mass production. SiPMs are in rapid evolution and benefit from the tremendous development of the Silicon technology in terms of cost production, design flexibility and performances. They have reached a high single photon detection sensitivity and photon detection efficiency, an excellent time resolution, an extended dynamic range. They require a low bias voltage and have a low power consumption, they are very compact, robust, flexible and cheap. Considering also their intrinsic insensitivity to magnetic field they result to have an extremely high potential in fundamental and applied science (particle and nuclear physics, astrophysics, biology, environmental science and nuclear medicine) and industry. The SiPM performances are influenced by some effects, as saturation, afterpulsing and crosstalk, which lead to an inherent non-proportional response with respect to the number of incident photons. Consequently, it is not trivial to relate the measured electronic signal to the corresponding light intensity. Since for most applications it is desirable to qualify the SiPM response (i.e in order to properly design a detector for a given application, perform corrections on measurements or on energy spectra, calibrate a SiPM for low light measurements, predict detector performance) the implementation of characterization procedures plays a key role. The SiPM field of application that has been considered in this thesis is the Positron Emission Tomography (PET). PET represents the most advanced in-vivo nuclear imaging modality: it provides functional information of the physiological and molecular processes of organs and tissues. Thanks to its diagnostic power, PET has a recognized superiority over all other imaging modalities in oncology, neurology and cardiology. SiPMs are usually successfully employed for the PET scanners because they allow the measurement of the Time Of Flight of the two coincidence photons to improve the signal to noise ratio of the reconstructed images. They also permit to perfectly combine the functional information with the anatomical one by inserting the PET scanner inside the Magnetic Resonance Imaging device. Recently, PET technology has also been applied to preclinical imaging to allow non invasive studies on small animals. The increasing demand for preclinical PET scanner is driven by the fact that small animals host a large number of human diseases. In-vivo imaging has the advantage to enable the measurement of the radiopharmaceutical distribution in the same animal for an extended period of time. As a result, PET represents a powerful research tool as it offers the possibility to study the abnormalities at the origin of a disease, understand its dynamics, evaluate the therapeutic response and develop new drugs and treatments. However, the cost and the complexity of the preclinical scanners are limiting factors for the spread of PET technology: 70-80% of small-animal PET is concentrated in academic or government research laboratories. The EasyPET concept proposed in this Thesis, protected under a patent filed by Aveiro University, aims to achieve a simple and affordable preclinical PET scanner. The innovative concept is based on a single pair of detector kept collinear during the whole data acquisition and a moving mechanism with two degrees of freedom to reproduce the functionalities of an entire PET ring. The main advantages are in terms of the reduction of the complexity and cost of the PET system. In addition the concept is bound to be robust against acollinear photoemission, scatter radiation and parallax error. The sensitivity is expected to represent a fragility due to the reduced geometrical acceptance. This drawback can be partially recovered by the possibility to accept Compton scattering events without introducing image degradation effects, thanks to the sensor alignment. A 2D imaging demonstrator has been realized in order to assess the EasyPET concept and its performance has been analyzed in this Thesis to verify the net balance between competing advantages and drawbacks. The demonstrator had a leading role in the outreach activity to promote the EasyPET concept and a significant outcome is represented by the new partners that recently joined the collaboration. The EasyPET has been licensed to Caen S.p.a. and, thanks to the participation of Nuclear Instruments to the electronic board re-designed, a new prototype has been realized with additional improvements concerning the mechanics and the control software. In this Thesis the prototype functionalities and performances are reported as a result of a commissioning procedure. The EasyPET will be commercialized by Caen S.p.a. as a product for the educational market and it will be addressed to high level didactic laboratories to show the operating principles and technology behind the PET imaging. The topics mentioned above will be examined in depth in the following Chapters according to the subsequent order. In Chapter 1 the Silicon Photomultiplier will be described in detail, from their operating principle to their main application fields passing through the advantages and the drawback effects connected with this type of sensor. Chapter 2 is dedicated to a SiPM standard characterization method based on the staircase and resolving power measurement. A more refined analysis involves the Multi-Photon spectrum, obtained by integrating the SiPM response to a light pulse. It exploits the SiPM single photon sensitivity and its photon number resolving capability to measure some of its properties of general interest for a multitude of potential applications, disentangling the features related to the statistics of the incident light. Chapter 3 reports another SiPM characterization method which implements a post-processing of the digitized SiPM waveforms with the aim of extracting a full picture of the sensor characteristics from a unique data-set. The procedure is very robust, effective and semi-automatic and suitable for sensors of various dimensions and produced by different vendors. Chapter 4 introduces the Positron Emission Tomography imaging: its principle, applications, related issues and state of the art of PET scanner will be explained. Chapter 5 deals with the preclinical PET, reporting the benefits and the technological challenges involved, the performance of the commercially available small animal PET scanners, the main applications and the frontier research in this field. In Chapter 6 the EasyPET concept is introduced. In particular, the basic idea behind the operating principle, the design layout and the image reconstruction will be illustrated and then assessed through the description and the performance analysis of the EasyPET proof of concept and demonstrator. The effect of the use of different sensor to improve the light collection and the coincidence detection efficiency, together with the analysis of the importance of the sensor and the crystal alignment will be reported in Chapter 7. The design, the functionalities and the commissioning of the EasyPET prototype addressed to the educational market will be defined in Chapter 8. Finally, Chapter 9 contains a summary of the conclusions and an outlook of the future research studies

Development of a silicon photomultiplier based innovative and low cost positron emission tomography scanner.

The Silicon Photomultiplier (SiPM) is a state-of-the-art semiconductor photodetector consisting of a high density matrix (up to 104) of independent pixels of micro-metric dimension (from 10 μm to 100 μm) which form a macroscopic unit of 1 to 6 mm2 area. Each pixel is a single-photon avalanche diode operated with a bias voltage of a few volts above the breakdown voltage. When a charge carrier is generated in a pixel by an incoming photon or a thermal effect, a Geiger discharge confined to that pixel is initiated and an intrinsic gain of about 106 is obtained. The output signal of a pixel is the same regardless of the number of interacting photons and provide only a binary information. Since the pixels are arranged on a common Silicon substrate and are connected in parallel to the same readout line, the SiPM combined output response corresponds to the sum of all fired pixel currents. As a result, the SiPM as a whole is an analogue detector, which can measure the incoming light intensity. Nowadays a great number of companies are investing increasing efforts in SiPM detector performances and high quality mass production. SiPMs are in rapid evolution and benefit from the tremendous development of the Silicon technology in terms of cost production, design flexibility and performances. They have reached a high single photon detection sensitivity and photon detection efficiency, an excellent time resolution, an extended dynamic range. They require a low bias voltage and have a low power consumption, they are very compact, robust, flexible and cheap. Considering also their intrinsic insensitivity to magnetic field they result to have an extremely high potential in fundamental and applied science (particle and nuclear physics, astrophysics, biology, environmental science and nuclear medicine) and industry. The SiPM performances are influenced by some effects, as saturation, afterpulsing and crosstalk, which lead to an inherent non-proportional response with respect to the number of incident photons. Consequently, it is not trivial to relate the measured electronic signal to the corresponding light intensity. Since for most applications it is desirable to qualify the SiPM response (i.e in order to properly design a detector for a given application, perform corrections on measurements or on energy spectra, calibrate a SiPM for low light measurements, predict detector performance) the implementation of characterization procedures plays a key role. The SiPM field of application that has been considered in this thesis is the Positron Emission Tomography (PET). PET represents the most advanced in-vivo nuclear imaging modality: it provides functional information of the physiological and molecular processes of organs and tissues. Thanks to its diagnostic power, PET has a recognized superiority over all other imaging modalities in oncology, neurology and cardiology. SiPMs are usually successfully employed for the PET scanners because they allow the measurement of the Time Of Flight of the two coincidence photons to improve the signal to noise ratio of the reconstructed images. They also permit to perfectly combine the functional information with the anatomical one by inserting the PET scanner inside the Magnetic Resonance Imaging device. Recently, PET technology has also been applied to preclinical imaging to allow non invasive studies on small animals. The increasing demand for preclinical PET scanner is driven by the fact that small animals host a large number of human diseases. In-vivo imaging has the advantage to enable the measurement of the radiopharmaceutical distribution in the same animal for an extended period of time. As a result, PET represents a powerful research tool as it offers the possibility to study the abnormalities at the origin of a disease, understand its dynamics, evaluate the therapeutic response and develop new drugs and treatments. However, the cost and the complexity of the preclinical scanners are limiting factors for the spread of PET technology: 70-80% of small-animal PET is concentrated in academic or government research laboratories. The EasyPET concept proposed in this Thesis, protected under a patent filed by Aveiro University, aims to achieve a simple and affordable preclinical PET scanner. The innovative concept is based on a single pair of detector kept collinear during the whole data acquisition and a moving mechanism with two degrees of freedom to reproduce the functionalities of an entire PET ring. The main advantages are in terms of the reduction of the complexity and cost of the PET system. In addition the concept is bound to be robust against acollinear photoemission, scatter radiation and parallax error. The sensitivity is expected to represent a fragility due to the reduced geometrical acceptance. This drawback can be partially recovered by the possibility to accept Compton scattering events without introducing image degradation effects, thanks to the sensor alignment. A 2D imaging demonstrator has been realized in order to assess the EasyPET concept and its performance has been analyzed in this Thesis to verify the net balance between competing advantages and drawbacks. The demonstrator had a leading role in the outreach activity to promote the EasyPET concept and a significant outcome is represented by the new partners that recently joined the collaboration. The EasyPET has been licensed to Caen S.p.a. and, thanks to the participation of Nuclear Instruments to the electronic board re-designed, a new prototype has been realized with additional improvements concerning the mechanics and the control software. In this Thesis the prototype functionalities and performances are reported as a result of a commissioning procedure. The EasyPET will be commercialized by Caen S.p.a. as a product for the educational market and it will be addressed to high level didactic laboratories to show the operating principles and technology behind the PET imaging. The topics mentioned above will be examined in depth in the following Chapters according to the subsequent order. In Chapter 1 the Silicon Photomultiplier will be described in detail, from their operating principle to their main application fields passing through the advantages and the drawback effects connected with this type of sensor. Chapter 2 is dedicated to a SiPM standard characterization method based on the staircase and resolving power measurement. A more refined analysis involves the Multi-Photon spectrum, obtained by integrating the SiPM response to a light pulse. It exploits the SiPM single photon sensitivity and its photon number resolving capability to measure some of its properties of general interest for a multitude of potential applications, disentangling the features related to the statistics of the incident light. Chapter 3 reports another SiPM characterization method which implements a post-processing of the digitized SiPM waveforms with the aim of extracting a full picture of the sensor characteristics from a unique data-set. The procedure is very robust, effective and semi-automatic and suitable for sensors of various dimensions and produced by different vendors. Chapter 4 introduces the Positron Emission Tomography imaging: its principle, applications, related issues and state of the art of PET scanner will be explained. Chapter 5 deals with the preclinical PET, reporting the benefits and the technological challenges involved, the performance of the commercially available small animal PET scanners, the main applications and the frontier research in this field. In Chapter 6 the EasyPET concept is introduced. In particular, the basic idea behind the operating principle, the design layout and the image reconstruction will be illustrated and then assessed through the description and the performance analysis of the EasyPET proof of concept and demonstrator. The effect of the use of different sensor to improve the light collection and the coincidence detection efficiency, together with the analysis of the importance of the sensor and the crystal alignment will be reported in Chapter 7. The design, the functionalities and the commissioning of the EasyPET prototype addressed to the educational market will be defined in Chapter 8. Finally, Chapter 9 contains a summary of the conclusions and an outlook of the future research studies

Common variants at ABCA7, MS4A6A/MS4A4E, EPHA1, CD33 and CD2AP are associated with Alzheimer's disease

We sought to identify new susceptibility loci for Alzheimer's disease through a staged association study (GERAD+) and by testing suggestive loci reported by the Alzheimer's Disease Genetic Consortium (ADGC) in a companion paper. We undertook a combined analysis of four genome-wide association datasets (stage 1) and identified ten newly associated variants with P ≤ 1 × 10−5. We tested these variants for association in an independent sample (stage 2). Three SNPs at two loci replicated and showed evidence for association in a further sample (stage 3). Meta-analyses of all data provided compelling evidence that ABCA7 (rs3764650, meta P = 4.5 × 10−17; including ADGC data, meta P = 5.0 × 10−21) and the MS4A gene cluster (rs610932, meta P = 1.8 × 10−14; including ADGC data, meta P = 1.2 × 10−16) are new Alzheimer's disease susceptibility loci. We also found independent evidence for association for three loci reported by the ADGC, which, when combined, showed genome-wide significance: CD2AP (GERAD+, P = 8.0 × 10−4; including ADGC data, meta P = 8.6 × 10−9), CD33 (GERAD+, P = 2.2 × 10−4; including ADGC data, meta P = 1.6 × 10−9) and EPHA1 (GERAD+, P = 3.4 × 10−4; including ADGC data, meta P = 6.0 × 10−10)

Common variants in Alzheimer’s disease and risk stratification by polygenic risk scores

Funder: Funder: Fundación bancaria ‘La Caixa’ Number: LCF/PR/PR16/51110003 Funder: Grifols SA Number: LCF/PR/PR16/51110003 Funder: European Union/EFPIA Innovative Medicines Initiative Joint Number: 115975 Funder: JPco-fuND FP-829-029 Number: 733051061Genetic discoveries of Alzheimer's disease are the drivers of our understanding, and together with polygenetic risk stratification can contribute towards planning of feasible and efficient preventive and curative clinical trials. We first perform a large genetic association study by merging all available case-control datasets and by-proxy study results (discovery n = 409,435 and validation size n = 58,190). Here, we add six variants associated with Alzheimer's disease risk (near APP, CHRNE, PRKD3/NDUFAF7, PLCG2 and two exonic variants in the SHARPIN gene). Assessment of the polygenic risk score and stratifying by APOE reveal a 4 to 5.5 years difference in median age at onset of Alzheimer's disease patients in APOE ɛ4 carriers. Because of this study, the underlying mechanisms of APP can be studied to refine the amyloid cascade and the polygenic risk score provides a tool to select individuals at high risk of Alzheimer's disease

New insights into the genetic etiology of Alzheimer's disease and related dementias

Characterization of the genetic landscape of Alzheimer's disease (AD) and related dementias (ADD) provides a unique opportunity for a better understanding of the associated pathophysiological processes. We performed a two-stage genome-wide association study totaling 111,326 clinically diagnosed/'proxy' AD cases and 677,663 controls. We found 75 risk loci, of which 42 were new at the time of analysis. Pathway enrichment analyses confirmed the involvement of amyloid/tau pathways and highlighted microglia implication. Gene prioritization in the new loci identified 31 genes that were suggestive of new genetically associated processes, including the tumor necrosis factor alpha pathway through the linear ubiquitin chain assembly complex. We also built a new genetic risk score associated with the risk of future AD/dementia or progression from mild cognitive impairment to AD/dementia. The improvement in prediction led to a 1.6- to 1.9-fold increase in AD risk from the lowest to the highest decile, in addition to effects of age and the APOE ε4 allele

Common variants in Alzheimer's disease and risk stratification by polygenic risk scores.

Funder: Funder: Fundación bancaria ‘La Caixa’ Number: LCF/PR/PR16/51110003 Funder: Grifols SA Number: LCF/PR/PR16/51110003 Funder: European Union/EFPIA Innovative Medicines Initiative Joint Number: 115975 Funder: JPco-fuND FP-829-029 Number: 733051061Genetic discoveries of Alzheimer's disease are the drivers of our understanding, and together with polygenetic risk stratification can contribute towards planning of feasible and efficient preventive and curative clinical trials. We first perform a large genetic association study by merging all available case-control datasets and by-proxy study results (discovery n = 409,435 and validation size n = 58,190). Here, we add six variants associated with Alzheimer's disease risk (near APP, CHRNE, PRKD3/NDUFAF7, PLCG2 and two exonic variants in the SHARPIN gene). Assessment of the polygenic risk score and stratifying by APOE reveal a 4 to 5.5 years difference in median age at onset of Alzheimer's disease patients in APOE ɛ4 carriers. Because of this study, the underlying mechanisms of APP can be studied to refine the amyloid cascade and the polygenic risk score provides a tool to select individuals at high risk of Alzheimer's disease

Multiancestry analysis of the HLA locus in Alzheimer’s and Parkinson’s diseases uncovers a shared adaptive immune response mediated by HLA-DRB1*04 subtypes

Across multiancestry groups, we analyzed Human Leukocyte Antigen (HLA) associations in over 176,000 individuals with Parkinson’s disease (PD) and Alzheimer’s disease (AD) versus controls. We demonstrate that the two diseases share the same protective association at the HLA locus. HLA-specific fine-mapping showed that hierarchical protective effects of HLA-DRB1*04 subtypes best accounted for the association, strongest with HLA-DRB1*04:04 and HLA-DRB1*04:07, and intermediary with HLA-DRB1*04:01 and HLA-DRB1*04:03. The same signal was associated with decreased neurofibrillary tangles in postmortem brains and was associated with reduced tau levels in cerebrospinal fluid and to a lower extent with increased Aβ42. Protective HLA-DRB1*04 subtypes strongly bound the aggregation-prone tau PHF6 sequence, however only when acetylated at a lysine (K311), a common posttranslational modification central to tau aggregation. An HLA-DRB1*04-mediated adaptive immune response decreases PD and AD risks, potentially by acting against tau, offering the possibility of therapeutic avenues

Development of a silicon photomultiplier based innovative and low cost positron emission tomography scanner.

The Silicon Photomultiplier (SiPM) is a state-of-the-art semiconductor photodetector consisting of a high density matrix (up to 104) of independent pixels of micro-metric dimension (from 10 μm to 100 μm) which form a macroscopic unit of 1 to 6 mm2 area. Each pixel is a single-photon avalanche diode operated with a bias voltage of a few volts above the breakdown voltage. When a charge carrier is generated in a pixel by an incoming photon or a thermal effect, a Geiger discharge confined to that pixel is initiated and an intrinsic gain of about 106 is obtained. The output signal of a pixel is the same regardless of the number of interacting photons and provide only a binary information. Since the pixels are arranged on a common Silicon substrate and are connected in parallel to the same readout line, the SiPM combined output response corresponds to the sum of all fired pixel currents. As a result, the SiPM as a whole is an analogue detector, which can measure the incoming light intensity. Nowadays a great number of companies are investing increasing efforts in SiPM detector performances and high quality mass production. SiPMs are in rapid evolution and benefit from the tremendous development of the Silicon technology in terms of cost production, design flexibility and performances. They have reached a high single photon detection sensitivity and photon detection efficiency, an excellent time resolution, an extended dynamic range. They require a low bias voltage and have a low power consumption, they are very compact, robust, flexible and cheap. Considering also their intrinsic insensitivity to magnetic field they result to have an extremely high potential in fundamental and applied science (particle and nuclear physics, astrophysics, biology, environmental science and nuclear medicine) and industry. The SiPM performances are influenced by some effects, as saturation, afterpulsing and crosstalk, which lead to an inherent non-proportional response with respect to the number of incident photons. Consequently, it is not trivial to relate the measured electronic signal to the corresponding light intensity. Since for most applications it is desirable to qualify the SiPM response (i.e in order to properly design a detector for a given application, perform corrections on measurements or on energy spectra, calibrate a SiPM for low light measurements, predict detector performance) the implementation of characterization procedures plays a key role. The SiPM field of application that has been considered in this thesis is the Positron Emission Tomography (PET). PET represents the most advanced in-vivo nuclear imaging modality: it provides functional information of the physiological and molecular processes of organs and tissues. Thanks to its diagnostic power, PET has a recognized superiority over all other imaging modalities in oncology, neurology and cardiology. SiPMs are usually successfully employed for the PET scanners because they allow the measurement of the Time Of Flight of the two coincidence photons to improve the signal to noise ratio of the reconstructed images. They also permit to perfectly combine the functional information with the anatomical one by inserting the PET scanner inside the Magnetic Resonance Imaging device. Recently, PET technology has also been applied to preclinical imaging to allow non invasive studies on small animals. The increasing demand for preclinical PET scanner is driven by the fact that small animals host a large number of human diseases. In-vivo imaging has the advantage to enable the measurement of the radiopharmaceutical distribution in the same animal for an extended period of time. As a result, PET represents a powerful research tool as it offers the possibility to study the abnormalities at the origin of a disease, understand its dynamics, evaluate the therapeutic response and develop new drugs and treatments. However, the cost and the complexity of the preclinical scanners are limiting factors for the spread of PET technology: 70-80% of small-animal PET is concentrated in academic or government research laboratories. The EasyPET concept proposed in this Thesis, protected under a patent filed by Aveiro University, aims to achieve a simple and affordable preclinical PET scanner. The innovative concept is based on a single pair of detector kept collinear during the whole data acquisition and a moving mechanism with two degrees of freedom to reproduce the functionalities of an entire PET ring. The main advantages are in terms of the reduction of the complexity and cost of the PET system. In addition the concept is bound to be robust against acollinear photoemission, scatter radiation and parallax error. The sensitivity is expected to represent a fragility due to the reduced geometrical acceptance. This drawback can be partially recovered by the possibility to accept Compton scattering events without introducing image degradation effects, thanks to the sensor alignment. A 2D imaging demonstrator has been realized in order to assess the EasyPET concept and its performance has been analyzed in this Thesis to verify the net balance between competing advantages and drawbacks. The demonstrator had a leading role in the outreach activity to promote the EasyPET concept and a significant outcome is represented by the new partners that recently joined the collaboration. The EasyPET has been licensed to Caen S.p.a. and, thanks to the participation of Nuclear Instruments to the electronic board re-designed, a new prototype has been realized with additional improvements concerning the mechanics and the control software. In this Thesis the prototype functionalities and performances are reported as a result of a commissioning procedure. The EasyPET will be commercialized by Caen S.p.a. as a product for the educational market and it will be addressed to high level didactic laboratories to show the operating principles and technology behind the PET imaging. The topics mentioned above will be examined in depth in the following Chapters according to the subsequent order. In Chapter 1 the Silicon Photomultiplier will be described in detail, from their operating principle to their main application fields passing through the advantages and the drawback effects connected with this type of sensor. Chapter 2 is dedicated to a SiPM standard characterization method based on the staircase and resolving power measurement. A more refined analysis involves the Multi-Photon spectrum, obtained by integrating the SiPM response to a light pulse. It exploits the SiPM single photon sensitivity and its photon number resolving capability to measure some of its properties of general interest for a multitude of potential applications, disentangling the features related to the statistics of the incident light. Chapter 3 reports another SiPM characterization method which implements a post-processing of the digitized SiPM waveforms with the aim of extracting a full picture of the sensor characteristics from a unique data-set. The procedure is very robust, effective and semi-automatic and suitable for sensors of various dimensions and produced by different vendors. Chapter 4 introduces the Positron Emission Tomography imaging: its principle, applications, related issues and state of the art of PET scanner will be explained. Chapter 5 deals with the preclinical PET, reporting the benefits and the technological challenges involved, the performance of the commercially available small animal PET scanners, the main applications and the frontier research in this field. In Chapter 6 the EasyPET concept is introduced. In particular, the basic idea behind the operating principle, the design layout and the image reconstruction will be illustrated and then assessed through the description and the performance analysis of the EasyPET proof of concept and demonstrator. The effect of the use of different sensor to improve the light collection and the coincidence detection efficiency, together with the analysis of the importance of the sensor and the crystal alignment will be reported in Chapter 7. The design, the functionalities and the commissioning of the EasyPET prototype addressed to the educational market will be defined in Chapter 8. Finally, Chapter 9 contains a summary of the conclusions and an outlook of the future research studies

Mechanistic modelling of avascular tumor growth and pharmacokinetics influence—Part I

A mechanistic model for the avascular tumor growth both for in “in vivo” and “in vitro” conditions is presented here. It involves the main cell physiology, like the growth (by substrate uptake), the mitosis, the apoptosis and the necrosis, all with their corresponding kinetics. The resulting population balance was solved through the moments’ method. Moreover, the model was combined with the classic equations of pharmacokinetics to consider also the presence of active drugs affecting either the kinetics of cell necrosis or growth. The model was compared with literature tumor growth data both for in vivo and in vitro conditions