Review and Practical Excursus of the Propensity Score: Low Protein Diet Compared to Mediterranean Diet in Patients With Chronic Kidney Disease

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Vincenzo Calabrese

Vincenzo Calabrese1, Guido Gembillo1, Martina Buda2, Valeria Cernaro1, Elisa Longhitano1, Antonello Pontoriero3, Matteo Polizzi4, Daniela Metro1, Domenico Santoro1

1 Unit of Nephrology and Dialysis, Department of Clinical and Experimental Medicine, A.O.U. ‘G. Martino’, University of Messina, Messina, Italy
2 General and Oncologic Surgery Unit, Faculty of Medicine, University of Messina, G. Martino University Hospital, Messina, Italy
3 Unit of Nephrology, Department of medicine ASP 5 Messina, P.O. Milazzo
4 University of Messina, Messina, Italy

Corresponding author:
Vincenzo Calabrese
Tel: 328736905
E-mail: v.calabrese@outlook.it

 

Abstract

Although Randomized clinical trials (RCT) represent the gold standard to compare two or more treatments, the impact of observational studies cannot be ignored. Obviously, these latter are performed on unbalanced sample, and differences among the compared groups could be detected. These differences could have an impact on the estimated association between our allocation and our outcome. To avoid it, some methods should be applied in the analysis of observational cohort.
Propensity score (PS) can be considered as a value which sums up and balances the known variables. It aims to adjust or balance the probability of receiving a specific allocation group, and could be used to match, stratify, weight, and perform a covariate adjustment. PS is calculated with a logistic regression, using allocation groups as the outcome. Thanks to PS, we compute the probability of being allocated to one group and we can match patients obtaining two balanced groups. It avoids computing analysis in unbalanced groups.
We compared low protein diet (LPD) and the Mediterranean diet in CKD patients and analysed them using the PS methods. Nutritional therapy is fundamental for the prevention, progression and treatment of Chronic Kidney Disease (CKD) and its complications. An individualized, stepwise approach is essential to guarantee high adherence to nutritional patterns and to reach therapeutic goals. The best dietary regimen is still a matter of discussion.  In our example, unbalanced analysis showed a significant renal function preservation in LPD, but this correlation was denied after the PS analysis.
In conclusion, although unmatched analysis showed differences between the two diets, after propensity analysis no differences were detected. If RCT cannot be performed, balancing the PS score allows to balance the sample and avoids biased results.

Keywords: Chronic Kidney Disease, Low Protein Diet, Matching, Mediterranean Diet, Nutritional Therapy, Propensity Score, Randomized Clinical Trials

Introduction

Clinical investigations are mainly categorized in observational and interventional studies, the latter including randomized controlled trials (RCT) [1]. Comparative effectiveness studies belong to the family of observational studies and aim to compare two active treatments to identify which one is more efficient in improving the time course of a disease or reducing the risk of a given condition in real life (i.e., in a context different from an RCT) [2]. From this perspective, this type of study design differs from RCTs because the latter specifically contemplate ‘no intervention’ (i.e., the placebo arm).

Treatments are candidates to be investigated by a study of comparative effectiveness only when the same treatment was proved to be effective versus a control in an RCT. The main reason why these studies are considered with caution by the scientific community is the lack of randomization, which implies that the results of these studies are prone to a peculiar type of bias called ‘confounding by indication’ [3]. In a given treatment-outcome pathway, a confounder is a variable that is associated with the treatment (i.e., it differs between the study arms). It is not an effect of the treatment, does not lie in the causal pathway between the treatment and the outcome, and represents a risk factor for the outcome. In real life, a confounder can increase, reduce, or definitely obscure the true effect of treatment on an outcome. Despite these challenges, observational studies of effectiveness offer opportunities to examine questions impossible to be investigated by RCTs [4]. First, they can be used to examine the effectiveness of medication that has already obtained marketing authorization and for which funding for further trials may be limited. Second, they can allow the examination of effectiveness for rare treatment indications. Third, a large observational study can be more representative of a clinical population and less prone to selection bias than a trial.

In observational studies of effectiveness, common methods used to adjust to confounding are multiple regression models [5], the use of instrumental variables [6], and the propensity score (PS) [7]. Briefly, multiple regression analyses are performed by including in the model all variables that meet the criteria to be considered as confounders. An instrument is a variable that predicts exposure, but conditional on exposure shows no independent association with the study outcome. As an example, we can consider an observational multicenter study that evaluates how different treatments can affect a clinical outcome. The facility allocation can be considered as the result of a ‘natural experiment’ by simulating a randomization. In this manuscript, we describe an efficient statistical technique used by researchers to mitigate the problem of confounding in observational studies of effectiveness.

 

Propensity score

The propensity score (PS) was described in 1983. This method allows adjusting or balancing for the probability to receive a specific allocation group, an estimation of the likelihood of being in one or in another group in relation to a set of covariates [8]. PS could be used to match, stratify, weight, and perform a covariate adjustment. If the outcome is a binary variable, matching has less bias than stratification or covariate adjustment, as in a time-dependent outcome both matching and Inverse Probability of Treatment Weighting (IPTW) are less biased than stratification or covariate adjustment. PS is calculated with a logistic regression, using allocation groups as outcome. Thanks to this method, we can compute the probability of confounder variables to be allocated in one group. Since PS has no limits of variables, it can be used in small samples and for rare diseases [9], unlike multivariate regression.

Matching

Matching with PS methods allows us to compare one or more patients with the same allocation probability, so it follows that matched patients have similar features, decreasing bias. This method consists of matching cases of two or more groups on the basis of similar predicted PS, thus allowing the comparison of groups with an equal distribution of confounders (covariate balance) [10, 11]. Imaging having two groups of patients, at first, we need to compute PS, corresponding to the probability of receiving allocation in group A, for each one of them [12]. By doing this, a binomial logistic regression is performed to select, among the study variables, those associated with the allocation variable. Patients with the same PS value are thus compared. Minimizing the differences between patients, and comparing homogeneous groups, confounding is reduced.

Stratification

The stratification by PS follows the matching methods. Strata will be created between subjects with similar PS of treatments. The Stratification method removes about 90% of bias due to covariate imbalance [13].

Formally, stratification by PS can be resumed as follows:

  • choosing variables included in the PS model among personal data, comorbidities, laboratory data, and variables clinically related to outcome
  • estimating PS value for each subject, with logistic regression using allocation as the dependent variable
  • calculating the Cumulative Distribution Function for each subject, able to define the distribution also in a discrete and binomial variable
  • ranking population based on PS value, dividing the whole sample into quartiles, tertiles, deciles, etc., based on PS values
  • assessing balance for each of the K (K is the indicator of the treatment group), analyzing the baseline features
  • retaining the PS value ordering that creates strata with the best covariate balance and conducting a stratified outcome analysis to estimate ATE or ATT [14].

The number of strata can be evaluated based on the number of covariates (2×covariates – 1) with groups of more than ten subjects [15]. In a large observational study, Cernaro V. et al. [16], on behalf of the Workgroup of the Sicilian Registry of Nephrology, analyzed the impact of convective dialysis on mortality and cardiovascular mortality. They performed Cox Regression analysis with incremental multivariate models but, although the independent impact of convective dialysis on mortality, many other variables were related to the outcome.

Thus, as highlighted in their methods section, PS stratification was computed to perform a sensitivity analysis [17]. PS was computed through a multivariate logistic regression model including age, gender, ethnicity, arterial hypertension, diabetes mellitus, and cardiac diseases. Then, the whole sample was divided into quartiles (based on PS value) and survival analyses computed in the whole sample were repeated. These latter results confirmed the independent impact of the treatment, but in subsamples that are theoretically more homogenous because PS value was computed on the bases of the possible confounding.

Inverse Probability of Treatment Weighting (IPTW) Estimation

IPTW analyses aimed to create a weighted sample in which the distribution of each confounding variable was the same between the compared groups [18]. Patients will be allocated the reciprocal of the PS value: each patient of the treated group receives the weight of 1/PS and each patient of the untreated group receives the weight of 1/(1-PS). A treated patient with a low PS value enters in the analysis with a high weighting because he is considered likely an untreated patient in terms of comorbidities, so a valid comparison can be made between the two [19]. Practically, in the analysis, each patient is evaluated as many times as their IPTW is.  A treated patient with a PS of 0.1 will weigh 1/0.1=10 and will be considered in the analysis ten times. Similarly, a treated patient with high PS, for example 0.8, will weigh 1/0.8=1.25 and it will be considered in the analysis 1.25 times. Moreover, IPTW was at the basis of the Marginal Structured Models, a multistep estimation procedure designed to control confounding variables at different time points in longitudinal studies [20]. IPTW method is not robust against the outliers.

Covariate adjustment

This method uses the PS values as a covariate in a linear regression analysis. Even if there is no significant association between the covariates used to compute PS value and the outcome, the use of PS value as a covariate allows us to approximate the effect of each of the aforementioned covariates [21].

 

Practical example

To explain these methods, we will use a dataset containing 75 non-randomized patients with CKD stage III-IV.

All the remaining patients gave written consent to data processing for research purposes in respect of privacy. Ethical approval was not necessary according to National Code on Clinical Trials declaration and according to Italian ministerial rules of September 6, 2002 n°6, because our observation derives from a real-life retrospective study.

Patients were followed up for one year.  40 patients followed an LPD, defined by a protein intake of 0.6 g/kg/day (Group A), and 35 patients were subjected to the Mediterranean diet (Group B). The allocation, according to the real-life observation design, was based on dietician suggestions, patient’ habits, and adherence abilities, which were evaluated during the baseline visit.  Supplementary Table 1 and Table 2 summarized the details about the quantity and the nature of both diet regimens. Laboratory data were collected at the baseline visit (T0) and the annual follow-up (T1), as follows: serum urea (mg/dl), serum creatinine(mg/dl), serum phosphorous (mg/dl), serum sodium (mmol/l), serum potassium (mmol/l), white blood cells (WBC) (cc/mmc).

The groups had significant differences in BMI (28.7 [25.0, 34.7] vs 26.4 [24.0, 28.0], p=0.02), age (68 ± 9 vs 74 + 13, p=0.04), and basal creatinine clearance (33 [25, 44] vs 27 [21, 36], p=0.03). Baseline features were summed up in Table 1.

Variable Whole sample Group A (n= 40) Group B (n= 35) p
Age (years) 71 ± 11 68 ± 9 74 + 13 0.04
Sex (M/F) 45/55 40/60 49/51 0.32
BMI (kg/mq) 27.4 [24.2 – 30] 28.7 [25.0 – 34.7] 26.4 [24.0 – 28.0] 0.02
Clearance (ml/min) 31 [23 – 41] 33 [25 – 44] 27 [21- 36] 0.03
Serum Urea (mg/dl) 73 [64 -102] 75 [65 -99] 73 [60 -121] 0.84
Serum creatinine (mg/dl) 1.8 [1.5 – 2.5] 1.7 [1.4 – 2.4] 2.0 [1.6 – 2.7] 0.03
Serum sodium (mmol/L) 141 ±3.3 4.7 [4.5 – 5.0] 4.4 [4.9 – 5.2] 0.40
Serum Potassium (mmol/l) 4.74 ± 0.58 4.72 ± 0.53 4.76 ± 0.64 0.68
Serum phosphorous (mg/dl) 3.8 [3.6 – 4.1] 3.7 [3.5 – 4.0] 3.8 [3.7 – 4.3] 0.35
WBC (cc/mmc) 7744 ± 1824 7575 ± 1947 7932 ±1683 0.46
Delta_Clearance -3.50/ 0.00/ 4.00 -0.25/ 1.00/ 7.25 -5.50/-2.00/ 2.00 0.001
Table 1. Baseline features of whole sample and into the two groups. Body mass index (BMI); White blood cells (WBC).

An unadjusted model with GLM for repeated measures showed a significant effect on creatinine clearance of the Mediterranean diet compared to LPD, with an estimate marginal mean of -9.98 ml/min [95% CI], 15.6/, 4.3]. Adjusted model for age, BMI and sex (Table 2) appeared to confirm this significance in the between-group mean in the joint mean difference (‒9.34, 95%CI ‒15.44/ ‒3.24) (Table 2).

Variable F p ᶇ2
Mediterranean diet vs low protein diet ‒9.34 0.003 0.119
Sex (Male vs female) 2.71 0.104 0.038
Age (years) 0.08 0.780 0.001
BMI (kg/m2) 0.04 0.947 0.000
Table 2. Between-group mean in the joint mean differences: Adjusted GLM model for repeated measures. Body mass index (BMI).

Due to the non-randomized study design and the unbalanced groups, we decided to implement the analysis with the PS matching. We computed PS value using the treatment as dependent variable of the logistic regression, and graphically evaluated it (Figure 1). The PS values were not equally distributed between the two groups. Carrying on with the matching, choosing a caliper of 0.2, 20 patients from group A were paired with 20 patients from group B (Table 3). Unmatched patients are excluded from the analysis, reducing sample’s size. This reduction of the patients admitted in the analysis is one of the major limitations of the matching.

Analyzing the standardized means of the baseline features before and after the matching, a better balance between the two groups could be shown (Figures 2a and 2b).

GLM for repeated measures performed in the matched sample did not show significant differences between the two groups (2.737, 95%CI –4.328/9.803). Also using the covariate adjustment, that uses the whole sample, the not significant relationship between the two treatments and the clearance progression was confirmed in the GLM for repeated measures including treatment and ps-value (-3.314, 95%CI -8.524/1.897).

Figure 1. Propensity score distribution before the matching.
Figure 1. Propensity score distribution before the matching.
Group A Group B PS value group A PS value group B
1 48 0.5728 0.5990
2 56 0.5029 0.4885
3 43 0.7979 0.8133
4 53 0.2244 0.2236
5 41 0.8256 0.8244
6 65 0.2370 0.2436
8 49 0.7872 0.7496
9 47 0.7313 0.7068
10 52 0.2709 0.2670
11 66 0.5662 0.5339
12 68 0.6588 0.6768
14 71 0.6731 0.6888
15 75 0.1971 0.2084
16 39 0.6640 0.6990
18 63 0.3849 0.3833
19 55 0.4595 0.6256
21 67 0.6014 0.6256
26 45 0.4350 0.4386
27 42 0.2674 0.2947
31 60 0.4544 0.4280
Table 3. Groups composition based on Propensity Score Matching.
Figure 2a. Balance of the covariate before and after the Matching.
Figure 2a. Balance of the covariate before and after the Matching.
Figure 2b. Propensity score distribution after the Matching.
Figure 2b. Propensity score distribution after the Matching.

 

Usefulness of propensity score

A few RCTs were conducted on ERSD patients due to high costs and their difficult organization. In these cases, a well-structured comparative effectiveness study could be done to generate hypothesis or to add results to existing RCT. For Example, Chan KE et al. conducted a large observational study including more than 10000 patients, the study’s population and structure were modeled on 4D study’s methods, using the same eligibility criteria, endpoints, and similar timeline. To reduce bias caused by known and unknown variables, patients were initially matched in statin-group and control-group based on similar lipid profiles and years of dialytic treatment. Subsequently, a logistic model was performed to compute the probability of receiving the therapy, also all Cox analyses were weighted using the IPTW methods. Differently from the unmatched baseline analysis, the baseline characteristic computed after propensity scoring showed two well-balanced groups. At the outcome analysis, all HRs computed in this observational study were compared with the HRs showed in the 4D Study, and no significant differences were found between these two studies (Figure 1). Furthermore, RCTs are often smaller than observational studies, due to the stronger inclusion criteria and the higher costs than observational design. As shown in Figure 1, PS methods computed in a big sample, allowed to find a smaller confidence interval compared to 4D RCT, without significant differences in anyone outcome.

Through these comparisons, although RCTs were the lowest-biased studies, we can speculate about the effective validity of observational comparative studies using PS methods to reduce biases.

 

Limitation of propensity score methods

PS is applicable when the treatment assignment is neglectable, with unknown and unmeasured confounders. Furthermore, PS value > 0 is necessary. According to G. et Lepeyre-Mestre M. [22], propensity score methods is not very able to reduce selection bias, information bias and instrumental bias. Despite PS reducing inhomogeneity between groups, some unconsidered variables can exist, hence residual bias should be taken into account in the interpretation of results and in the critical appraisal of the study [23].

Leisman D.E. et al., resumed ten “Pearls and Pitfalls” about the use of matching method [24]. They highlighted problems regarding the reduction of sample size: the number of cases does not represent the whole sample because every unpaired subject is excluded from the analysis.  This can impair the external validity of the study, reducing its applicability. Consequently, the power of the study should be computed on the balanced sample, excluding the unmatched patients. Indeed, the analysis reflects the matched sample, losing information about the excluded cases. However, no patients were excluded by the analysis using the covariate adjustment and the IPTW. We highlighted that, similarly to our sample, no significant differences between matching and covariate adjustment were found. However, can be useful performing more PS methods, to compare the results. Furthermore, machine learning methods can be used to compute PS, and they reduce the variability of the PS.

Last but not least, a limitation of these methods is the inability to detect interaction variables. In correlated subgroup effects, these variables could indeed invalidate the PS model and should be excluded from it [25].

 

Discussion

Our analysis seemed to show a slow CKD progression in patients treated with LPD compared to patients treated with Mediterranean diet. However, the unbalanced covariate distribution between the two groups must be highlighted. Conversely to classic analysis, our result showed no difference between the two groups in matched sample, where the two groups were well balanced.

Healthy dietary habits are essential to contrast the progression of chronic diseases such as CKD and the risk factors related to its development. A tailored diet that follows patients’ eating habits can enhance compliance with nutritional therapy, improving the conservative management of CKD patients.

In patients with renal impairment, optimal eating is crucial, representing a high-impact modifiable lifestyle factor for the primary prevention of CKD progression [26], and it avoids the dysregulation of fluid status, pH, electrolytes [27, 29], chronic metabolic acidosis [30], all factors that should be corrected by an adequate dietary regimen and balanced supplementation of the missing nutrients.

Nutritional therapy can be useful to slow CKD progression and delay ESRD with a consistent improvement of the patient’s quality of life [31]. LPD should be started from GFR <30 ml/min, with a protein intake below 0.8 mg/kg/die, and it shown slower CKD progression and reduction of the mortality [32]. Rhee et al. (2018) [33] in their meta-analysis of randomized controlled trials (RCTs) found that the risk of progression to ESRD was significantly lower in patients with LPD regimens than those with higher‐protein diets, with serum bicarbonate augmentation. Notwithstanding its restrictions, LPD does not seem to impair the quality of life of CKD patients. The study of Piccoli et al. (2020) [34] on 422 CKD patients with stages III-V demonstrated that moderately protein-restricted diets (0.6 g/kg/day) guaranteed good compliance to therapy, with a median dietary satisfaction of 4 on a 1-5 scale with a minimal dropout.

The Mediterranean diet is a nutritious regimen first proposed by Keys in the mid-1980s that has been demonstrated to exert a favourable action on inflammation, CKD, cardiovascular health, and overall mortality [35, 37]. Different studies demonstrated a tight link between CKD prevention and Mediterranean diet regimen [38, 39]. How the Mediterranean diet exerts kidney protection is still under debate, and the anti-inflammatory and antioxidant effects were suggested [40, 41]. Moreover, tighter adherence to a healthy plant-based diet was associated with a slower eGFR decrease [42].

Asghari et al. (2017) [43] showed, in a six-year follow-up study, that adherence to the Mediterranean diet is associated with a reduced risk of 50% of incident CKD. These results are in line with the ones from the Northern Manhattan Study. In this cohort of patients, the patients with relatively preserved renal function and high adherence to the Mediterranean diet experienced an approximate 50% decreased odds for incidence of eGFR<60 ml/min/1.73m2.

The effectiveness of LPD compared to the Mediterranean diet is still a matter of debate. Mediterranean diet is characterized by free fat, abundant vegetables, legumes, fresh fruits, cereals, moderate wine consumption, low milk and milk products, low meat/animal products, and frequent fish. Moreover, both the Mediterranean diet and LPD are effective in the modulation of gut microbiota, reducing protein-bound uremic toxins levels, especially in patients suffering from moderate to advanced CKD.

Davis et al. (2015) [44] tried to define nutrient content and range of servings for the Mediterranean diet, analysing the variations in the quantity of this diet components in recent literature. The Mediterranean diet’s positive effects are not only limited to metabolic influence, but the conviviality, culinary and physical activity exerts a beneficial effect on mental health, ameliorating body homeostasis and reactivity to the chronic disease [45].

A diet regimen feasible in different settings is essential for adherence to nutritional therapy. Different dietetic strategies have been investigated over the years, but which is the best nutritional regimen remains controversial. Kim et al. analysed the data of 4343 incident CKD patients, during a median follow-up of 24 years and showed that higher adherence to a balanced diet was linked to a lower risk of CKD progression.

In conclusion, although our previous analysis showed differences between the two diets, after propensity match no differences were detected, as well as after the covariate adjustment methods. In the study of Hu et al. (2021) [46] adherence to healthy nutritional patterns was associated with lower risk for renal impairment progression and all-cause mortality in CKD patients. Thus, based on our results and according to the literature, the Mediterranean diet should be a good choice for patients who are not compliant with a low-protein diet, without a significant increase of CKD progression risk [47].

 

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Carmelo Giordano (1930-2016): uremia therapy by protein alimentation and sorbents

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Natale Gaspare De Santo

Natale G. De Santo1, Ernesto Quarto2, Malcolm E Phillips3, Carlo de Pascale4, Biagio Di Iorio5

1Emeritus Professor, Department of Medicine, University of Campania Luigi Vanvitelli, Naples, Italy;
2Retired Professor of Bioengineering, University Federico II, Naples, Italy;
3Retired Nephrologist and Medical Director of Charing Cross and Hammersmith Hospitals Trust London, United Kingdom;
4Retired Physician in Chief of the Renal Unit at Cotugno Hospital, Naples, Italy;
5Division of Nephrology, Solofra General Hospital, Avellino, Italy.

Corresponding Author:
Natale G De Santo, MD
Emeritus Professor University of Campania Luigi Vanvitelli
Via Pansini 5, Pad 17, Nephrology, 80131 Naples, Italy,
phone +393484117376,
E-mail: nataleg.desanto@unicampania.it

 

Abstract

Carmelo Giordano was born on August 23, 1930 in Naples and died there on May 12, 2016. He qualified MD in 1954 and then trained with Professor Magrassi and later Professor John Merrill in the USA.

Returning to Naples he established a clinical research laboratory at the University Federico II which was funded for many years from the National Institute of Health in Bethesda. In 1969 he became a full Professor of Nephrology and established the postgraduate school of nephrology.

Giordano developed a worldwide reputation for his work on dietary management of uremia, recognised by the eponym “the Giordano–Giovannetti diet”. In this field he followed on from a galaxy of clinicians dating from antiquity and he worthily followed their high reputations.

He studied treatment of chronic renal failure (CRF) with low protein diets, essential amino acid diets/supplements and was the first to use ketoacids. The effect of these diets was assessed by nitrogen balance studies. He collaborated with other centres in this work including London and Stockholm.

Giordano’s other major interest and contribution to the conservative management of CRF was in the field of sorbents. He manufactured and studied, in patients and animals, the sorbent effects of oxidised starch-oxystarch and oxycellulose in removing, through the gut, significant amounts of nitrogenous waste. These studies raise the possibility of managing CRF using a combination of oral sorbent treatment and hemoperfusion. The latter is discussed in this paper as is dialysate regeneration and “portable” dialyzers.

Keywords: Carmelo Giordano, Low Protein Diet, ketoacids in CKD, oxystarch, oxycellulose, cold carbon apparatus, portable artificial kidneys, wearable artificial kidneys

A Short Biography

Carmelo Giordano (Carmine, Luigi, Giuseppe Giordano) (Figure 1) was born in Naples on August 23, 1930 in the house of Raffaele and Anna Tirone. He received the MD cum laude in 1954, at the Faculty of Medicine of the University Federico II of Naples, the oldest state university of the world. He was fellow and assistant to Professor Flaviano Magrassi (1908-1974). From 1958 to1960 he trained in nephrology with Professor John P. Merrill (1917-1984). At the Peter Bent Brigham Hospital of Harvard University where “no institution had done more for propagating dialysis in the United States”, he was viewed by some as “the father of nephrology as a discipline” (1). The relationship between Giordano and his mentor was extraordinary, both from the intellectual and the professional points of view. It was strengthened by the fact that Giordano during the first year in USA stayed in Merrill’s home. So, he had the privilege to learn directly from the maestro not only during the working hours at the university but also at home (2-8).

On his return to Naples Giordano organized a clinical research laboratory at the Department of Medicine of the University Federico II, where he developed a program of low protein alimentation for patients with CKD, utilizing a grant from the National Institute of Health of The United States in Bethesda. The laboratory was subsequently financed with a series of 33 grants by the National Institutes of Health till 1985 (2-8). He also started hemodialysis for AKI by utilizing an artificial kidney (Brigham Merrill rotating drum) which was a personal gift to him by Mr. Olson, the manufacturer. Maintenance hemodialysis and peritoneal dialysis were started in 1966.

In 1961 Giordano was enrolled as assistant professor of medicine at the university Federico II in Naples where, in the years 1969-1985, he was Professor of Nephrology and chief of the renal unit. There he also established the postgraduate school of nephrology and the kidney transplantation program. In the years 1986-2002 he was Professor of Medicine at the Second University of Naples and physician in chief of the Division of Nephrology. After retirement he continued to attend congresses of medicine and nephrology and directed a successful renal unit in a private hospital until his death in 2016. In 2016 he participated in Survival is Not Enough, an event organized by the Italian Institute for Philosophical Studies on the occasion of World Kidney Day. In his welcome address to the participants he underlined the need to increase the number of renal transplants because of the quality of life this treatment provides, its lower cost and the longer patient survival.

Details about his achievements in science and clinical medicine, the investigators he trained and promoted in the academy and hospitals, the papers and the books he published, the selective Capri Conferences on Uremia (1973-1980), the guest professors, his hobbies and his family have been described elsewhere (1-8). Historical reconstruction of Giordano’s contributions to nephrology have been presented by De Santo at the Congress of the International Society of Nephrology in Milan (2010), at the meetings of the International Association for the History of Nephrology (IAHN) in Wloclawek (2017) and at the 58th ERA-EDTA Congress in Madrid (2017). Biagio di Iorio highlighted the Giordano-Giovannetti diet at the IAHN Congress in Olympia-Patras (2012). Giovambattista Capasso illustrated Giordano’s achievements at the 2017 annual meeting of the Campania-Sicily branch of the Italian Society of Nephrology in Avellino.

Giordano’s name is known worldwide for his contributions to uremia therapy by means of low protein diets and by sorbents (2-8). His name is linked to the eponym: the Giordano-Giovannetti Diet (9).

 

Prehistory of renal nutrition

We have already traced the timeline of the progress in the field (2-4). Herein we will expand on some of his forerunners listed in Table 1, compiled taking also advantage of a recent paper on history of uremia research (10). Forerunners are important in science. Only Archimedes did not have one thus he started everything on his own. Indeed John of Salisbury (Methalogicon, 1159 AC) recounts that his maestro Bernard of Chartres used to say that “we have seen further and farther since we stood on the shoulders of giants”.

 

Galen (c129-c.130-c.200/216 AC Pergamon and Rome): Food and Diet (after 168 AC)

Excessive food intake is harmful. In Ian Johnston’s translation and editing of Galen’s On Diseases and Symptoms (11) one reads:

“.. the excessive intake of what are to the animal the most useful and nourishing foods is a cause of cold diseases. However, many of the things eaten and drunk that are too cold in nature (VII.14K) are also causes of cold diseases. These, then, are the causes of dry diseases. All the opposites (are causes) of moist diseases: an abundance of foods that are moist in capacity, an excess of drinks, an altogether more luxurious way of life”.

 

Prospero Alpini (1563-1616)

In 1591 the printing house of Franciscus De Franciscis in Venice published a book entitled De Medicina Aegyptiorum Libri quatuor/Egyptian medicine, four books (12). It was the opera prima of a young physician who later became professor of medicine, lecturer in simples and prefect of the Botanical Garden (the first worldwide) at the University of Padua (13). The book―an innovative output of a travelling physician (14)― reported on the personal experience of Alpini in Cairo from March 1581 to October 1584 as physician to Giorgio Emo, Consul of Venice. The book, dedicated to Antonio Morosini Senator of Venice, described for the first time the use of coffee, a popular drink in Cairo. Coffee was previously unknown in the western world. We have translated into English some passages related to various medical practices of Egyptian physicians. In Book I, Chapter X, Alpini describes Egyptian alimentation:

“They prepare their meals using milk and eat all dairy products. They eat very simple foods, many of them at lunch and dinner may eat a water melon or corn bread, which is utilized by everyone. They also use broth made of the roots of colocassia, of the bamnia fruit or barley corn or lentils or other legumes or with the green part of the sugar cane, or they feed themselves with grapes, figs, cucumbers and similar. As a beverage the Egyptian followers of Mohammed use Nile water which for its quality is to be preferred to all others”.

In Book I, Chapter XI, Alpini reports on Egyptian longevity:

“Therefore I think that the main reason which grants long life to Egyptians is their sobriety and abstention from an abundance of meat (…), the water of the Nile. In fact in Europe by much eating and drinking excessive quantities of wine, inhabitants of Germany and Poland live less”.

This is the first description of what in the twentieth century was defined as a Mediterranean diet. In Egypt they made use of corn bread, consumed great amounts of fresh or cooked vegetables including lentils and other legumes, and of fruits. They also used milk and dairy products, drank the Nile water or coffee prepared with the same water. Such a diet links to the longevity of the population giving a preventive role to abstention from meat and wine.

 

Mariano Semmola (1831-1895)

Semmola was born in Naples, studied at the University Federico II and obtained the MD in 1852. He studied in France under Claude Bernard, Trousseau and Rayer, and later was Professor of Pharmacology in Naples. He is credited with 28 national and international papers on Bright’s disease.

As a medical student he illustrated at the Academy of Medicine and Surgery in Naples (on January 26, February 23 and April 22, 1850) seminal experiments on the effects of different protein intakes on: (i) urinary specific gravity, (ii) urinary urea excretion and (iii) albuminuria in patients with primary albuminuria receiving either a) a usual mixed diet, or b) a meat diet (600-700 g of boiled meat), or c) a vegetable soup based on greens and bread, or d) a nitrogen-free diet based on fat, tomatoes and chestnuts. Urinary specific gravity was highest under the meat regimen, whereas albuminuria and urinary urea excretion were lowest under the nitrogen-free diet (15-17).

These studies were well received in France and were praised by Sigismund Jaccoud (1630-1930), François Henri Hallopeau (1842-1919), and Georges Dieulafoy (1839-1911). The studies were described at the Academy of Medicine in Paris and appeared in its Bulletin in 1892. That means that Semmola worked in the field for 42 years after 1850 (16).

 

Fernand Widal and Adolphe Javal

These scientists made significant contributions to the patho-physiology of Bright’s disease demonstrating that blood urea increased with the protein content of the diets, and that knowing the composition of the latter was a prerequisite to understanding the meaning of blood urea concentration. These studies were important for Leo Ambard during his studies on the urea-secretory constant (19, 20).

 

The history of low protein nutrition in CKD: The role of Carmelo Giordano

Coming back to the origins of the Giordano-Giovannetti diet, we now illustrate the experiments Giordano performed in the years 1961-1963 which shook the world of uremia specialists. His debut was unexpected, pregnant scientifically, and promised a new perspective for patients with chronic renal disease. Giordano’s studies opened a new era and further results are still expected.

Giordano’s first study (21) was a self-experimentation on one healthy subject (himself). He undertook a 4 period protocol (A,B,C,D) for a total of 53 days. In A he ingested a diet made from essential amino acids + 3 g of nitrogen (N) in the form of glycine. In Period B only 0.5 g of N as glycine supplemented the essential amino acids. In C essential amino acids were supplemented with 2 g of N as ammonium citrate. In D essential amino acids were supplemented with 2 g of N derived from urea. Nitrogen balance was positive and body weight remained constant throughout the experiment.

In the same year Giordano (22) reported on two patients with advanced renal failure treated with essential amino acids (a total of 2 g of N a day) along with 2500 calories. A significant reduction of blood urea concentration occurred during the treatment.

At the Second Congress of the International Society of Nephrology in 1963 in Prague, Giordano (23) reported studies on 23 CKD patients (Table 2) followed with a dietary protocol for 5 weeks. In week 1 and 5 they ate a low protein diet providing 3.8 g of N (23 g of proteins of high biological value (HBV) rich in energy (2,300-3,100 calories). In weeks 2,3 and 4 they consumed a diet containing 2.4 g of N (85% as L-essential amino acids) and providing a high energy supply. Blood urea was reduced by the amino acid diet which normalized N balance after 1 week. At this world convention there were no other presentations on low protein alimentation in renal disease.

In September 1963 Giordano published a paper in the Journal of Laboratory and Clinical Medicine (24). He reported data on 8 CKD patients (eGFR 3-26 ml/min) seven of whom were hypertensive (Table 3). They received for 7 weeks a diet providing L-essential amino acids (2 g of N a day). The energy content provided 2,300 calories in women and 3,100 in men. Thereafter they were given a low protein diet providing 23 g of HBV proteins. Blood urea was reduced under amino acids, nitrogen balance started to be positive after 3 weeks.

A series of seminal studies were presented by Giordano and his initial group of fellows at the 3rd Congress of the International Society of Nephrology in Washington 1966 (25). They reported on 221 patients followed for 60 months. The patients started with 0.3g/Kg of HBV proteins associated with 35 kcal/kg and were followed by assessing the nitrogen balance. When the N balance was negative, 2-3 g of proteins were added (in total 24 g for a 70 kg man). The study reported on more than 1000 days of N balance in 25 of the patients, given various dietary intakes (free intake, 8-11-g L-essential amino acids, and low protein diets providing 17-g, 20-g, 23-g and 25g). 85.7% per cent of the patients were in positive nitrogen balance with 25 g of proteins. This anticipated the evidence that with a 40g protein diet all CKD patients would receive an adequate amount of protein, as demonstrated in 1968 by Kopple et al (26). The study of Giordano et al (25) also disclosed a reduced phenylalanine to tyrosine ratio and a loss of 10-20 g of amino acids and peptides during a dialysis session of six hours.

Three studies documented for the first time the potential of ketoacids in the treatment of CKD. The first was a study on amino acids L and DL, the remaining two mark the origin of ketoacid therapy by using the ketoacids of phenylalanine and valine (27-29). The experiments were made in collaboration with the group of Peter Richards at the St. Mary Hospital in London, where the ketoacids of phenylalanine and valine were administered and their effects evaluated by nitrogen balance studies and 15N incorporation. Plasma albumin was broken down and their constituent amino acid were separated in Naples. Peter Fürst evaluated the 15N enrichment of each amino acid at the Institute for Mass Spectrometry of the Karolinska Institute in Stockholm directed by Garnar Ryhage.

The concept began with a paper on the effects on nitrogen balance of D-isomers of essential amino acids in uremia (27). It was hypothesized that it was the ketoacid of the D-isomers of amino acids that would be utilized. Two papers were published in 1971 showing the feasibility of a low protein diet based on ketoanalogues (28, 29). Ketoacids of the essential amino acids valine and phenylalanine could be utilized in studies with nitrogen balance and 15N incorporation. It was shown that phenylalanine and valine may be synthesized by healthy and uremic individuals. Walser et al. brought strong additional evidence to the importance of ketoacids (30) and nurtured the field for the subsequent 30 years. However, the initial enthusiasm of Giordano et al. for ketoacids diminished since anoxic infants on ketoacid formulations failed to achieve catch-up growth whereas with amino acid formulations they did (31). Thus a new reference pattern was proposed (32). In this way Giordano and his associates lost the advantage they had generated in 1964 (27) and it took many years for Giordano to acknowledge the importance of ketoacids (33).

 

Prehistory of sorbents

Athanasios Diamandopoulos, historian of nephrology, once wrote:

“nature uses various natural membranes to eliminate toxic substances. The membranes used for this purpose are those of the gastrointestinal system and of the skin. Humans tried to imitate nature… the beginnings of these practices can be dated to at least 4000 years ago. Herodotus described the practices of enemas among Egyptian who preserve good health by clystering themselves 2-3 times a month”. He also quotes Aetius Amidanus (6th Century AD) for treating acute renal failure with clysters made of “mallow, linseed oil, peeled barley, warm water, reed, camomille and dill”, a practice also suggested by Albucasis (10th century) and by Avicenna (11th century). On the other hand Hippocrates suggests to “purge to get rid of the rest from above and from below” (34).

Terra sigillata/ sealed earth from the Island of Lemnos in Greece, packed together and bearing the head of Artemis should be considered as the first sorbent for medical use as reported by Dioscorides in De Materia Medica (40 BC).

Spyros Marketos, a founder and president of the Hippocratic Foundation of Kos, produced a seminal paper on purgatives, charcoal and artificial kidney (35). He says that Hippocrates in Aphorisms suggests “Bodies that are to be purged must be rendered fluent… If the matters purged be such as should be purged, the patient profits and bears up well. If not, the contrary”.

Therein one also learns that charcoal was a recognized drug in Ancient Egypt (36) and Pliny the Elder in Naturalis Historia (90 AD) described its virtues for “disease of the spleen, of the kidney abundant menstruation, poisonous serpents’ wounds”. Its use was supported by Thonery, a French pharmacist who used it in the course of self-experimentation by ingesting it along with strychnine before the Medical Academy of France (37). But it was Yatzidis who introduced carbon hemoperfusion for intoxication (38, 39).

Santorio Santorio (1561-1636) in De statica medicina (1514) started a medicine based on measurements by measuring food intake, drinks, urine, feces and calculating perspiration and by suggesting remedies capable to affect the quantity of excreta (40).

 

On the history of sorbents and the contribution of Carmelo Giordano in the years 1968-1984

A total of 31 papers (41-71) represent an incomplete list of the output of a strong, motivated team which included Carmelo Giordano, Renato Esposito (chief of the laboratory, Associate Professor of Nephrology, nutritionist, immunologist and expert in clinical chemistry), Ernesto Quarto (Associate Professor of Bioengineering), Giovanni Demma and Piero Bello (both doctors in Chemistry), Giacomino Randazzo (Full University Professor of Biochemistry), Miss Maria Pluvio (Dr in biology and medicine, nephrologist and Ph. D in Nephrological Sciences), Mrs Norina Lanzetti (physician, nephrologist and Ph. D in Nephrological Sciences), Mr. Tonino Ariano (laboratory technician).

 

Lavage of intestinal wastes

Lavage of intestinal wastes was reported by Kolff in New Ways of Treating Uremia (20). (Kolff created a double ended ileostomy in an isolated ileal loop with an intact blood supply in a 57 year old uremic man. As much as 0.48 g of urea/hour was removed by the patient who performed home intestinal dialysis assisted by his wife for two months until his death. Prolongation of life by intestinal dialysis has been accomplished in dogs (73) and man (74, 75). Clearances during isolated jejunal loop dialysis in uremic patients were reported by Schloerb (74) as 5 to 10 ml/min for creatinine and 3.2 to 5.0 ml/min for uric acid, values about one third and one eighth as efficient, respectively, as obtained with peritoneal and hemodialysis. Intestinal perfusates contain smaller but significant amounts of larger molecules including aldosterone and 17-oxyhydroxycorticosteroids.

By 1960, hemodialysis was made practical by the development of an external plastic arteriovenous shunt. A slowly increasing number of patients were sustained (albeit suboptimally) by periodic intestinal dialysis. Analyzing 15 cases in the literature plus five of their own, Clark et al. (75) reached the conclusion that intestinal dialysis “remains the best method of adjunctive management of progressive uremia.” Thereafter, the improving success rate of maintenance hemodialysis diverted interest from the quest for nitrogenous waste extraction from the gut.

 

Removing urea from blood and/or intestinal tract and the birth of oxystarch and oxycellulose

Activated charcoals have a low sorption capacity for urea although they effectively remove other uremic toxic substances. To provide a urea-reactive adsorbent, a chemically modified oxystarch with albumin or gelatin was prepared. Elemental analysis and Fourier transform infrared (FT-IR) spectroscopic analysis demonstrated that the reaction of a small amount of protein (albumin or gelatin) with oxystarch had taken place possibly by chemical combination (41-46).

The influence of the dialdehyde content of the oxystarch on urea sorption, its sorption isotherm, and the adsorption rates were investigated. It was found that the swelling factor of oxystarch is closely related to the sorption activity under physiological conditions (pH 7.2-7.4 at 37° C). Adsorption studies showed that sorption capacity was increased by surface treatment and can reach 6-8.2 g urea/kg-dried adsorbent (initial urea concentration was 70 mg/dL). The oxystarch had 49.2% of glucose unit oxidized and was surface treated with albumin. These results suggested that the newly prepared surface-treated oxystarch would be utilized as an effective chemisorbent for urea removal under physiological conditions.

Sorbents in the Management of Uremia (60) documented easy transfer of urea from plasma into the intestinal lumen. The potential for treating renal failure by extraction of nitrogen waste from the gut became self-evident. Urea in the gut is degraded to ammonia by bowel bacteria to the extent that normal human feces contain no urea. In healthy volunteer subjects given an antibiotic cocktail, stool urea concentrations increase to blood levels while the fecal ammonia content decreases. This supports the inference that urea in the bowel is biodegraded by luminal microorganisms. Estimates of the quantity of urea converted to ammonia in the gut have been computed by Man et al. (79) from 4 to 7 g/day in normal patients and from 17 to 50 g/day in uremic patients.

Promising additional data indicating that gastrointestinal sorbents can bind to and remove, in the feces, clinically important amounts of nitrogenous wastes were demonstrated by Giordano and associates (5, 41-46) using oxidized starch (oxystarch) and oxidized cellulose (oxycellulose) (Figure 2 and Figure 3).

Corn starch or potato starch suspended in a solution of sodium periodate at 4’C for 24 hours slowly oxidizes to dialdehyde starch (oxystarch). Cellulose treated similarly, oxidizes to oxycellulose. At body pH and temperature, each repeat unit of oxystarch binds 1.5 to 1.9 moles of ammonia in vitro in an 0.3N ammonia solution; when present in excess, oxystarch will bind all the ammonia in a 0.3N solution. Oxystarch also adsorbs urea.

Oxystarch adsorbs aspartic acid in vitro, but it does not bind creatinine, uric acid, L-lysine or albumin. In weanling mice fed 2 per cent oxystarch in a casein diet, growth and development are normal. In rats fed 2 per cent oxystarch in a casein diet severe diarrhoea develops, whereas dogs tolerate as much as 5 per cent dietary oxystarch without apparent adverse effect. Explosive diarrhoea and a cholera-like fluid and electrolyte depletion syndrome occur in dogs fed more than 10 per cent of oxystarch in their diets. In uremic patients fed 20 to 35 g of oxystarch in divided doses stool volume increases by 200 to 600 ml/day and the frequency of bowel movements is increased, but frank diarrhoea does not develop. Giordano’s initial trials of oxystarch manufactured in his laboratories (42-44) showed that uremic patients (creatinine clearances of 0.4 to 3.2 ml/min) tolerated divided doses of 20 g/day well for two months and that, in each case, there was a significant fall in the blood urea nitrogen level. Fecal nitrogen content increased to a mean of 1,450 mg/day (range 730 to 8,050 mg/day). Confirmation of increased stool nitrogen content during oxystarch treatment was provided by a double blind starch/oxystarch full balance study (76-80). In this study seven uremic patients (creatinine clearances of 6 to 30 ml/min) were fed 29 g of oxystarch or starch daily in four equal doses added to a diet containing 40 to 50 g of protein and 2 to 4 g of salt. Blood urea nitrogen levels fell 33 per cent during oxystarch treatment from a mean of 93.1 mg/ 100 ml to a mean of 62.1 mg/100ml. There was no significant change in serum creatinine, plasma amino acid, uric acid and plasma glucose levels during oxystarch ingestion. Oxystarch significantly increased fecal nitrogen from a control mean of I.4 g/24 hours to 2.5 g/24 hours. A concomitant decrease in urinary nitrogen excretion, however, from a control mean of 7.6 g/24 hours to 5.5 g/24 hours during oxystarch treatment prevented development of negative nitrogen balance.

During minimal nitrogen ingestion, uremic patients fed oxystarch (28 g) daily have an increased fecal excretion of nitrogen and potassium, and a counterbalancing decrease in urinary nitrogen and potassium excretion (81). There was a significant increase in the fecal potassium content when oxystarch was ingested, ranging from 5 to 22 mEq/day, which was also counterbalanced by a decrease in urinary potassium excretion. To exclude the possibility that increased fecal nitrogen content noted during oxystarch treatment was due to direct binding of unabsorbed undigested dietary nitrogen rather than bound intestinal nitrogen, four uremic patients were fed oxystarch while ingesting a “no protein” diet (82). In these patients the increases in fecal nitrogen and potassium were similar to those in the previous group indicating that the origin of the extra fecal nitrogen was indeed nitrogenous waste. Will feeding oxystarch to uremic patients have clinical import? In urine-producing patients the counterbalancing decrease in urinary nitrogen excretion tends to detract from the benefit of increased fecal nitrogen content. What will be the effect on nitrogen balance in anuric patients?

 

Oxystarch in bilaterally nephrectomized rats

While awaiting completion of sorbent trials in functionally anephric (undergoing dialytic maintenance) patients, several helpful animal experiments have been completed. To date, chronically uremic animals in need of dialysis have not been sustained by sorbents alone. Gavage feeding of oxystarch alone or in combination with charcoal will prolong the life of anephric rats of three days to five days. Friedman et al. (81) investigated the mechanism of sorbent-induced life extension in bilaterally nephrectomized rats fed charcoal (1 g daily), oxystarch (1 g daily) or oxystarch plus charcoal (1 g of each daily). In sorbent-treated rats the increase in blood urea concentration was less than in untreated nephrectomized controls, but they also had lower serum potassium concentrations throughout their increased life span. Both actions of oxystarch, increased fecal excretion of nitrogen and potassium, were detectable in this in vivo model of fatal acute renal failure.

 

Charcoal as an oral sorbent and for hemoperfusion

The work of Yatzidis on charcoal (38, 39) is important. Administered in oral doses of 20 to 50 g daily, with or without sorbitol as a vehicle, Yatzidis (82) was also able to manage patients with end-stage renal failure for 4 to 20 months without resorting to dialysis.

For completeness in this survey, the technique of direct exposure of blood to a sorbent, termed hemoperfusion, will be mentioned. During a single passage over granular activated charcoal, creatinine, uric acid, indican, phenols, guanidines and organic acids are nearly totally extracted from the blood. Only negligible quantities of urea, magnesium and phosphate are adsorbed on charcoal from blood. Each gram of powdered charcoal will in vitro bind simultaneously 9 mg of creatinine, 8 mg of uric acid, 1.75 mg of phenols, 1 mg of guanidines and 35 mg of urea.

Yatzidis (38, 39) devised a hemoperfusion device containing 200 g of activated charcoal in a siliconized glass cylinder 20 cm in length and 6 cm in diameter. Based on an experience of 20 humans undergoing hemoperfusion, Yatzidis estimated that 60 minutes of blood exposure to two or three 200 g charcoal columns had about the same extraction efficiency (for uremic patients) as a 4 to 6 hours hemodialysis. Hemoperfusion was advocated for the treatment of renal insufficiency, gouty arthritis, and intoxications with salicylates, barbiturates and glutethimide (82-84).

 

Charcoal microencapsulation

Chang et al. (85, 86) have systematically studied several approaches to microencapsulation of charcoal and they developed a blood-compatible albumin-complexed polymer. Chang’s microencapsulated “kidney” contains 300 g of double coated charcoal granules 2 to 5 mm in diameter with a surface area of 2.25 m2. This device achieves clearances in vitro, which are superior for middle molecules (MW 200 to 1,800), to hollow fiber, coil or parallel flow hemodialyzers. Periodic hemoperfusion as a sole treatment for uremia is inadequate because of the need to extract water and probably urea to maintain acceptable morbidity. Combination of hemoperfusion in series with ultrafiltration of blood for water removal might prove a workable therapy for uremic patients who ingest ammonia binding sorbents such as oxidized starch. The efficiency advantage (shorter treatments) of hemoperfusion over hemodialysis in renal failure is sufficiently attractive to consider sorbents in the management of uremia, coupling hemoperfusion with oral sorbent ingestion.

 

Dialysate regeneration

The field of closed circuit artificial kidneys was opened by Yatzidis (38, 39) who introduced carbon to remove uremia waste products. Gordon (87, 88) introduced the use of zirconium phosphate which adsorbs ammonium ions in presence of sodium and releases Na+ and H+. This allowed regeneration of dialysate through a sorbent cartridge.

A remarkable reduction in dialysate volume to 1.5 liters was devised by Gordon and co-workers by the clever means of converting urea in dialysate to ammonium ion and carbonate by urease treatment. Ammonium ion is adsorbed by zirconium phosphate which also extracts calcium and magnesium necessitating continuous reinfusion of these ions. Zirconium oxide binds phosphate and fluoride while charcoal extracts uric acid, creatinine, guanidines, organic acid and phenols. The total weight of the sorbent cartridge is less than 2 kg. The importance of the Gordon (89) system is not only the size reduction, which makes a “travel-suitcase” artificial kidney practical, but it is also a clear demonstration of the value of sorbents in simplifying the therapy of uremia. Zirconium phosphate could also be used in association with charcoal, starch and oxystarch (48-58) by Giordano and his associates for portable artificial kidneys (Figure 4, Figure 5 and Figure 6).

 

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