Mathematical modelling in nuclear medicine

Modern imaging techniques can provide sequences of images giving signals proportional to the concentrations of tracers (by emission tomography), of X-ray-absorbing contrast materials (fast CT or perhaps NMR contrast), or of native chemical substances (NMR) in tissue regions at identifiable locations in 3D space. Methods for the analysis of the concentration-time curves with mathematical models describing the physiological processes and the appropriate anatomy are now available to give a quantitative portrayal of both structure and function: such is the approach to metabolic or functional imaging. One formulates a model first by defining what it should represent: this is the hypothesis. When translated into a self-consistent set of differential equations, the model becomes a mathematical model, a quantitative version of the hypothesis. This is what one would like to test against data. However, the next step is to reduce the mathematical model to a computable form; anatomically and physiologically realistic models account of the spatial gradients in concentrations within blood-tissue exchange units, while compartmental models simplify the equations by using the average concentrations. The former are known as distributed models and the latter as lumped compartmental or mixing chamber models. Since both are derived from the same ideas, the parameters are usually the same; their differences are in their ability to represent the hypothesis correctly, quantitatively, and sometimes in their computability. In this essay we review the philosophical and practical aspects of such modelling analysis for translating image sequences into physiological terms.     

Scatter modelling and compensation in emission tomography

In nuclear medicine, clinical assessment and diagnosis are generally based on qualitative assessment of the distribution pattern of radiotracers used. In addition, emission tomography (SPECT and PET) imaging methods offer the possibility of quantitative assessment of tracer concentration in vivo to quantify relevant parameters in clinical and research settings, provided accurate correction for the physical degrading factors (e.g. attenuation, scatter, partial volume effects) hampering their quantitative accuracy are applied. This review addresses the problem of Compton scattering as the dominant photon interaction phenomenon in emission tomography and discusses its impact on both the quality of reconstructed clinical images and the accuracy of quantitative analysis. After a general introduction, there is a section in which scatter modelling in uniform and non-uniform media is described in detail. This is followed by an overview of scatter compensation techniques and evaluation strategies used for the assessment of these correction methods. In the process, emphasis is placed on the clinical impact of image degradation due to Compton scattering. This, in turn, stresses the need for implementation of more accurate algorithms in software supplied by scanner manufacturers, although the choice of a general-purpose algorithm or algorithms may be difficult.     

P-gp功能的PET显像剂的研究进展

肿瘤对化疗药物产生耐药性是肿瘤治疗失败的主要原因,引起肿瘤对化疗药物耐药的重要机制是ATP结合盒（ABC）转运蛋白的过度表达.P-糖蛋白（P-gp）是ABC转运蛋白超家族中研究最广、最深入的一类转运蛋白,目前检测P-gp主要依赖于组织活检或术后病理组织在体外进行定性、定量分析,这些检测方法受取材技术、肿瘤标本差异等因素的限制,因此,寻找一种无创性、可以动态检测肿瘤多药耐药的方法就显得尤为重要.目前许多^18F、^11C标记的P-gp底物及抑制剂的正电子显像剂已经进行基础研究,部分进入了临床试验阶段.该文对P-gp的PET显像剂现状进行综述.     

Comprehensive model for simultaneous MRI determination of perfusion and permeability using a blood-pool agent in rats rhabdomyosarcoma

To present a new compartmental analysis model developed to simultaneously measure tissue perfusion and capillary permeability in a tumor using MRI and a macromolecular contrast medium. Rhadomyosarcomas were implanted subcutaneously in 20 rats and studied by 1.5-T MRI using a fast gradient echo sequence (2D fast SPGR TR/TE/ 13 ms/1.2 ms/60°) after injection of a macromolecular contrast medium. The left ventricle and tumor signal intensities were converted into concentrations and modeled using compartmental analysis, yielding tumor perfusion F, distribution volume V_distribution, volume transfer constant K^trans, rate constant of influx k_pe, and initial extraction (fraction) E. Tumor perfusion was F=43±29 ml·min^–1·100 g^–1. The permeability study allowed the measurement of k_pe=0.37±0.12 min^–1 and K^trans=0.01±0.0031 min^–1. The blood volume could be assimilated to the distribution volume (V_distribution=2.9±1.01%) since the capillary leakage was small. The simultaneous assessment of perfusion and permeability allowed quantification of the initial extraction (fraction) E=2.34±1.05%. Quantification of both tumor perfusion and capillary leakage is feasible using MRI using a macromolecular blood pool agent. The method should improve tumor characterization.     

Cardiac nuclear medicine tomographic systems

There are two competitive measuring techniques in emission tomography: SPECT and PET. The superiority of PET is founded not only on using physiological radionuclides and tracers such as carbon 11, oxygen 15, and nitrogen 13, but also on achieving a physical performance far in excess of that of SPECT. Considering the demands of cardiac studies, the performance of both methods is analyzed and compared and the inherent limitations are stated.Dedicated to Prof. Heinz Hundeshagen on the occasion of his 60th birthday     

Cardiac nuclear medicine: Positron emission tomography in clinical medicine

Positron-emission tomography (PET) and radioactively labelled substrates permit metabolic studies to be carried out in vivo and in situ with few if any limitations regarding the choice of substrates as long as they can be tagged with positron-emitting radionuclides, especially those like ¹¹C and ¹³N. With respect to cardiology, ¹³N-ammonia and ⁸²Rb are helpful in the examination of myocardial perfusion. The evaluation of myocardial glucose and fatty acid metabolism with ¹⁸F-deoxyglucose (FDG) and ¹¹C-palmitate has proved to be clinically useful. Thus, myocardial ischemia and hypoxia, infarct size, the transmural extent of the infarction and tissue viability after it can all be examined as can pathological biochemistry in patients with primary or secondary cardiomyopathies. Single-photon-emitting labelled substances such as ¹²³I-labelled fatty acid analogues also provide information equivalent to that which can be gathered by PET for clinical use. Thus, one major task of PET is the validation of methods and the transformation of these methods to single-photon-emitting radiotracers for broad clinical application, in situations where the expense of PET cannot at present be justified.Dedicated to Prof. Heinz Hundeshagen on the occasion of his 60th birthday     

Quantitative analysis of99mTc-HMPAO kinetics in epilepsy

A convection-diffusion model is applied for the determination of cerebral circulation parameters in patients with frontal lobe epilepsy. The method employs^99mTc-HMPAO, dynamic brain imaging and SPECT. The model takes into account both the capillary and cell permeabilities of HMPAO. Experiments were performed in 41 patients with epilepsy and 10 patients with out evident cerebrovascular disease. The results indicate that in the inter ictal epileptic foci, cerebral blood flow was reduced (18%±19%), cerebral blood volume was increased (21%±14%), and the capillary permeability of HMPAO in the affected side was on the average 50% of the value in the contralateral side, whereas the reflux from brain tissue to blood was increased. These findings mean that HMPAO diffusion across the blood brain barrier is restricted and HMPAO slackly interacts with the intra cellular component of the inter ictal epileptic foci.     

Pulmonary nuclear medicine

This article reviews the contribution made by nuclear imaging to the assessment, diagnosis and monitoring of patients with respiratory disease. It focuses on several specific areas including the diagnosis of pulmonary embolism, the investigation of intrapulmonary infection and neoplasm and the role of positron emission tomography (PET) scanning. Offprint requests to: R.F. Miller     

胰岛β细胞的分子核医学显像进展

糖尿病是严重威胁人类健康的常见病和多发病.糖尿病主要是由于胰岛β细胞选择性破坏或胰岛e细胞分泌胰岛素迟缓和胰岛素抵抗而使胰岛素相对不足所致.β细胞的数量只有减少50%～60%时才会出现相关的症状.由于胰腺位置较深,β细胞含量少,目前临床诊断主要采用有创性方法,且难于进行早期诊断.因此,通过无创性的方法进行β细胞相关代谢疾病的早期诊断,越来越受到人们的关注,影像学诊断也就成了关注焦点,但是如何进行β细胞数量和功能的评估仍是目前影像学诊断面临的重要课题.     

Characterization of right or left ventricular contraction heterogeneity using Fourier phase analysis

The standard deviation of the first harmonic Fourier phase histogram is an indicator of the contraction heterogeneity of the heart ventricles. This approach has been applied to analyse tomographic blood pool (^99mTc) examinations in a group of 32 patients with angiographically verified mainly right (RV) but also left (LV) kinetic disorders in relation to severe ventricular arrhythmias and suspicion of arrhythmogenic right ventricular dysplasia (ARVD). The reference group consisted of ten patients with low probability of cardiac kinetic abnormalities.Thick tomographic slices including both ventricles have been reconstructed in the horizontal long axis orientation from a series of 32 gated projections recorded over a 360° rotation. Separately for each ventricle the Fourier phase histograms have been computed and characterized by their standard deviations (PSD). Normal values (mean±standard deviation, LV=11°±5°, RV=12°±5°) were significantly lower (P<0.01 and P<0.001) than those measured in abnormal cases (LV=19°±10° and RV=31°±17°).Detailed analysis of the data supports the hypothesis of a primary RV disease in ARVD, with secondary LV extension. PSD seems to be a good predictor of an organic cardiac disease underlying ventricular arrhythmias and may be used for screening the patients.This work has been supported by a contract of the National Health Insurance Office of France (Caisse Nationale d'Assurance Maladie des Travailleurs Salariés)     

CT及核医学技术在肺栓塞诊断中的应用价值

肺动脉栓塞是指内源性或外源性栓子经静脉回流最终嵌塞在肺动脉及其分支,导致组织血液供应受阻所引起的一系列临床和病理生理综合征,其发病率和病死率均很高。CT和核医学技术是目前临床上诊断肺栓塞最常用的影像技术。随着计算机技术的不断更新,这两种技术也取得了一定的进展。综述CT及核医学技术在肺栓塞诊断上的进展,比较各种诊断方法的优势与不足,以期为临床选择合适的诊断方法提供参考。     

Effect of intravascular ligand binding on parameter estimates derived from tracer kinetic modelling

The purpose of this study was to assess the effect of intravascular ligand binding on parameter estimates derived from tracer kinetic modelling. To this end intravascular ligand kinetics between the free and a bound compartment in plasma and the exchange of tracer between the capillary space and tissue were analysed using a simple compartment model. The effect of non-equilibrated intravascular compartments on parameter estimates was evaluated in a computer simulation. It was found that three kinetic situations must be distinguished. If the intravascular compartments are fully equilibrated when the ligand reaches the target organ, intravascular binding simply acts as a scale factor for the transport-related parameterK ₁. If the intravascular kinetics is very slow, only minimal binding will occur. In between there is a range where ongoing equilibration leads to time variability ofK ₁. Since tracer kinetic modelling usually does not account for such time variability, the parameter estimates become biased, the degree of the bias depending on the intravascular binding kinetics. Furthermore the bias may be dependent on receptor density, meaning that model-derived receptor estimates are not linearly related to the true receptor density. It is concluded that intravascular ligand binding can severely affect parameter estimates derived from tracer kinetic modelling. Especially disturbing are effects due to ongoing intravascular equilibration following the arrival of the ligand in the target organ. These can be avoided by letting the ligand equilibrate with blood in a syringe prior to injection.     

In vivo assessment of cardiac insulin resistance by nuclear probes using an iodinated tracer of glucose transport

Purpose Insulin resistance, implying depressed cellular sensitivity to insulin, is a risk factor for type 2 diabetes and cardiovascular disease. This study is the first step towards the development of a technique of insulin resistance measurement in humans with a new tracer of glucose transport, [¹²³I]6-deoxy-6-iodo-D-glucose (6DIG). Methods We investigated 6DIG kinetics in anaesthetised control rats and in three models of insulin-resistant rats: fructose fed, Zucker and ZDF. The study of myocardial 6DIG activity was performed under two conditions: first, 6DIG was injected under the baseline condition and then it was injected after a bolus injection of insulin. After each injection, radioactivity was measured over 45 min by external detection via NaI probes, in the heart and blood. A tri-compartment model was developed to obtain fractional transfer coefficients of 6DIG from the blood to the heart. Results These coefficients were significantly increased with insulin in control rats and did not change significantly in insulin-resistant rats. The ratio of the coefficient obtained under insulin to that obtained under basal conditions gave an index of cardiac insulin resistance for each animal. The mean values of these ratios were significantly lower in insulin-resistant than in control rats: 1.16 ± 0.06 vs 2.28 ± 0.18 (p < 0.001) for the fructose-fed group, 0.92 ± 0.05 vs 1.62 ± 0.25 (p < 0.01) for the Zucker group and 1.34 ± 0.06 vs 2.01 ± 0.26 (p < 0.05) for the ZDF group. Conclusion These results show that 6DIG could be a useful tracer to image cardiac insulin resistance.     

核医学显像在心脏淀粉样变性中的应用进展

淀粉样变性是由多种原因造成的淀粉样物质在体内各脏器细胞间的沉积,其可使受累脏器的功能逐渐衰竭。淀粉样物质累及心脏时即导致心脏淀粉样变性（CA）,其预后最差。CA中以转甲状腺素蛋白淀粉样变性型及免疫球蛋白轻链型最常见,二者的中位生存期及治疗方法存在巨大差异,因此,早期诊断及准确分型对于患者的治疗至关重要。核医学显像可以对CA患者进行无创性诊断及准确分型,在临床上逐渐得到了广泛应用。笔者就核医学显像在CA中的最新研究进展作一综述,以提高临床医师对于CA的认识,便于早期诊断CA。     

PET分子探针在类风湿关节炎中的研究进展

类风湿关节炎（RA）是一种病因未明的、以滑膜炎为主要特征的慢性自身免疫性疾病,多累及手、足部小关节,呈对称性、侵袭性关节炎改变,最终导致关节畸形甚至功能丧失。不同于传统的影像学检查方法,PET提供了一种在细胞水平上的显像方法,是一种潜在的、高度灵敏的滑膜炎评估方法。笔者就PET分子探针在RA中的临床应用及研究进展进行综述,旨在为RA的诊断提供思路。     

核医学显像在诊断淋巴瘤药物相关早期肺脏损伤中的研究进展

药物相关肺脏损伤(DALI)是影响淋巴瘤患者预后的重要因素之一,早期识别并及时干预DALI至关重要。目前常用的影像学检查(高分辨CT)及实验室检查均具有滞后性,从而使肺脏损伤不可逆,而核医学显像对DALI提供了早于形态学改变之前的功能代谢信息,使患者获得及早干预。本文就核医学显像在淋巴瘤DALI中的应用进行综述。     

Dosimetry of transmission measurements in nuclear medicine: a study using anthropomorphic phantoms and thermoluminescent dosimeters

Quantification in positron emission tomography (PET) and single photon emission tomographic (SPET) relies on attenuation correction which is generally obtained with an additional transmission measurement. Therefore, the evaluation of the radiation doses received by patients needs to include the contribution of transmission procedures in SPET (SPET-TM) and PET (PET-TM). In this work we have measured these doses for both PET-TM and SPET-TM. PET-TM was performed on an ECAT EXACT HR+ (CTI/Siemens) equipped with three rod sources of germanium-68 (380 MBq total) and extended septa. SPET-TM was performed on a DST (SMV) equipped with two collimated line sources of gadolinium-153 (4 GBq total). Two anthropomorphic phantoms representing a human head and a human torso, were used to estimate the doses absorbed in typical cardiac and brain transmission studies. Measurements were made with thermoluminescent dosimeters (TLDs, consisting of lithium fluoride) having characteristics suitable for dosimetry investigations in nuclear medicine. Sets of TLDs were placed inside small plastic bags and then attached to different organs of the phantoms (at least two TLDs were assigned to a given organ). Before and after irradiation the TLDs were placed in a 2.5-cm-thick lead container to prevent exposure from occasional sources. Ambient radiation was monitored and taken into account in calculations. Transmission scans were performed for more than 12 h in each case to decrease statistical noise fluctuations. The doses absorbed by each organ were calculated by averaging the values obtained for each corresponding TLD. These values were used to evaluate the effective dose (ED) following guidelines described in ICRP report number 60. The estimated ED values for cardiac acquisitions were 7.7×10^–4±0.4×10^–4 mSv/MBq · h and 1.9×10^–6±0.4×10^–6 ███/MBq · h for PET-TM and SPET-TM. respectively. For brain scans, the values of ED were calculated as 2.7×10^–4±0.2×10^–4 mSv/MBq · h for PET-TM and 5.2×10^–7±2.3×10^–7 mSv/MBq · h for SPET-TM. In our institution, PET-TM is usually performed for 15 min prior to emission. SPET-TM is performed simultaneously with emission and usually lasts 30 and 15 min for brain and cardiac acquisitions respectively. Under these conditions ED values, estimated for typical source activities at delivery time (22000 MBq in SPET and 555 MBq for PET), were 1.1×10^–1± 0.1×10^–1 mSv and 1.1×10^–2±0.2×10^–2 mSv for cardiac PET-TM and SPET-TM respectively. For brain acquisitions, the ED values obtained under the same conditions were 3.7×10^–2±0.3×10^–2 mSv and 5.8×10^–3±2.6×10^–3███ for PET-TM and SPET-TM respectively. These measurements show that the dose received by a patient during a transmission scan adds little to the typical dose received in a routine nuclear medicine procedure. Radiation dose, therefore, does not represent a limit to the generalised use of transmission measurements in clinical SPET or PET. Received 12 May and in revised form 1 July 1998     

PET kinetic analysis: error consideration of quantitative analysis in dynamic studies

Positron emission tomography dynamic studies have been performed to quantify several biomedical functions. In a quantitative analysis of these studies, kinetic parameters were estimated by mathematical methods, such as a nonlinear least-squares algorithm with compartmental model and graphical analysis. In this estimation, the uncertainty in the estimated kinetic parameters depends on the signal-to-noise ratio and quantitative analysis method. This review describes the reliability of parameter estimates for various analysis methods in reversible and irreversible models.     

ARRONAX,a high-energy and high-intensity cyclotron for nuclear medicine

PURPOSE: This study was aimed at establishing a list of radionuclides of interest for nuclear medicine that can be produced in a high-intensity and high-energy cyclotron. METHODS: We have considered both therapeutic and positron emission tomography radionuclides that can be produced using a high-energy and a high-intensity cyclotron such as ARRONAX, which will be operating in Nantes (France) by the end of 2008. Novel radionuclides or radionuclides of current limited availability have been selected according to the following criteria: emission of positrons, low-energy beta or alpha particles, stable or short half-life daughters, half-life between 3 h and 10 days or generator-produced, favourable dosimetry, production from stable isotopes with reasonable cross sections. RESULTS: Three radionuclides appear well suited to targeted radionuclide therapy using beta ((67)Cu, (47)Sc) or alpha ((211)At) particles. Positron emitters allowing dosimetry studies prior to radionuclide therapy ((64)Cu, (124)I, (44)Sc), or that can be generator-produced ((82)Rb, (68)Ga) or providing the opportunity of a new imaging modality ((44)Sc) are considered to have a great interest at short term whereas (86)Y, (52)Fe, (55)Co, (76)Br or (89)Zr are considered to have a potential interest at middle term. CONCLUSIONS: Several radionuclides not currently used in routine nuclear medicine or not available in sufficient amount for clinical research have been selected for future production. High-energy, high-intensity cyclotrons are necessary to produce some of the selected radionuclides and make possible future clinical developments in nuclear medicine. Associated with appropriate carriers, these radionuclides will respond to a maximum of unmet clinical needs.     

Compartment modelling in nuclear medicine: a new program for the determination of transfer coefficients

In many investigations concerning transport/exchange of matter in a natural system, e.g. functional studies in nuclear medicine, it is advantageous to relate experimental results to a model of the system. This paper presents a new computer program for the determination of linear transfer coefficients in a compartment model from experimentally observed time-compartment content curves. The program performs a least-square fit with the specified precision of the observed values as weight factors. The resulting uncertainty in the calculated transfer coefficients may also be assessed. The application of the program in nuclear medicine is demonstrated and discussed.